A new approach for modular robot system behavioral modeling: Base on Petri net and category theory

NASA Astrophysics Data System (ADS)

Zhang, Yun; Wei, Hongxing; Yang, Bo

2018-04-01

To design modular robot system, Petri nets and category theory are combined and the ability of simulation of Petri net is discussed. According to category theory, the method of describing the category of components in the dynamic characteristics of the system is deduced. Moreover, a modular robot system is analyzed, which provides a verifiable description of the dynamic characteristics of the system.

General dynamical density functional theory for classical fluids.

PubMed

Goddard, Benjamin D; Nold, Andreas; Savva, Nikos; Pavliotis, Grigorios A; Kalliadasis, Serafim

2012-09-21

We study the dynamics of a colloidal fluid including inertia and hydrodynamic interactions, two effects which strongly influence the nonequilibrium properties of the system. We derive a general dynamical density functional theory which shows very good agreement with full Langevin dynamics. In suitable limits, we recover existing dynamical density functional theories and a Navier-Stokes-like equation with additional nonlocal terms.

Koopman operator theory: Past, present, and future

NASA Astrophysics Data System (ADS)

Brunton, Steven; Kaiser, Eurika; Kutz, Nathan

2017-11-01

Koopman operator theory has emerged as a dominant method to represent nonlinear dynamics in terms of an infinite-dimensional linear operator. The Koopman operator acts on the space of all possible measurement functions of the system state, advancing these measurements with the flow of the dynamics. A linear representation of nonlinear dynamics has tremendous potential to enable the prediction, estimation, and control of nonlinear systems with standard textbook methods developed for linear systems. Dynamic mode decomposition has become the leading data-driven method to approximate the Koopman operator, although there are still open questions and challenges around how to obtain accurate approximations for strongly nonlinear systems. This talk will provide an introductory overview of modern Koopman operator theory, reviewing the basics and describing recent theoretical and algorithmic developments. Particular emphasis will be placed on the use of data-driven Koopman theory to characterize and control high-dimensional fluid dynamic systems. This talk will also address key advances in the rapidly growing fields of machine learning and data science that are likely to drive future developments.

Canonical transformation path to gauge theories of gravity

NASA Astrophysics Data System (ADS)

Struckmeier, J.; Muench, J.; Vasak, D.; Kirsch, J.; Hanauske, M.; Stoecker, H.

2017-06-01

In this paper, the generic part of the gauge theory of gravity is derived, based merely on the action principle and on the general principle of relativity. We apply the canonical transformation framework to formulate geometrodynamics as a gauge theory. The starting point of our paper is constituted by the general De Donder-Weyl Hamiltonian of a system of scalar and vector fields, which is supposed to be form-invariant under (global) Lorentz transformations. Following the reasoning of gauge theories, the corresponding locally form-invariant system is worked out by means of canonical transformations. The canonical transformation approach ensures by construction that the form of the action functional is maintained. We thus encounter amended Hamiltonian systems which are form-invariant under arbitrary spacetime transformations. This amended system complies with the general principle of relativity and describes both, the dynamics of the given physical system's fields and their coupling to those quantities which describe the dynamics of the spacetime geometry. In this way, it is unambiguously determined how spin-0 and spin-1 fields couple to the dynamics of spacetime. A term that describes the dynamics of the "free" gauge fields must finally be added to the amended Hamiltonian, as common to all gauge theories, to allow for a dynamic spacetime geometry. The choice of this "dynamics" Hamiltonian is outside of the scope of gauge theory as presented in this paper. It accounts for the remaining indefiniteness of any gauge theory of gravity and must be chosen "by hand" on the basis of physical reasoning. The final Hamiltonian of the gauge theory of gravity is shown to be at least quadratic in the conjugate momenta of the gauge fields—this is beyond the Einstein-Hilbert theory of general relativity.

The Marriage of Science and Spirit: Dynamic Systems Theory and the Development of Spirituality

ERIC Educational Resources Information Center

Cupit, C. Glenn

2007-01-01

The adherence of traditional developmental theories to a linear paradigm is incompatible with the nature of "spirit". Dynamic Systems Theory (DST), a recent contributor to understanding child development, offers an alternative which avoids these paradigmatic limitations. Concepts of agency, "top-down" causality, emergence and…

Panarchy: discontinuities reval similarities in the dynamic system structure of ecological and social systems

EPA Science Inventory

Debates on the organization, structure and dynamics of ecosystems across scales of space and time have waxed and waned in the literature for a century. From successional theory to ecosystem theories of resilience and robustness, from hierarchy to ascendency to panarchy theory, e...

Role of the Pair Correlation Function in the Dynamical Transition Predicted by Mode Coupling Theory

NASA Astrophysics Data System (ADS)

Nandi, Manoj Kumar; Banerjee, Atreyee; Dasgupta, Chandan; Bhattacharyya, Sarika Maitra

2017-12-01

In a recent study, we have found that for a large number of systems the configurational entropy at the pair level Sc 2, which is primarily determined by the pair correlation function, vanishes at the dynamical transition temperature Tc. Thus, it appears that the information of the transition temperature is embedded in the structure of the liquid. In order to investigate this, we describe the dynamics of the system at the mean field level and, using the concepts of the dynamical density functional theory, show that the dynamical transition temperature depends only on the pair correlation function. Thus, this theory is similar in spirit to the microscopic mode coupling theory (MCT). However, unlike microscopic MCT, which predicts a very high transition temperature, the present theory predicts a transition temperature that is similar to Tc. This implies that the information of the dynamical transition temperature is embedded in the pair correlation function.

A Dynamic Interactive Theory of Person Construal

ERIC Educational Resources Information Center

Freeman, Jonathan B.; Ambady, Nalini

2011-01-01

A dynamic interactive theory of person construal is proposed. It assumes that the perception of other people is accomplished by a dynamical system involving continuous interaction between social categories, stereotypes, high-level cognitive states, and the low-level processing of facial, vocal, and bodily cues. This system permits lower-level…

Gauge theory for finite-dimensional dynamical systems.

PubMed

Gurfil, Pini

2007-06-01

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.

Black hole dynamics in Einstein-Maxwell-dilaton theory

NASA Astrophysics Data System (ADS)

Hirschmann, Eric W.; Lehner, Luis; Liebling, Steven L.; Palenzuela, Carlos

2018-03-01

We consider the properties and dynamics of black holes within a family of alternative theories of gravity, namely Einstein-Maxwell-dilaton theory. We analyze the dynamical evolution of individual black holes as well as the merger of binary black hole systems. We do this for a wide range of parameter values for the family of Einstein-Maxwell-dilaton theories, investigating, in the process, the stability of these black holes. We examine radiative degrees of freedom, explore the impact of the scalar field on the dynamics of merger, and compare with other scalar-tensor theories. We argue that the dilaton can largely be discounted in understanding merging binary systems and that the end states essentially interpolate between charged and uncharged, rotating black holes. For the relatively small charge values considered here, we conclude that these black hole systems will be difficult to distinguish from their analogs within General Relativity.

Dynamical Systems Theory: Application to Pedagogy

NASA Astrophysics Data System (ADS)

Abraham, Jane L.

Theories of learning affect how cognition is viewed, and this subsequently leads to the style of pedagogical practice that is used in education. Traditionally, educators have relied on a variety of theories on which to base pedagogy. Behavioral learning theories influenced the teaching/learning process for over 50 years. In the 1960s, the information processing approach brought the mind back into the learning process. The current emphasis on constructivism integrates the views of Piaget, Vygotsky, and cognitive psychology. Additionally, recent scientific advances have allowed researchers to shift attention to biological processes in cognition. The problem is that these theories do not provide an integrated approach to understanding principles responsible for differences among students in cognitive development and learning ability. Dynamical systems theory offers a unifying theoretical framework to explain the wider context in which learning takes place and the processes involved in individual learning. This paper describes how principles of Dynamic Systems Theory can be applied to cognitive processes of students, the classroom community, motivation to learn, and the teaching/learning dynamic giving educational psychologists a framework for research and pedagogy.

Nonlinear Synergistic Emergence and Predictability in Complex Systems: Theory and Hydro-Climatic Applications

NASA Astrophysics Data System (ADS)

Perdigão, Rui A. P.; Hall, Julia; Pires, Carlos A. L.; Blöschl, Günter

2017-04-01

Classical and stochastic dynamical system theories assume structural coherence and dynamic recurrence with invariants of motion that are not necessarily so. These are grounded on the unproven assumption of universality in the dynamic laws derived from statistical kinematic evaluation of non-representative empirical records. As a consequence, the associated formulations revolve around a restrictive set of configurations and intermittencies e.g. in an ergodic setting, beyond which any predictability is essentially elusive. Moreover, dynamical systems are fundamentally framed around dynamic codependence among intervening processes, i.e. entail essentially redundant interactions such as couplings and feedbacks. That precludes synergistic cooperation among processes that, whilst independent from each other, jointly produce emerging dynamic behaviour not present in any of the intervening parties. In order to overcome these fundamental limitations, we introduce a broad class of non-recursive dynamical systems that formulate dynamic emergence of unprecedented states in a fundamental synergistic manner, with fundamental principles in mind. The overall theory enables innovations to be predicted from the internal system dynamics before any a priori information is provided about the associated dynamical properties. The theory is then illustrated to anticipate, from non-emergent records, the spatiotemporal emergence of multiscale hyper chaotic regimes, critical transitions and structural coevolutionary changes in synthetic and real-world complex systems. Example applications are provided within the hydro-climatic context, formulating and dynamically forecasting evolving hydro-climatic distributions, including the emergence of extreme precipitation and flooding in a structurally changing hydro-climate system. Validation is then conducted with a posteriori verification of the simulated dynamics against observational records. Agreement between simulations and observations is confirmed with robust nonlinear information diagnostics.

Gauge theory for finite-dimensional dynamical systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gurfil, Pini

2007-06-15

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 differentialmore » 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.« less

Computational Methods for Nonlinear Dynamic Problems in Solid and Structural Mechanics: Progress in the Theory and Modeling of Friction and in the Control of Dynamical Systems with Frictional Forces

DTIC Science & Technology

1989-03-31

present several numerical studies designed to reveal the effect that some of the governing parameters have on the behavior of the system and, whenever...Friction and in the Control of Dynamical Systems with Frictional Forces FINAL TECHNICAL REPORT March 31, 1989 _ -- I -.7: .-.- - : AFOSR Contract F49620...SOLID AND STRUCTURAL MECHANICS: Progress in the Theory and Modeling of Friction and in the Control of Dynamical Systems with Frictional Forces I I * FINAL

Role of the Pair Correlation Function in the Dynamical Transition Predicted by Mode Coupling Theory.

PubMed

Nandi, Manoj Kumar; Banerjee, Atreyee; Dasgupta, Chandan; Bhattacharyya, Sarika Maitra

2017-12-29

In a recent study, we have found that for a large number of systems the configurational entropy at the pair level S_{c2}, which is primarily determined by the pair correlation function, vanishes at the dynamical transition temperature T_{c}. Thus, it appears that the information of the transition temperature is embedded in the structure of the liquid. In order to investigate this, we describe the dynamics of the system at the mean field level and, using the concepts of the dynamical density functional theory, show that the dynamical transition temperature depends only on the pair correlation function. Thus, this theory is similar in spirit to the microscopic mode coupling theory (MCT). However, unlike microscopic MCT, which predicts a very high transition temperature, the present theory predicts a transition temperature that is similar to T_{c}. This implies that the information of the dynamical transition temperature is embedded in the pair correlation function.

Galactic evolution. I - Single-zone models. [encompassing stellar evolution and gas-star dynamic theories

NASA Technical Reports Server (NTRS)

Thuan, T. X.; Hart, M. H.; Ostriker, J. P.

1975-01-01

The two basic approaches of physical theory required to calculate the evolution of a galactic system are considered, taking into account stellar evolution theory and the dynamics of a gas-star system. Attention is given to intrinsic (stellar) physics, extrinsic (dynamical) physics, and computations concerning the fractionation of an initial mass of gas into stars. The characteristics of a 'standard' model and its variants are discussed along with the results obtained with the aid of these models.

Global Optimal Trajectory in Chaos and NP-Hardness

NASA Astrophysics Data System (ADS)

Latorre, Vittorio; Gao, David Yang

This paper presents an unconventional theory and method for solving general nonlinear dynamical systems. Instead of the direct iterative methods, the discretized nonlinear system is first formulated as a global optimization problem via the least squares method. A newly developed canonical duality theory shows that this nonconvex minimization problem can be solved deterministically in polynomial time if a global optimality condition is satisfied. The so-called pseudo-chaos produced by linear iterative methods are mainly due to the intrinsic numerical error accumulations. Otherwise, the global optimization problem could be NP-hard and the nonlinear system can be really chaotic. A conjecture is proposed, which reveals the connection between chaos in nonlinear dynamics and NP-hardness in computer science. The methodology and the conjecture are verified by applications to the well-known logistic equation, a forced memristive circuit and the Lorenz system. Computational results show that the canonical duality theory can be used to identify chaotic systems and to obtain realistic global optimal solutions in nonlinear dynamical systems. The method and results presented in this paper should bring some new insights into nonlinear dynamical systems and NP-hardness in computational complexity theory.

The road not taken: Applications of fluorescence spectroscopy and electronic structure theory to systems of materials and biological relevance

NASA Astrophysics Data System (ADS)

Carlson, Philip Joseph

Applications of Fluorescence Spectroscopy and Electronic Structure Theory to Systems of Materials and Biological Relevance. The photophysics of curcumin was studied in micelles and the solvation dynamics were probed. The high-energy ionic liquid HEATN was also studied using the fragment molecular orbital method. The solvation dynamics of the HEATN system were determined. This marks the first study of the solvation dynamics in a triazolium ionic liquid system.

Relevance of deterministic chaos theory to studies in functioning of dynamical systems

NASA Astrophysics Data System (ADS)

Glagolev, S. N.; Bukhonova, S. M.; Chikina, E. D.

2018-03-01

The paper considers chaotic behavior of dynamical systems typical for social and economic processes. Approaches to analysis and evaluation of system development processes are studies from the point of view of controllability and determinateness. Explanations are given for necessity to apply non-standard mathematical tools to explain states of dynamical social and economic systems on the basis of fractal theory. Features of fractal structures, such as non-regularity, self-similarity, dimensionality and fractionality are considered.

A review of human factors challenges of complex adaptive systems: discovering and understanding chaos in human performance.

PubMed

Karwowski, Waldemar

2012-12-01

In this paper, the author explores a need for a greater understanding of the true nature of human-system interactions from the perspective of the theory of complex adaptive systems, including the essence of complexity, emergent properties of system behavior, nonlinear systems dynamics, and deterministic chaos. Human performance, more often than not, constitutes complex adaptive phenomena with emergent properties that exhibit nonlinear dynamical (chaotic) behaviors. The complexity challenges in the design and management of contemporary work systems, including service systems, are explored. Examples of selected applications of the concepts of nonlinear dynamics to the study of human physical performance are provided. Understanding and applications of the concepts of theory of complex adaptive and dynamical systems should significantly improve the effectiveness of human-centered design efforts of a large system of systems. Performance of many contemporary work systems and environments may be sensitive to the initial conditions and may exhibit dynamic nonlinear properties and chaotic system behaviors. Human-centered design of emergent human-system interactions requires application of the theories of nonlinear dynamics and complex adaptive system. The success of future human-systems integration efforts requires the fusion of paradigms, knowledge, design principles, and methodologies of human factors and ergonomics with those of the science of complex adaptive systems as well as modern systems engineering.

Cosmological dynamics with non-minimally coupled scalar field and a constant potential function

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hrycyna, Orest; Szydłowski, Marek, E-mail: orest.hrycyna@ncbj.gov.pl, E-mail: marek.szydlowski@uj.edu.pl

2015-11-01

Dynamical systems methods are used to investigate global behaviour of the spatially flat Friedmann-Robertson-Walker cosmological model in gravitational theory with a non-minimally coupled scalar field and a constant potential function. We show that the system can be reduced to an autonomous three-dimensional dynamical system and additionally is equipped with an invariant manifold corresponding to an accelerated expansion of the universe. Using this invariant manifold we find an exact solution of the reduced dynamics. We investigate all solutions for all admissible initial conditions using theory of dynamical systems to obtain a classification of all evolutional paths. The right-hand sides of themore » dynamical system depend crucially on the value of the non-minimal coupling constant therefore we study bifurcation values of this parameter under which the structure of the phase space changes qualitatively. We found a special bifurcation value of the non-minimal coupling constant which is distinguished by dynamics of the model and may suggest some additional symmetry in matter sector of the theory.« less

COLLABORATIVE RESEARCH AND DEVELOPMENT (CR&D) Delivery Order 0059: Molecular Dynamics Modeling Support

DTIC Science & Technology

2008-03-01

Molecular Dynamics Simulations 5 Theory: Equilibrium Molecular Dynamics Simulations 6 Theory: Non...Equilibrium Molecular Dynamics Simulations 8 Carbon Nanotube Simulations : Approach and results from equilibrium and non-equilibrium molecular dynamics ...touched from the perspective of molecular dynamics simulations . However, ordered systems such as “Carbon Nanotubes” have been investigated in terms

Analytical structure, dynamics, and coarse graining of a kinetic model of an active fluid

NASA Astrophysics Data System (ADS)

Gao, Tong; Betterton, Meredith D.; Jhang, An-Sheng; Shelley, Michael J.

2017-09-01

We analyze one of the simplest active suspensions with complex dynamics: a suspension of immotile "extensor" particles that exert active extensile dipolar stresses on the fluid in which they are immersed. This is relevant to several experimental systems, such as recently studied tripartite rods that create extensile flows by consuming a chemical fuel. We first describe the system through a Doi-Onsager kinetic theory based on microscopic modeling. This theory captures the active stresses produced by the particles that can drive hydrodynamic instabilities, as well as the steric interactions of rodlike particles that lead to nematic alignment. This active nematic system yields complex flows and disclination defect dynamics very similar to phenomenological Landau-deGennes Q -tensor theories for active nematic fluids, as well as by more complex Doi-Onsager theories for polar microtubule-motor-protein systems. We apply the quasiequilibrium Bingham closure, used to study suspensions of passive microscopic rods, to develop a nonstandard Q -tensor theory. We demonstrate through simulation that this B Q -tensor theory gives an excellent analytical and statistical accounting of the suspension's complex dynamics, at a far reduced computational cost. Finally, we apply the B Q -tensor model to study the dynamics of extensor suspensions in circular and biconcave domains. In circular domains, we reproduce previous results for systems with weak nematic alignment, but for strong alignment we find unusual dynamics with activity-controlled defect production and absorption at the boundaries of the domain. In biconcave domains, a Fredericks-like transition occurs as the width of the neck connecting the two disks is varied.

Chua's Circuit and the Qualitative Theory of Dynamical Systems

NASA Astrophysics Data System (ADS)

Mira, Christian

Simple electronic oscillators were at the origin of many studies related to the qualitative theory of dynamical systems. Chua's circuit ([Chua, 1992; Madan, 1993; Chua, 1993; Chua & Pivka, 1995; Wu & Chua, 1996; Pivka et al., 1996]) is now playing an equivalent role for the generation and understanding of complex dynamics. In honour of my friend Leon Chua on his 60th birthday.

A nonlinear dynamical system for combustion instability in a pulse model combustor

NASA Astrophysics Data System (ADS)

Takagi, Kazushi; Gotoda, Hiroshi

2016-11-01

We theoretically and numerically study the bifurcation phenomena of nonlinear dynamical system describing combustion instability in a pulse model combustor on the basis of dynamical system theory and complex network theory. The dynamical behavior of pressure fluctuations undergoes a significant transition from steady-state to deterministic chaos via the period-doubling cascade process known as Feigenbaum scenario with decreasing the characteristic flow time. Recurrence plots and recurrence networks analysis we adopted in this study can quantify the significant changes in dynamic behavior of combustion instability that cannot be captured in the bifurcation diagram.

Stability of Dynamical Systems with Discontinuous Motions:

NASA Astrophysics Data System (ADS)

Michel, Anthony N.; Hou, Ling

In this paper we present a stability theory for discontinuous dynamical systems (DDS): continuous-time systems whose motions are not necessarily continuous with respect to time. We show that this theory is not only applicable in the analysis of DDS, but also in the analysis of continuous dynamical systems (continuous-time systems whose motions are continuous with respect to time), discrete-time dynamical systems (systems whose motions are defined at discrete points in time) and hybrid dynamical systems (HDS) (systems whose descriptions involve simultaneously continuous-time and discrete-time). We show that the stability results for DDS are in general less conservative than the corresponding well-known classical Lyapunov results for continuous dynamical systems and discrete-time dynamical systems. Although the DDS stability results are applicable to general dynamical systems defined on metric spaces (divorced from any kind of description by differential equations, or any other kinds of equations), we confine ourselves to finite-dimensional dynamical systems defined by ordinary differential equations and difference equations, to make this paper as widely accessible as possible. We present only sample results, namely, results for uniform asymptotic stability in the large.

Symmetric linear systems - An application of algebraic systems theory

NASA Technical Reports Server (NTRS)

Hazewinkel, M.; Martin, C.

1983-01-01

Dynamical systems which contain several identical subsystems occur in a variety of applications ranging from command and control systems and discretization of partial differential equations, to the stability augmentation of pairs of helicopters lifting a large mass. Linear models for such systems display certain obvious symmetries. In this paper, we discuss how these symmetries can be incorporated into a mathematical model that utilizes the modern theory of algebraic systems. Such systems are inherently related to the representation theory of algebras over fields. We will show that any control scheme which respects the dynamical structure either implicitly or explicitly uses the underlying algebra.

Butterflies, Black swans and Dragon kings: How to use the Dynamical Systems Theory to build a "zoology" of mid-latitude circulation atmospheric extremes?

NASA Astrophysics Data System (ADS)

Faranda, D.; Yiou, P.; Alvarez-Castro, M. C. M.

2015-12-01

A combination of dynamical systems and statistical techniques allows for a robust assessment of the dynamical properties of the mid-latitude atmospheric circulation. Extremes at different spatial and time scales are not only associated to exceptionally intense weather structures (e.g. extra-tropical cyclones) but also to rapid changes of circulation regimes (thunderstorms, supercells) or the extreme persistence of weather structure (heat waves, cold spells). We will show how the dynamical systems theory of recurrence combined to the extreme value theory can take into account the spatial and temporal dependence structure of the mid-latitude circulation structures and provide information on the statistics of extreme events.

PROCEEDINGS OF THE SYMPOSIUM ON SYSTEM THEORY, NEW YORK, N. Y. APRIL 20, 21, 22 1965. VOLUME XV.

DTIC Science & Technology

The papers presented at the symposium may be grouped as follows: (1) What is system theory ; (2) Representations of systems; (3) System dynamics; (4...Non-deterministic systems; (5) Optimal systems; and (6) Applications of system theory .

Identification of dynamic systems, theory and formulation

NASA Technical Reports Server (NTRS)

Maine, R. E.; Iliff, K. W.

1985-01-01

The problem of estimating parameters of dynamic systems is addressed in order to present the theoretical basis of system identification and parameter estimation in a manner that is complete and rigorous, yet understandable with minimal prerequisites. Maximum likelihood and related estimators are highlighted. The approach used requires familiarity with calculus, linear algebra, and probability, but does not require knowledge of stochastic processes or functional analysis. The treatment emphasizes unification of the various areas in estimation in dynamic systems is treated as a direct outgrowth of the static system theory. Topics covered include basic concepts and definitions; numerical optimization methods; probability; statistical estimators; estimation in static systems; stochastic processes; state estimation in dynamic systems; output error, filter error, and equation error methods of parameter estimation in dynamic systems, and the accuracy of the estimates.

Chiral dynamics with (non)strange quarks

NASA Astrophysics Data System (ADS)

Kubis, Bastian; Meißner, Ulf-G.

2017-01-01

We review the results and achievements of the project B.3. Topics addressed include pion photoproduction off the proton and off deuterium, three-flavor chiral perturbation theory studies, chiral symmetry tests in Goldstone boson decays, the development of unitarized chiral perturbation theory to next-to-leading order, the two-pole structure of the Λ(1405), the dynamical generation of the lowest S11 resonances, the theory of hadronic atoms and its application to various systems, precision studies in light-meson decays based on dispersion theory, the Roy-Steiner analysis of pion-nucleon scattering, a high-precision extraction of the elusive pion-nucleon σ-term, and aspects of chiral dynamics in few-nucleon systems.

A model of gene expression based on random dynamical systems reveals modularity properties of gene regulatory networks.

PubMed

Antoneli, Fernando; Ferreira, Renata C; Briones, Marcelo R S

2016-06-01

Here we propose a new approach to modeling gene expression based on the theory of random dynamical systems (RDS) that provides a general coupling prescription between the nodes of any given regulatory network given the dynamics of each node is modeled by a RDS. The main virtues of this approach are the following: (i) it provides a natural way to obtain arbitrarily large networks by coupling together simple basic pieces, thus revealing the modularity of regulatory networks; (ii) the assumptions about the stochastic processes used in the modeling are fairly general, in the sense that the only requirement is stationarity; (iii) there is a well developed mathematical theory, which is a blend of smooth dynamical systems theory, ergodic theory and stochastic analysis that allows one to extract relevant dynamical and statistical information without solving the system; (iv) one may obtain the classical rate equations form the corresponding stochastic version by averaging the dynamic random variables (small noise limit). It is important to emphasize that unlike the deterministic case, where coupling two equations is a trivial matter, coupling two RDS is non-trivial, specially in our case, where the coupling is performed between a state variable of one gene and the switching stochastic process of another gene and, hence, it is not a priori true that the resulting coupled system will satisfy the definition of a random dynamical system. We shall provide the necessary arguments that ensure that our coupling prescription does indeed furnish a coupled regulatory network of random dynamical systems. Finally, the fact that classical rate equations are the small noise limit of our stochastic model ensures that any validation or prediction made on the basis of the classical theory is also a validation or prediction of our model. We illustrate our framework with some simple examples of single-gene system and network motifs. Copyright © 2016 Elsevier Inc. All rights reserved.

On Restructurable Control System Theory

NASA Technical Reports Server (NTRS)

Athans, M.

1983-01-01

The state of stochastic system and control theory as it impacts restructurable control issues is addressed. The multivariable characteristics of the control problem are addressed. The failure detection/identification problem is discussed as a multi-hypothesis testing problem. Control strategy reconfiguration, static multivariable controls, static failure hypothesis testing, dynamic multivariable controls, fault-tolerant control theory, dynamic hypothesis testing, generalized likelihood ratio (GLR) methods, and adaptive control are discussed.

Spaceflight dynamics 1993; AAS/NASA International Symposium, 8th, Greenbelt, MD, Apr. 26-30, 1993, Parts 1 & 2

NASA Technical Reports Server (NTRS)

Teles, Jerome (Editor); Samii, Mina V. (Editor)

1993-01-01

A conference on spaceflight dynamics produced papers in the areas of orbit determination, spacecraft tracking, autonomous navigation, the Deep Space Program Science Experiment Mission (DSPSE), the Global Positioning System, attitude control, geostationary satellites, interplanetary missions and trajectories, applications of estimation theory, flight dynamics systems, low-Earth orbit missions, orbital mechanics, mission experience in attitude dynamics, mission experience in sensor studies, attitude dynamics theory and simulations, and orbit-related experience. These papaers covered NASA, European, Russian, Japanese, Chinese, and Brazilian space programs and hardware.

Traditional Chinese medicine: potential approaches from modern dynamical complexity theories.

PubMed

Ma, Yan; Zhou, Kehua; Fan, Jing; Sun, Shuchen

2016-03-01

Despite the widespread use of traditional Chinese medicine (TCM) in clinical settings, proving its effectiveness via scientific trials is still a challenge. TCM views the human body as a complex dynamical system, and focuses on the balance of the human body, both internally and with its external environment. Such fundamental concepts require investigations using system-level quantification approaches, which are beyond conventional reductionism. Only methods that quantify dynamical complexity can bring new insights into the evaluation of TCM. In a previous article, we briefly introduced the potential value of Multiscale Entropy (MSE) analysis in TCM. This article aims to explain the existing challenges in TCM quantification, to introduce the consistency of dynamical complexity theories and TCM theories, and to inspire future system-level research on health and disease.

Design tools for complex dynamic security systems.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Byrne, Raymond Harry; Rigdon, James Brian; Rohrer, Brandon Robinson

2007-01-01

The development of tools for complex dynamic security systems is not a straight forward engineering task but, rather, a scientific task where discovery of new scientific principles and math is necessary. For years, scientists have observed complex behavior but have had difficulty understanding it. Prominent examples include: insect colony organization, the stock market, molecular interactions, fractals, and emergent behavior. Engineering such systems will be an even greater challenge. This report explores four tools for engineered complex dynamic security systems: Partially Observable Markov Decision Process, Percolation Theory, Graph Theory, and Exergy/Entropy Theory. Additionally, enabling hardware technology for next generation security systemsmore » are described: a 100 node wireless sensor network, unmanned ground vehicle and unmanned aerial vehicle.« less

Floquet–Magnus theory and generic transient dynamics in periodically driven many-body quantum systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kuwahara, Tomotaka, E-mail: tomotaka.phys@gmail.com; WPI, Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577; Mori, Takashi

2016-04-15

This work explores a fundamental dynamical structure for a wide range of many-body quantum systems under periodic driving. Generically, in the thermodynamic limit, such systems are known to heat up to infinite temperature states in the long-time limit irrespective of dynamical details, which kills all the specific properties of the system. In the present study, instead of considering infinitely long-time scale, we aim to provide a general framework to understand the long but finite time behavior, namely the transient dynamics. In our analysis, we focus on the Floquet–Magnus (FM) expansion that gives a formal expression of the effective Hamiltonian onmore » the system. Although in general the full series expansion is not convergent in the thermodynamics limit, we give a clear relationship between the FM expansion and the transient dynamics. More precisely, we rigorously show that a truncated version of the FM expansion accurately describes the exact dynamics for a certain time-scale. Our theory reveals an experimental time-scale for which non-trivial dynamical phenomena can be reliably observed. We discuss several dynamical phenomena, such as the effect of small integrability breaking, efficient numerical simulation of periodically driven systems, dynamical localization and thermalization. Especially on thermalization, we discuss a generic scenario on the prethermalization phenomenon in periodically driven systems. -- Highlights: •A general framework to describe transient dynamics for periodically driven systems. •The theory is applicable to generic quantum many-body systems including long-range interacting systems. •Physical meaning of the truncation of the Floquet–Magnus expansion is rigorously established. •New mechanism of the prethermalization is proposed. •Revealing an experimental time-scale for which non-trivial dynamical phenomena can be reliably observed.« less

Dynamic Systems Theory and Team Sport Coaching

ERIC Educational Resources Information Center

Gréhaigne, Jean-Francis; Godbout, Paul

2014-01-01

This article examines the theory of dynamic systems and its use in the domains of the study and coaching of team sports. The two teams involved in a match are looked at as two interacting systems in movement, where opposition is paramount. A key element for the observation of game play is the notion of configuration of play and its ever-changing…

Behavioral and neural Darwinism: selectionist function and mechanism in adaptive behavior dynamics.

PubMed

McDowell, J J

2010-05-01

An evolutionary theory of behavior dynamics and a theory of neuronal group selection share a common selectionist framework. The theory of behavior dynamics instantiates abstractly the idea that behavior is selected by its consequences. It implements Darwinian principles of selection, reproduction, and mutation to generate adaptive behavior in virtual organisms. The behavior generated by the theory has been shown to be quantitatively indistinguishable from that of live organisms. The theory of neuronal group selection suggests a mechanism whereby the abstract principles of the evolutionary theory may be implemented in the nervous systems of biological organisms. According to this theory, groups of neurons subserving behavior may be selected by synaptic modifications that occur when the consequences of behavior activate value systems in the brain. Together, these theories constitute a framework for a comprehensive account of adaptive behavior that extends from brain function to the behavior of whole organisms in quantitative detail. Copyright (c) 2009 Elsevier B.V. All rights reserved.

A Dynamic Systems Theory Model of Visual Perception Development

ERIC Educational Resources Information Center

Coté, Carol A.

2015-01-01

This article presents a model for understanding the development of visual perception from a dynamic systems theory perspective. It contrasts to a hierarchical or reductionist model that is often found in the occupational therapy literature. In this proposed model vision and ocular motor abilities are not foundational to perception, they are seen…

Defending Qualitative Change: The View from Dynamical Systems Theory

ERIC Educational Resources Information Center

Spencer, John P.; Perone, Sammy

2008-01-01

A central controversy in developmental science, enflamed by nativist accounts, is whether development is best viewed as a series of qualitative or continuous changes. This article defends the notion of qualitative change from the perspective of dynamical systems theory (DST). Qualitative change within DST refers to the shift that occurs when a…

A Dynamic Ensemble for Second Language Research: Putting Complexity Theory into Practice

ERIC Educational Resources Information Center

Hiver, Phil; Al-Hoorie, Ali H.

2016-01-01

In this article, we introduce a template of methodological considerations, termed "the dynamic ensemble," for scholars doing or evaluating empirical second language development (SLD) research within a complexity/dynamic systems theory (CDST) framework. Given that CDST principles have yielded significant insight into SLD and have become…

Rotorcraft control system design for uncertain vehicle dynamics using quantitative feedback theory

NASA Technical Reports Server (NTRS)

Hess, R. A.

1994-01-01

Quantitative Feedback Theory describes a frequency-domain technique for the design of multi-input, multi-output control systems which must meet time or frequency domain performance criteria when specified uncertainty exists in the linear description of the vehicle dynamics. This theory is applied to the design of the longitudinal flight control system for a linear model of the BO-105C rotorcraft. Uncertainty in the vehicle model is due to the variation in the vehicle dynamics over a range of airspeeds from 0-100 kts. For purposes of exposition, the vehicle description contains no rotor or actuator dynamics. The design example indicates the manner in which significant uncertainty exists in the vehicle model. The advantage of using a sequential loop closure technique to reduce the cost of feedback is demonstrated by example.

Spatial dynamics of invasion: the geometry of introduced species.

PubMed

Korniss, Gyorgy; Caraco, Thomas

2005-03-07

Many exotic species combine low probability of establishment at each introduction with rapid population growth once introduction does succeed. To analyse this phenomenon, we note that invaders often cluster spatially when rare, and consequently an introduced exotic's population dynamics should depend on locally structured interactions. Ecological theory for spatially structured invasion relies on deterministic approximations, and determinism does not address the observed uncertainty of the exotic-introduction process. We take a new approach to the population dynamics of invasion and, by extension, to the general question of invasibility in any spatial ecology. We apply the physical theory for nucleation of spatial systems to a lattice-based model of competition between plant species, a resident and an invader, and the analysis reaches conclusions that differ qualitatively from the standard ecological theories. Nucleation theory distinguishes between dynamics of single- and multi-cluster invasion. Low introduction rates and small system size produce single-cluster dynamics, where success or failure of introduction is inherently stochastic. Single-cluster invasion occurs only if the cluster reaches a critical size, typically preceded by a number of failed attempts. For this case, we identify the functional form of the probability distribution of time elapsing until invasion succeeds. Although multi-cluster invasion for sufficiently large systems exhibits spatial averaging and almost-deterministic dynamics of the global densities, an analytical approximation from nucleation theory, known as Avrami's law, describes our simulation results far better than standard ecological approximations.

Trends in modern system theory

NASA Technical Reports Server (NTRS)

Athans, M.

1976-01-01

The topics considered are related to linear control system design, adaptive control, failure detection, control under failure, system reliability, and large-scale systems and decentralized control. It is pointed out that the design of a linear feedback control system which regulates a process about a desirable set point or steady-state condition in the presence of disturbances is a very important problem. The linearized dynamics of the process are used for design purposes. The typical linear-quadratic design involving the solution of the optimal control problem of a linear time-invariant system with respect to a quadratic performance criterion is considered along with gain reduction theorems and the multivariable phase margin theorem. The stumbling block in many adaptive design methodologies is associated with the amount of real time computation which is necessary. Attention is also given to the desperate need to develop good theories for large-scale systems, the beginning of a microprocessor revolution, the translation of the Wiener-Hopf theory into the time domain, and advances made in dynamic team theory, dynamic stochastic games, and finite memory stochastic control.

A Dynamic Systems Approach to Internationalization of Higher Education

ERIC Educational Resources Information Center

Zhou, Jiangyuan

2016-01-01

Research shows that internationalization of higher education is a process rather than an end product. This paper applies the Dynamic Systems Theory to examine the nature and development of internationalization of higher education, and proposes that internationalization of higher education is a dynamic system. A dynamic framework of…

Use of measurement theory for operationalization and quantification of psychological constructs in systems dynamics modelling

NASA Astrophysics Data System (ADS)

Fitkov-Norris, Elena; Yeghiazarian, Ara

2016-11-01

The analytical tools available to social scientists have traditionally been adapted from tools originally designed for analysis of natural science phenomena. This article discusses the applicability of systems dynamics - a qualitative based modelling approach, as a possible analysis and simulation tool that bridges the gap between social and natural sciences. After a brief overview of the systems dynamics modelling methodology, the advantages as well as limiting factors of systems dynamics to the potential applications in the field of social sciences and human interactions are discussed. The issues arise with regards to operationalization and quantification of latent constructs at the simulation building stage of the systems dynamics methodology and measurement theory is proposed as a ready and waiting solution to the problem of dynamic model calibration, with a view of improving simulation model reliability and validity and encouraging the development of standardised, modular system dynamics models that can be used in social science research.

Aubry-Mather Theory for Conformally Symplectic Systems

NASA Astrophysics Data System (ADS)

Marò, Stefano; Sorrentino, Alfonso

2017-09-01

In this article we develop an analogue of Aubry-Mather theory for a class of dissipative systems, namely conformally symplectic systems, and prove the existence of interesting invariant sets, which, in analogy to the conservative case, will be called the Aubry and the Mather sets. Besides describing their structure and their dynamical significance, we shall analyze their attracting/repelling properties, as well as their noteworthy role in driving the asymptotic dynamics of the system.

Theoretical approaches for dynamical ordering of biomolecular systems.

PubMed

Okumura, Hisashi; Higashi, Masahiro; Yoshida, Yuichiro; Sato, Hirofumi; Akiyama, Ryo

2018-02-01

Living systems are characterized by the dynamic assembly and disassembly of biomolecules. The dynamical ordering mechanism of these biomolecules has been investigated both experimentally and theoretically. The main theoretical approaches include quantum mechanical (QM) calculation, all-atom (AA) modeling, and coarse-grained (CG) modeling. The selected approach depends on the size of the target system (which differs among electrons, atoms, molecules, and molecular assemblies). These hierarchal approaches can be combined with molecular dynamics (MD) simulation and/or integral equation theories for liquids, which cover all size hierarchies. We review the framework of quantum mechanical/molecular mechanical (QM/MM) calculations, AA MD simulations, CG modeling, and integral equation theories. Applications of these methods to the dynamical ordering of biomolecular systems are also exemplified. The QM/MM calculation enables the study of chemical reactions. The AA MD simulation, which omits the QM calculation, can follow longer time-scale phenomena. By reducing the number of degrees of freedom and the computational cost, CG modeling can follow much longer time-scale phenomena than AA modeling. Integral equation theories for liquids elucidate the liquid structure, for example, whether the liquid follows a radial distribution function. These theoretical approaches can analyze the dynamic behaviors of biomolecular systems. They also provide useful tools for exploring the dynamic ordering systems of biomolecules, such as self-assembly. This article is part of a Special Issue entitled "Biophysical Exploration of Dynamical Ordering of Biomolecular Systems" edited by Dr. Koichi Kato. Copyright © 2017 Elsevier B.V. All rights reserved.

Lexical Complexity Development from Dynamic Systems Theory Perspective: Lexical Density, Diversity, and Sophistication

ERIC Educational Resources Information Center

Kalantari, Reza; Gholami, Javad

2017-01-01

This longitudinal case study explored Iranian EFL learners' lexical complexity (LC) through the lenses of Dynamic Systems Theory (DST). Fifty independent essays written by five intermediate to advanced female EFL learners in a TOEFL iBT preparation course over six months constituted the corpus of this study. Three Coh-Metrix indices (Graesser,…

Learning and dynamics in social systems. Comment on "Collective learning modeling based on the kinetic theory of active particles" by D. Burini et al.

NASA Astrophysics Data System (ADS)

Dolfin, Marina

2016-03-01

The interesting novelty of the paper by Burini et al. [1] is that the authors present a survey and a new approach of collective learning based on suitable development of methods of the kinetic theory [2] and theoretical tools of evolutionary game theory [3]. Methods of statistical dynamics and kinetic theory lead naturally to stochastic and collective dynamics. Indeed, the authors propose the use of games where the state of the interacting entities is delivered by probability distributions.

General System Theory: Toward a Conceptual Framework for Science and Technology Education for All.

ERIC Educational Resources Information Center

Chen, David; Stroup, Walter

1993-01-01

Suggests using general system theory as a unifying theoretical framework for science and technology education for all. Five reasons are articulated: the multidisciplinary nature of systems theory, the ability to engage complexity, the capacity to describe system dynamics, the ability to represent the relationship between microlevel and…

Multiscale structure in eco-evolutionary dynamics

NASA Astrophysics Data System (ADS)

Stacey, Blake C.

In a complex system, the individual components are neither so tightly coupled or correlated that they can all be treated as a single unit, nor so uncorrelated that they can be approximated as independent entities. Instead, patterns of interdependency lead to structure at multiple scales of organization. Evolution excels at producing such complex structures. In turn, the existence of these complex interrelationships within a biological system affects the evolutionary dynamics of that system. I present a mathematical formalism for multiscale structure, grounded in information theory, which makes these intuitions quantitative, and I show how dynamics defined in terms of population genetics or evolutionary game theory can lead to multiscale organization. For complex systems, "more is different," and I address this from several perspectives. Spatial host--consumer models demonstrate the importance of the structures which can arise due to dynamical pattern formation. Evolutionary game theory reveals the novel effects which can result from multiplayer games, nonlinear payoffs and ecological stochasticity. Replicator dynamics in an environment with mesoscale structure relates to generalized conditionalization rules in probability theory. The idea of natural selection "acting at multiple levels" has been mathematized in a variety of ways, not all of which are equivalent. We will face down the confusion, using the experience developed over the course of this thesis to clarify the situation.

A hundred years of latency: from Freudian psychosexual theory to dynamic systems nonlinear development in middle childhood.

PubMed

Knight, Rona

2014-04-01

A focus on the latency phase is used to illustrate how theory and developmental research have influenced our psychoanalytic views of development over the past hundred years. Beginning with Freud's psychosexual theory and his conception of latency, an historical overview of the major psychoanalytic contributions bearing on this developmental period over the past century is presented. Recent longitudinal research in latency supports a nonlinear dynamic systems approach to development. This approach obliges us to reconsider our linear theories and how we think about and work with our patients.

Information Processing Capacity of Dynamical Systems

NASA Astrophysics Data System (ADS)

Dambre, Joni; Verstraeten, David; Schrauwen, Benjamin; Massar, Serge

2012-07-01

Many dynamical systems, both natural and artificial, are stimulated by time dependent external signals, somehow processing the information contained therein. We demonstrate how to quantify the different modes in which information can be processed by such systems and combine them to define the computational capacity of a dynamical system. This is bounded by the number of linearly independent state variables of the dynamical system, equaling it if the system obeys the fading memory condition. It can be interpreted as the total number of linearly independent functions of its stimuli the system can compute. Our theory combines concepts from machine learning (reservoir computing), system modeling, stochastic processes, and functional analysis. We illustrate our theory by numerical simulations for the logistic map, a recurrent neural network, and a two-dimensional reaction diffusion system, uncovering universal trade-offs between the non-linearity of the computation and the system's short-term memory.

Information Processing Capacity of Dynamical Systems

PubMed Central

Dambre, Joni; Verstraeten, David; Schrauwen, Benjamin; Massar, Serge

2012-01-01

Many dynamical systems, both natural and artificial, are stimulated by time dependent external signals, somehow processing the information contained therein. We demonstrate how to quantify the different modes in which information can be processed by such systems and combine them to define the computational capacity of a dynamical system. This is bounded by the number of linearly independent state variables of the dynamical system, equaling it if the system obeys the fading memory condition. It can be interpreted as the total number of linearly independent functions of its stimuli the system can compute. Our theory combines concepts from machine learning (reservoir computing), system modeling, stochastic processes, and functional analysis. We illustrate our theory by numerical simulations for the logistic map, a recurrent neural network, and a two-dimensional reaction diffusion system, uncovering universal trade-offs between the non-linearity of the computation and the system's short-term memory. PMID:22816038

Accelerated Expansion of the Early and Late Universe in Terms of the Scalar-Tensor Theory of Gravitation. II

NASA Astrophysics Data System (ADS)

Avagyan, R. M.; Harutyunyan, G. H.

2018-03-01

The cosmological dynamics of a quasi-de Sitter model is described in an "Einstein" representation of the modified Jordan theory using a qualitative theory of dynamic systems. An inflationary picture of the expansion is obtained for a range of the dimensionless acceleration parameter from one to zero.

Network destabilization and transition in depression: New methods for studying the dynamics of therapeutic change

PubMed Central

Hayes, Adele M.; Yasinski, Carly; Barnes, J. Ben; Bockting, Claudi L. H.

2015-01-01

The science of dynamic systems is the study of pattern formation and system change. Dynamic systems theory can provide a useful framework for understanding the chronicity of depression and its treatment. We propose a working model of therapeutic change with potential to organize findings from psychopathology and treatment research, suggest new ways to study change, facilitate comparisons across studies, and stimulate treatment innovation. We describe a treatment for depression that we developed to apply principles from dynamic systems theory and then present a program of research to examine the utility of this application. Recent methodological and technological developments are also discussed to further advance the search for mechanisms of therapeutic change. PMID:26197726

Laser dynamics: The system dynamics and network theory of optoelectronic integrated circuit design

NASA Astrophysics Data System (ADS)

Tarng, Tom Shinming-T. K.

Laser dynamics is the system dynamics, communication and network theory for the design of opto-electronic integrated circuit (OEIC). Combining the optical network theory and optical communication theory, the system analysis and design for the OEIC fundamental building blocks is considered. These building blocks include the direct current modulation, inject light modulation, wideband filter, super-gain optical amplifier, E/O and O/O optical bistability and current-controlled optical oscillator. Based on the rate equations, the phase diagram and phase portrait analysis is applied to the theoretical studies and numerical simulation. The OEIC system design methodologies are developed for the OEIC design. Stimulating-field-dependent rate equations are used to model the line-width narrowing/broadening mechanism for the CW mode and frequency chirp of semiconductor lasers. The momentary spectra are carrier-density-dependent. Furthermore, the phase portrait analysis and the nonlinear refractive index is used to simulate the single mode frequency chirp. The average spectra of chaos, period doubling, period pulsing, multi-loops and analog modulation are generated and analyzed. The bifurcation-chirp design chart with modulation depth and modulation frequency as parameters is provided for design purpose.

Moving From Static to Dynamic Models of the Onset of Mental Disorder: A Review.

PubMed

Nelson, Barnaby; McGorry, Patrick D; Wichers, Marieke; Wigman, Johanna T W; Hartmann, Jessica A

2017-05-01

In recent years, there has been increased focus on subthreshold stages of mental disorders, with attempts to model and predict which individuals will progress to full-threshold disorder. Given this research attention and the clinical significance of the issue, this article analyzes the assumptions of the theoretical models in the field. Psychiatric research into predicting the onset of mental disorder has shown an overreliance on one-off sampling of cross-sectional data (ie, a snapshot of clinical state and other risk markers) and may benefit from taking dynamic changes into account in predictive modeling. Cross-disciplinary approaches to complex system structures and changes, such as dynamical systems theory, network theory, instability mechanisms, chaos theory, and catastrophe theory, offer potent models that can be applied to the emergence (or decline) of psychopathology, including psychosis prediction, as well as to transdiagnostic emergence of symptoms. Psychiatric research may benefit from approaching psychopathology as a system rather than as a category, identifying dynamics of system change (eg, abrupt vs gradual psychosis onset), and determining the factors to which these systems are most sensitive (eg, interpersonal dynamics and neurochemical change) and the individual variability in system architecture and change. These goals can be advanced by testing hypotheses that emerge from cross-disciplinary models of complex systems. Future studies require repeated longitudinal assessment of relevant variables through either (or a combination of) micro-level (momentary and day-to-day) and macro-level (month and year) assessments. Ecological momentary assessment is a data collection technique appropriate for micro-level assessment. Relevant statistical approaches are joint modeling and time series analysis, including metric-based and model-based methods that draw on the mathematical principles of dynamical systems. This next generation of prediction studies may more accurately model the dynamic nature of psychopathology and system change as well as have treatment implications, such as introducing a means of identifying critical periods of risk for mental state deterioration.

A Model for Teaching the Dynamical Theory of Tides.

ERIC Educational Resources Information Center

Railsback, L. Bruce

1991-01-01

The dynamical theory of tides is often neglected in teaching oceanography because students have difficulty in visualizing the movements of the tides across the glove. A schematic diagram portraying amphidromic systems as mechanical gears helps overcome these problems. (Author)

From synthetic modeling of social interaction to dynamic theories of brain-body-environment-body-brain systems.

PubMed

Froese, Tom; Iizuka, Hiroyuki; Ikegami, Takashi

2013-08-01

Synthetic approaches to social interaction support the development of a second-person neuroscience. Agent-based models and psychological experiments can be related in a mutually informing manner. Models have the advantage of making the nonlinear brain-body-environment-body-brain system as a whole accessible to analysis by dynamical systems theory. We highlight some general principles of how social interaction can partially constitute an individual's behavior.

Application of dynamical systems theory to nonlinear aircraft dynamics

NASA Technical Reports Server (NTRS)

Culick, Fred E. C.; Jahnke, Craig C.

1988-01-01

Dynamical systems theory has been used to study nonlinear aircraft dynamics. A six degree of freedom model that neglects gravity has been analyzed. The aerodynamic model, supplied by NASA, is for a generic swept wing fighter and includes nonlinearities as functions of the angle of attack. A continuation method was used to calculate the steady states of the aircraft, and bifurcations of these steady states, as functions of the control deflections. Bifurcations were used to predict jump phenomena and the onset of periodic motion for roll coupling instabilities and high angle of attack maneuvers. The predictions were verified with numerical simulations.

Solitary Waves, Periodic Peakons and Pseudo-Peakons of the Nonlinear Acoustic Wave Model in Rotating Magnetized Plasma

NASA Astrophysics Data System (ADS)

Li, Jibin

The dynamical model of the nonlinear acoustic wave in rotating magnetized plasma is governed by a partial differential equation system. Its traveling system is a singular traveling wave system of first class depending on two parameters. By using the bifurcation theory and method of dynamical systems and the theory of singular traveling wave systems, in this paper, we show that there exist parameter groups such that this singular system has pseudo-peakons, periodic peakons and compactons as well as different solitary wave solutions.

Non-equilibrium phase transition in mesoscopic biochemical systems: from stochastic to nonlinear dynamics and beyond

PubMed Central

Ge, Hao; Qian, Hong

2011-01-01

A theory for an non-equilibrium phase transition in a driven biochemical network is presented. The theory is based on the chemical master equation (CME) formulation of mesoscopic biochemical reactions and the mathematical method of large deviations. The large deviations theory provides an analytical tool connecting the macroscopic multi-stability of an open chemical system with the multi-scale dynamics of its mesoscopic counterpart. It shows a corresponding non-equilibrium phase transition among multiple stochastic attractors. As an example, in the canonical phosphorylation–dephosphorylation system with feedback that exhibits bistability, we show that the non-equilibrium steady-state (NESS) phase transition has all the characteristics of classic equilibrium phase transition: Maxwell construction, a discontinuous first-derivative of the ‘free energy function’, Lee–Yang's zero for a generating function and a critical point that matches the cusp in nonlinear bifurcation theory. To the biochemical system, the mathematical analysis suggests three distinct timescales and needed levels of description. They are (i) molecular signalling, (ii) biochemical network nonlinear dynamics, and (iii) cellular evolution. For finite mesoscopic systems such as a cell, motions associated with (i) and (iii) are stochastic while that with (ii) is deterministic. Both (ii) and (iii) are emergent properties of a dynamic biochemical network. PMID:20466813

Structural aspects of Hamilton-Jacobi theory

NASA Astrophysics Data System (ADS)

Cariñena, J. F.; Gràcia, X.; Marmo, G.; Martínez, E.; Muñoz-Lecanda, M. C.; Román-Roy, N.

2016-12-01

In our previous papers [J. F. Cariñena, X. Gràcia, G. Marmo, E. Martínez, M. C. Muñoz-Lecanda and N. Román-Roy, Geometric Hamilton-Jacobi theory, Int. J. Geom. Meth. Mod. Phys. 3 (2006) 1417-1458; Geometric Hamilton-Jacobi theory for nonholonomic dynamical systems, Int. J. Geom. Meth. Mod. Phys. 7 (2010) 431-454] we showed that the Hamilton-Jacobi problem can be regarded as a way to describe a given dynamics on a phase space manifold in terms of a family of dynamics on a lower-dimensional manifold. We also showed how constants of the motion help to solve the Hamilton-Jacobi equation. Here we want to delve into this interpretation by considering the most general case: a dynamical system on a manifold that is described in terms of a family of dynamics (slicing vector fields) on lower-dimensional manifolds. We identify the relevant geometric structures that lead from this decomposition of the dynamics to the classical Hamilton-Jacobi theory, by considering special cases like fibered manifolds and Hamiltonian dynamics, in the symplectic framework and the Poisson one. We also show how a set of functions on a tangent bundle can determine a second-order dynamics for which they are constants of the motion.

Influence of changes in initial conditions for the simulation of dynamic systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kotyrba, Martin

2015-03-10

Chaos theory is a field of study in mathematics, with applications in several disciplines including meteorology, sociology, physics, engineering, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions—a paradigm popularly referred to as the butterfly effect. Small differences in initial conditions field widely diverging outcomes for such dynamical systems, rendering long-term prediction impossible in general. This happens even though these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved. In this paperinfluence of changes in initial conditions will bemore » presented for the simulation of Lorenz system.« less

Time-Dependent Density Functional Theory for Open Systems and Its Applications.

PubMed

Chen, Shuguang; Kwok, YanHo; Chen, GuanHua

2018-02-20

Photovoltaic devices, electrochemical cells, catalysis processes, light emitting diodes, scanning tunneling microscopes, molecular electronics, and related devices have one thing in common: open quantum systems where energy and matter are not conserved. Traditionally quantum chemistry is confined to isolated and closed systems, while quantum dissipation theory studies open quantum systems. The key quantity in quantum dissipation theory is the reduced system density matrix. As the reduced system density matrix is an O(M! × M!) matrix, where M is the number of the particles of the system of interest, quantum dissipation theory can only be employed to simulate systems of a few particles or degrees of freedom. It is thus important to combine quantum chemistry and quantum dissipation theory so that realistic open quantum systems can be simulated from first-principles. We have developed a first-principles method to simulate the dynamics of open electronic systems, the time-dependent density functional theory for open systems (TDDFT-OS). Instead of the reduced system density matrix, the key quantity is the reduced single-electron density matrix, which is an N × N matrix where N is the number of the atomic bases of the system of interest. As the dimension of the key quantity is drastically reduced, the TDDFT-OS can thus be used to simulate the dynamics of realistic open electronic systems and efficient numerical algorithms have been developed. As an application, we apply the method to study how quantum interference develops in a molecular transistor in time domain. We include electron-phonon interaction in our simulation and show that quantum interference in the given system is robust against nuclear vibration not only in the steady state but also in the transient dynamics. As another application, by combining TDDFT-OS with Ehrenfest dynamics, we study current-induced dissociation of water molecules under scanning tunneling microscopy and follow its time dependent dynamics. Given the rapid development in ultrafast experiments with atomic resolution in recent years, time dependent simulation of open electronic systems will be useful to gain insight and understanding of such experiments. This Account will mainly focus on the practical aspects of the TDDFT-OS method, describing the numerical implementation and demonstrating the method with applications.

Large scale dynamic systems

NASA Technical Reports Server (NTRS)

Doolin, B. F.

1975-01-01

Classes of large scale dynamic systems were discussed in the context of modern control theory. Specific examples discussed were in the technical fields of aeronautics, water resources and electric power.

Dynamic density functional theory with hydrodynamic interactions: theoretical development and application in the study of phase separation in gas-liquid systems.

PubMed

Kikkinides, E S; Monson, P A

2015-03-07

Building on recent developments in dynamic density functional theory, we have developed a version of the theory that includes hydrodynamic interactions. This is achieved by combining the continuity and momentum equations eliminating velocity fields, so the resulting model equation contains only terms related to the fluid density and its time and spatial derivatives. The new model satisfies simultaneously continuity and momentum equations under the assumptions of constant dynamic or kinematic viscosity and small velocities and/or density gradients. We present applications of the theory to spinodal decomposition of subcritical temperatures for one-dimensional and three-dimensional density perturbations for both a van der Waals fluid and for a lattice gas model in mean field theory. In the latter case, the theory provides a hydrodynamic extension to the recently studied dynamic mean field theory. We find that the theory correctly describes the transition from diffusive phase separation at short times to hydrodynamic behaviour at long times.

Dynamic density functional theory with hydrodynamic interactions: Theoretical development and application in the study of phase separation in gas-liquid systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kikkinides, E. S.; Monson, P. A.

Building on recent developments in dynamic density functional theory, we have developed a version of the theory that includes hydrodynamic interactions. This is achieved by combining the continuity and momentum equations eliminating velocity fields, so the resulting model equation contains only terms related to the fluid density and its time and spatial derivatives. The new model satisfies simultaneously continuity and momentum equations under the assumptions of constant dynamic or kinematic viscosity and small velocities and/or density gradients. We present applications of the theory to spinodal decomposition of subcritical temperatures for one-dimensional and three-dimensional density perturbations for both a van dermore » Waals fluid and for a lattice gas model in mean field theory. In the latter case, the theory provides a hydrodynamic extension to the recently studied dynamic mean field theory. We find that the theory correctly describes the transition from diffusive phase separation at short times to hydrodynamic behaviour at long times.« less

Optimal Linear Responses for Markov Chains and Stochastically Perturbed Dynamical Systems

NASA Astrophysics Data System (ADS)

Antown, Fadi; Dragičević, Davor; Froyland, Gary

2018-03-01

The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the linear response of the equilibrium distribution of the system, (ii) maximise the linear response of the expectation of a specified observable, and (iii) maximise the linear response of the rate of convergence of the system to the equilibrium distribution. We also consider the inhomogeneous, sequential, or time-dependent situation where the governing dynamics is not stationary and one wishes to select a sequence of small perturbations so as to maximise the overall linear response at some terminal time. We develop the theory for finite-state Markov chains, provide explicit solutions for some illustrative examples, and numerically apply our theory to stochastically perturbed dynamical systems, where the Markov chain is replaced by a matrix representation of an approximate annealed transfer operator for the random dynamical system.

Complexity Leadership: A Theoretical Perspective

ERIC Educational Resources Information Center

Baltaci, Ali; Balci, Ali

2017-01-01

Complex systems are social networks composed of interactive employees interconnected through collaborative, dynamic ties such as shared goals, perspectives and needs. Complex systems are largely based on "the complex system theory". The complex system theory focuses mainly on finding out and developing strategies and behaviours that…

MaxEnt-Based Ecological Theory: A Template for Integrated Catchment Theory

NASA Astrophysics Data System (ADS)

Harte, J.

2017-12-01

The maximum information entropy procedure (MaxEnt) is both a powerful tool for inferring least-biased probability distributions from limited data and a framework for the construction of complex systems theory. The maximum entropy theory of ecology (METE) describes remarkably well widely observed patterns in the distribution, abundance and energetics of individuals and taxa in relatively static ecosystems. An extension to ecosystems undergoing change in response to disturbance or natural succession (DynaMETE) is in progress. I describe the structure of both the static and the dynamic theory and show a range of comparisons with census data. I then propose a generalization of the MaxEnt approach that could provide a framework for a predictive theory of both static and dynamic, fully-coupled, eco-socio-hydrological catchment systems.

Linkages between Families and Political Extremism: A Theory of the Authoritarian Personality and Family System Dynamics.

ERIC Educational Resources Information Center

Gaziano, Cecilie

This paper seeks to integrate some ideas from family systems theory and attachment theory within a theory of public opinion and social movement. Citing the classic "The Authoritarian Personality," the paper states that the first authorities children know, their parents or other caregivers, shape children's attitudes toward all…

Moving to higher ground: The dynamic field theory and the dynamics of visual cognition

PubMed Central

Johnson, Jeffrey S.; Spencer, John P.; Schöner, Gregor

2009-01-01

In the present report, we describe a new dynamic field theory that captures the dynamics of visuo-spatial cognition. This theory grew out of the dynamic systems approach to motor control and development, and is grounded in neural principles. The initial application of dynamic field theory to issues in visuo-spatial cognition extended concepts of the motor approach to decision making in a sensori-motor context, and, more recently, to the dynamics of spatial cognition. Here we extend these concepts still further to address topics in visual cognition, including visual working memory for non-spatial object properties, the processes that underlie change detection, and the ‘binding problem’ in vision. In each case, we demonstrate that the general principles of the dynamic field approach can unify findings in the literature and generate novel predictions. We contend that the application of these concepts to visual cognition avoids the pitfalls of reductionist approaches in cognitive science, and points toward a formal integration of brains, bodies, and behavior. PMID:19173013

Intelligent data management for real-time spacecraft monitoring

NASA Technical Reports Server (NTRS)

Schwuttke, Ursula M.; Gasser, Les; Abramson, Bruce

1992-01-01

Real-time AI systems have begun to address the challenge of restructuring problem solving to meet real-time constraints by making key trade-offs that pursue less than optimal strategies with minimal impact on system goals. Several approaches for adapting to dynamic changes in system operating conditions are known. However, simultaneously adapting system decision criteria in a principled way has been difficult. Towards this end, a general technique for dynamically making such trade-offs using a combination of decision theory and domain knowledge has been developed. Multi-attribute utility theory (MAUT), a decision theoretic approach for making one-time decisions is discussed and dynamic trade-off evaluation is described as a knowledge-based extension of MAUT that is suitable for highly dynamic real-time environments, and provides an example of dynamic trade-off evaluation applied to a specific data management trade-off in a real-world spacecraft monitoring application.

Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems

NASA Astrophysics Data System (ADS)

Kuwahara, Tomotaka; Mori, Takashi; Saito, Keiji

2016-04-01

This work explores a fundamental dynamical structure for a wide range of many-body quantum systems under periodic driving. Generically, in the thermodynamic limit, such systems are known to heat up to infinite temperature states in the long-time limit irrespective of dynamical details, which kills all the specific properties of the system. In the present study, instead of considering infinitely long-time scale, we aim to provide a general framework to understand the long but finite time behavior, namely the transient dynamics. In our analysis, we focus on the Floquet-Magnus (FM) expansion that gives a formal expression of the effective Hamiltonian on the system. Although in general the full series expansion is not convergent in the thermodynamics limit, we give a clear relationship between the FM expansion and the transient dynamics. More precisely, we rigorously show that a truncated version of the FM expansion accurately describes the exact dynamics for a certain time-scale. Our theory reveals an experimental time-scale for which non-trivial dynamical phenomena can be reliably observed. We discuss several dynamical phenomena, such as the effect of small integrability breaking, efficient numerical simulation of periodically driven systems, dynamical localization and thermalization. Especially on thermalization, we discuss a generic scenario on the prethermalization phenomenon in periodically driven systems.

Multilevel Dynamic Systems Affecting Introduction of HIV/STI Prevention Innovations among Chinese Women in Sex Work Establishments

ERIC Educational Resources Information Center

Weeks, Margaret R.; Li, Jianghong; Liao, Susu; Zhang, Qingning; Dunn, Jennifer; Wang, Yanhong; Jiang, Jingmei

2013-01-01

Social and public health scientists are increasingly interested in applying system dynamics theory to improve understanding and to harness the forces of change within complex, multilevel systems that affect community intervention implementation, effects, and sustainability. Building a system dynamics model based on ethnographic case study has the…

Vlasov dynamics of periodically driven systems

NASA Astrophysics Data System (ADS)

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.

Systems and complexity thinking in the general practice literature: an integrative, historical narrative review.

PubMed

Sturmberg, Joachim P; Martin, Carmel M; Katerndahl, David A

2014-01-01

Over the past 7 decades, theories in the systems and complexity sciences have had a major influence on academic thinking and research. We assessed the impact of complexity science on general practice/family medicine. We performed a historical integrative review using the following systematic search strategy: medical subject heading [humans] combined in turn with the terms complex adaptive systems, nonlinear dynamics, systems biology, and systems theory, limited to general practice/family medicine and published before December 2010. A total of 16,242 articles were retrieved, of which 49 were published in general practice/family medicine journals. Hand searches and snowballing retrieved another 35. After a full-text review, we included 56 articles dealing specifically with systems sciences and general/family practice. General practice/family medicine engaged with the emerging systems and complexity theories in 4 stages. Before 1995, articles tended to explore common phenomenologic general practice/family medicine experiences. Between 1995 and 2000, articles described the complex adaptive nature of this discipline. Those published between 2000 and 2005 focused on describing the system dynamics of medical practice. After 2005, articles increasingly applied the breadth of complex science theories to health care, health care reform, and the future of medicine. This historical review describes the development of general practice/family medicine in relation to complex adaptive systems theories, and shows how systems sciences more accurately reflect the discipline's philosophy and identity. Analysis suggests that general practice/family medicine first embraced systems theories through conscious reorganization of its boundaries and scope, before applying empirical tools. Future research should concentrate on applying nonlinear dynamics and empirical modeling to patient care, and to organizing and developing local practices, engaging in community development, and influencing health care reform.

Systems and Complexity Thinking in the General Practice Literature: An Integrative, Historical Narrative Review

PubMed Central

Sturmberg, Joachim P.; Martin, Carmel M.; Katerndahl, David A.

2014-01-01

PURPOSE Over the past 7 decades, theories in the systems and complexity sciences have had a major influence on academic thinking and research. We assessed the impact of complexity science on general practice/family medicine. METHODS We performed a historical integrative review using the following systematic search strategy: medical subject heading [humans] combined in turn with the terms complex adaptive systems, nonlinear dynamics, systems biology, and systems theory, limited to general practice/family medicine and published before December 2010. A total of 16,242 articles were retrieved, of which 49 were published in general practice/family medicine journals. Hand searches and snowballing retrieved another 35. After a full-text review, we included 56 articles dealing specifically with systems sciences and general/family practice. RESULTS General practice/family medicine engaged with the emerging systems and complexity theories in 4 stages. Before 1995, articles tended to explore common phenomenologic general practice/family medicine experiences. Between 1995 and 2000, articles described the complex adaptive nature of this discipline. Those published between 2000 and 2005 focused on describing the system dynamics of medical practice. After 2005, articles increasingly applied the breadth of complex science theories to health care, health care reform, and the future of medicine. CONCLUSIONS This historical review describes the development of general practice/family medicine in relation to complex adaptive systems theories, and shows how systems sciences more accurately reflect the discipline’s philosophy and identity. Analysis suggests that general practice/family medicine first embraced systems theories through conscious reorganization of its boundaries and scope, before applying empirical tools. Future research should concentrate on applying nonlinear dynamics and empirical modeling to patient care, and to organizing and developing local practices, engaging in community development, and influencing health care reform. PMID:24445105

Space and time in the quantum universe.

NASA Astrophysics Data System (ADS)

Smolin, L.

This paper is devoted to the problem of constructing a quantum theory that could describe a closed system - a quantum cosmology. The author argues that this problem is an aspect of a much older problem - that of how to eliminate from the physical theories "ideal elements", which are elements of the mathematical structure whose interpretation requires the existence of things outside the dynamical system described by the theory. This discussion is aimed at uncovering criteria that a theory of quantum cosmology must satisfy, if it is to give physically sensible predictions. The author proposes three such criteria and shows that conventional quantum cosmology can only satisfy them, if there is an intrinsic time coordinate on the phase space of the theory. It is shown that approaches based on correlations in the wave function, that do not use an inner product, cannot satisfy these criteria. As example, the author discusses the problem of quantizing a class of relational dynamical models invented by Barbour and Bertotti. The dynamical structure of these theories is closely analogous to general relativity, and the problem of their measurement theory is also similar. It is concluded that these theories can only be sensibly quantized if they contain an intrinsic time.

Detection and control of combustion instability based on the concept of dynamical system theory.

PubMed

Gotoda, Hiroshi; Shinoda, Yuta; Kobayashi, Masaki; Okuno, Yuta; Tachibana, Shigeru

2014-02-01

We propose an online method of detecting combustion instability based on the concept of dynamical system theory, including the characterization of the dynamic behavior of combustion instability. As an important case study relevant to combustion instability encountered in fundamental and practical combustion systems, we deal with the combustion dynamics close to lean blowout (LBO) in a premixed gas-turbine model combustor. The relatively regular pressure fluctuations generated by thermoacoustic oscillations transit to low-dimensional intermittent chaos owing to the intermittent appearance of burst with decreasing equivalence ratio. The translation error, which is characterized by quantifying the degree of parallelism of trajectories in the phase space, can be used as a control variable to prevent LBO.

Detection and control of combustion instability based on the concept of dynamical system theory

NASA Astrophysics Data System (ADS)

Gotoda, Hiroshi; Shinoda, Yuta; Kobayashi, Masaki; Okuno, Yuta; Tachibana, Shigeru

2014-02-01

We propose an online method of detecting combustion instability based on the concept of dynamical system theory, including the characterization of the dynamic behavior of combustion instability. As an important case study relevant to combustion instability encountered in fundamental and practical combustion systems, we deal with the combustion dynamics close to lean blowout (LBO) in a premixed gas-turbine model combustor. The relatively regular pressure fluctuations generated by thermoacoustic oscillations transit to low-dimensional intermittent chaos owing to the intermittent appearance of burst with decreasing equivalence ratio. The translation error, which is characterized by quantifying the degree of parallelism of trajectories in the phase space, can be used as a control variable to prevent LBO.

Treating Sibling Incest Using a Family Systems Approach.

ERIC Educational Resources Information Center

Haskins, Cora

2003-01-01

Discusses family systems theory as a framework for understanding the common family dynamics observed in families where there is sibling abuse. Presents a case example using family systems theory as a framework for conceptualizing and developing treatment. (Contains 45 references.) (GCP)

The emergence of learning-teaching trajectories in education: a complex dynamic systems approach.

PubMed

Steenbeek, Henderien; van Geert, Paul

2013-04-01

In this article we shall focus on learning-teaching trajectories ='successful' as well as 'unsuccessful' ones - as emergent and dynamic phenomena resulting from the interactions in the entire educational context, in particular the interaction between students and teachers viewed as processes of intertwining self-, other- and co-regulation. The article provides a review of the educational research literature on action regulation in learning and teaching, and interprets this literature in light of the theory of complex dynamic systems. Based on this reinterpretation of the literature, two dynamic models are proposed, one focusing on the short-term dynamics of learning-teaching interactions as they take place in classrooms, the other focusing on the long-term dynamics of interactions in a network of variables encompassing concerns, evaluations, actions and action effects (such as learning) students and teachers. The aim of presenting these models is to demonstrate, first, the possibility of transforming existing educational theory into dynamic models and, second, to provide some suggestions as to how such models can be used to further educational theory and practice.

Dynamical Systems and Jung, with a Note on Language

ERIC Educational Resources Information Center

Barrett, Bruce E.

2011-01-01

Comments on the original article "Rethinking intractable conflict: The perspective of dynamical systems," by R. R. Vallacher, P. T. Coleman, A. Nowak, and L. Bui-Wrzosinska. Vallacher et al presented an intriguing description of dynamical systems theory as applied to the understanding of intractable conflicts ranging from the intrapsychic to the…

Frontiers in Applied and Computational Mathematics 05’

DTIC Science & Technology

2005-03-01

dynamics, forcing subsets to have the same oscillation numbers and interleaving spiking times . Our analysis follows the theory of coupled systems of...continuum is described by a continuous- time stochastic process, as are their internal dynamics. Soluble factors, such as cytokines, are represent- ed...scale of a partide pas- sage time through the reaction zone. Both are realistic for many systems of physical interest. A higher order theory includes

Molecular Dynamics Simulation Studies of Fracture in Two Dimensions

DTIC Science & Technology

1980-05-01

reversibility of trajectories. The microscopic elastic constants, dispersion relation and phonon spectrum of the system were determined by lattice dynamics. These... linear elasticity theory of a two-dimensional crack embedded in an infinite medium. System con- sists of 436 particles arranged in a tri- angular lattice ...satisfying these demands. In evaluating the mechanical energy of his model, Griffith used a result from linear elasticity theory, namely that for any body

Potential and flux field landscape theory. I. Global stability and dynamics of spatially dependent non-equilibrium systems.

PubMed

Wu, Wei; Wang, Jin

2013-09-28

We established a potential and flux field landscape theory to quantify the global stability and dynamics of general spatially dependent non-equilibrium deterministic and stochastic systems. We extended our potential and flux landscape theory for spatially independent non-equilibrium stochastic systems described by Fokker-Planck equations to spatially dependent stochastic systems governed by general functional Fokker-Planck equations as well as functional Kramers-Moyal equations derived from master equations. Our general theory is applied to reaction-diffusion systems. For equilibrium spatially dependent systems with detailed balance, the potential field landscape alone, defined in terms of the steady state probability distribution functional, determines the global stability and dynamics of the system. The global stability of the system is closely related to the topography of the potential field landscape in terms of the basins of attraction and barrier heights in the field configuration state space. The effective driving force of the system is generated by the functional gradient of the potential field alone. For non-equilibrium spatially dependent systems, the curl probability flux field is indispensable in breaking detailed balance and creating non-equilibrium condition for the system. A complete characterization of the non-equilibrium dynamics of the spatially dependent system requires both the potential field and the curl probability flux field. While the non-equilibrium potential field landscape attracts the system down along the functional gradient similar to an electron moving in an electric field, the non-equilibrium flux field drives the system in a curly way similar to an electron moving in a magnetic field. In the small fluctuation limit, the intrinsic potential field as the small fluctuation limit of the potential field for spatially dependent non-equilibrium systems, which is closely related to the steady state probability distribution functional, is found to be a Lyapunov functional of the deterministic spatially dependent system. Therefore, the intrinsic potential landscape can characterize the global stability of the deterministic system. The relative entropy functional of the stochastic spatially dependent non-equilibrium system is found to be the Lyapunov functional of the stochastic dynamics of the system. Therefore, the relative entropy functional quantifies the global stability of the stochastic system with finite fluctuations. Our theory offers an alternative general approach to other field-theoretic techniques, to study the global stability and dynamics of spatially dependent non-equilibrium field systems. It can be applied to many physical, chemical, and biological spatially dependent non-equilibrium systems.

Toward Control of Universal Scaling in Critical Dynamics

DTIC Science & Technology

2016-01-27

program that aims to synergistically combine two powerful and very successful theories for non-linear stochastic dynamics of cooperative multi...RESPONSIBLE PERSON 19b. TELEPHONE NUMBER Uwe Tauber Uwe C. T? uber , Michel Pleimling, Daniel J. Stilwell 611102 c. THIS PAGE The public reporting burden...to synergistically combine two powerful and very successful theories for non-linear stochastic dynamics of cooperative multi-component systems, namely

Free-time and fixed end-point optimal control theory in dissipative media: application to entanglement generation and maintenance.

PubMed

Mishima, K; Yamashita, K

2009-07-07

We develop monotonically convergent free-time and fixed end-point optimal control theory (OCT) in the density-matrix representation to deal with quantum systems showing dissipation. Our theory is more general and flexible for tailoring optimal laser pulses in order to control quantum dynamics with dissipation than the conventional fixed-time and fixed end-point OCT in that the optimal temporal duration of laser pulses can also be optimized exactly. To show the usefulness of our theory, it is applied to the generation and maintenance of the vibrational entanglement of carbon monoxide adsorbed on the copper (100) surface, CO/Cu(100). We demonstrate the numerical results and clarify how to combat vibrational decoherence as much as possible by the tailored shapes of the optimal laser pulses. It is expected that our theory will be general enough to be applied to a variety of dissipative quantum dynamics systems because the decoherence is one of the quantum phenomena sensitive to the temporal duration of the quantum dynamics.

Boundary Dynamics: Implications for Building Parent-School Partnerships

ERIC Educational Resources Information Center

Price-Mitchell, Marilyn

2009-01-01

This article draws on systems theory, complexity theory, and the organizational sciences to engage boundary dynamics in the creation of parent-school partnerships. These partnerships help children succeed through an emergent process of dialogue and relationship building in the peripheral spaces where parents and schools interact on behalf of…

Chaos Theory: Implications for Nonlinear Dynamics in Counseling.

ERIC Educational Resources Information Center

Stickel, Sue A.

The purpose of this paper is to explore the implications of chaos theory for counseling. The scientific notion of chaos refers to the tendency of dynamical, nonlinear systems toward irregular, sometimes unpredictable, yet deterministic behavior. Therapists, especially those working from a brief approach, have noted the importance of the client's…

Adaptive modeling, identification, and control of dynamic structural systems. I. Theory

USGS Publications Warehouse

Safak, Erdal

1989-01-01

A concise review of the theory of adaptive modeling, identification, and control of dynamic structural systems based on discrete-time recordings is presented. Adaptive methods have four major advantages over the classical methods: (1) Removal of the noise from the signal is done over the whole frequency band; (2) time-varying characteristics of systems can be tracked; (3) systems with unknown characteristics can be controlled; and (4) a small segment of the data is needed during the computations. Included in the paper are the discrete-time representation of single-input single-output (SISO) systems, models for SISO systems with noise, the concept of stochastic approximation, recursive prediction error method (RPEM) for system identification, and the adaptive control. Guidelines for model selection and model validation and the computational aspects of the method are also discussed in the paper. The present paper is the first of two companion papers. The theory given in the paper is limited to that which is necessary to follow the examples for applications in structural dynamics presented in the second paper.

Dynamics of a New 5D Hyperchaotic System of Lorenz Type

NASA Astrophysics Data System (ADS)

Zhang, Fuchen; Chen, Rui; Wang, Xingyuan; Chen, Xiusu; Mu, Chunlai; Liao, Xiaofeng

Ultimate boundedness of chaotic dynamical systems is one of the fundamental concepts in dynamical systems, which plays an important role in investigating the stability of the equilibrium, estimating the Lyapunov dimension of attractors and the Hausdorff dimension of attractors, the existence of periodic solutions, chaos control, chaos synchronization. However, it is often difficult to obtain the bounds of the hyperchaotic systems due to the complex algebraic structure of the hyperchaotic systems. This paper has investigated the boundedness of solutions of a nonlinear hyperchaotic system. We have obtained the global exponential attractive set and the ultimate bound set for this system. To obtain the ellipsoidal ultimate bound, the ultimate bound of the proposed system is theoretically estimated using Lagrange multiplier method, Lyapunov stability theory and optimization theory. To show the ultimate bound region, numerical simulations are provided.

Application of dynamical systems theory to the high angle of attack dynamics of the F-14

NASA Technical Reports Server (NTRS)

Jahnke, Craig C.; Culick, Fred E. C.

1990-01-01

Dynamical systems theory has been used to study the nonlinear dynamics of the F-14. An eight degree of freedom model that does not include the control system present in operational F-14s has been analyzed. The aerodynamic model, supplied by NASA, includes nonlinearities as functions of the angles of attack and sideslip, the rotation rate, and the elevator deflection. A continuation method has been used to calculate the steady states of the F-14 as continuous functions of the control surface deflections. Bifurcations of these steady states have been used to predict the onset of wing rock, spiral divergence, and jump phenomena which cause the aircraft to enter a spin. A simple feedback control system was designed to eliminate the wing rock and spiral divergence instabilities. The predictions were verified with numerical simulations.

Spinor matter fields in SL(2,C) gauge theories of gravity: Lagrangian and Hamiltonian approaches

NASA Astrophysics Data System (ADS)

Antonowicz, Marek; Szczyrba, Wiktor

1985-06-01

We consider the SL(2,C)-covariant Lagrangian formulation of gravitational theories with the presence of spinor matter fields. The invariance properties of such theories give rise to the conservation laws (the contracted Bianchi identities) having in the presence of matter fields a more complicated form than those known in the literature previously. A general SL(2,C) gauge theory of gravity is cast into an SL(2,C)-covariant Hamiltonian formulation. Breaking the SL(2,C) symmetry of the system to the SU(2) symmetry, by introducing a spacelike slicing of spacetime, we get an SU(2)-covariant Hamiltonian picture. The qualitative analysis of SL(2,C) gauge theories of gravity in the SU(2)-covariant formulation enables us to define the dynamical symplectic variables and the gauge variables of the theory under consideration as well as to divide the set of field equations into the dynamical equations and the constraints. In the SU(2)-covariant Hamiltonian formulation the primary constraints, which are generic for first-order matter Lagrangians (Dirac, Weyl, Fierz-Pauli), can be reduced. The effective matter symplectic variables are given by SU(2)-spinor-valued half-forms on three-dimensional slices of spacetime. The coupled Einstein-Cartan-Dirac (Weyl, Fierz-Pauli) system is analyzed from the (3+1) point of view. This analysis is complete; the field equations of the Einstein-Cartan-Dirac theory split into 18 gravitational dynamical equations, 8 dynamical Dirac equations, and 7 first-class constraints. The system has 4+8=12 independent degrees of freedom in the phase space.

Applied Nonlinear Dynamics and Stochastic Systems Near The Millenium. Proceedings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kadtke, J.B.; Bulsara, A.

These proceedings represent papers presented at the Applied Nonlinear Dynamics and Stochastic Systems conference held in San Diego, California in July 1997. The conference emphasized the applications of nonlinear dynamical systems theory in fields as diverse as neuroscience and biomedical engineering, fluid dynamics, chaos control, nonlinear signal/image processing, stochastic resonance, devices and nonlinear dynamics in socio{minus}economic systems. There were 56 papers presented at the conference and 5 have been abstracted for the Energy Science and Technology database.(AIP)

High-Q Photonic-Crystal Cavities for Light Amplification and Lasing

DTIC Science & Technology

2011-06-10

Neoclassical Theory of Electric Charges", to appear in Discrete and Continuous Dynamical Systems, Vol. 27, Number 4, August 2010. - A. Figotin, I...dynamics of PDE", ICMS, Edinburgh, September, 2010 - A. Figotn and A. Babin, "Some Mathematical Problems in a Neoclassical Theory of Electric Charges...34, Weizmann Institute, Rehovot, Israel, August, 2010. - A. Figotn and A. Babin, "Some Mathematical Problems in a Neoclassical Theory of Electric

Guidance of Nonlinear Nonminimum-Phase Dynamic Systems

NASA Technical Reports Server (NTRS)

Devasia, Santosh

1997-01-01

The first two years research work has advanced the inversion-based guidance theory for: (1) systems with non-hyperbolic internal dynamics; (2) systems with parameter jumps; (3) systems where a redesign of the output trajectory is desired; and (4) the generation of recovery guidance maneuvers.

Chaos as a psychological construct: historical roots, principal findings, and current growth directions.

PubMed

Guastello, Stephen J

2009-07-01

The landmarks in the use of chaos and related constructs in psychology were entwined with the growing use of other nonlinear dynamical constructs, especially catastrophes and self-organization. The growth in substantive applications of chaos in psychology is partially related to the development of methodologies that work within the constraints of psychological data. The psychological literature includes rigorous theory with testable propositions, lighter-weight metaphorical uses of the construct, and colloquial uses of "chaos" with no particular theoretical intent. The current state of the chaos construct and supporting empirical research in psychological theory is summarized in neuroscience, psychophysics, psychomotor skill and other learning phenomena, clinical and abnormal psychology, and group dynamics and organizational behavior. Trends indicate that human systems do not remain chaotic indefinitely; they eventually self-organize, and the concept of the complex adaptive system has become prominent. Chaotic turbulence is generally higher in healthy systems compared to unhealthy systems, although opposite appears true in mood disorders. Group dynamics research shows trends consistent with the complex adaptive system, whereas organizational behavior lags behind in empirical studies relative to the quantity of its theory. Future directions for research involving the chaos construct and other nonlinear dynamics are outlined.

Oscillators and relaxation phenomena in Pleistocene climate theory

PubMed Central

Crucifix, Michel

2012-01-01

Ice sheets appeared in the northern hemisphere around 3 Ma (million years) ago and glacial–interglacial cycles have paced Earth's climate since then. Superimposed on these long glacial cycles comes an intricate pattern of millennial and sub-millennial variability, including Dansgaard–Oeschger and Heinrich events. There are numerous theories about these oscillations. Here, we review a number of them in order to draw a parallel between climatic concepts and dynamical system concepts, including, in particular, the relaxation oscillator, excitability, slow–fast dynamics and homoclinic orbits. Namely, almost all theories of ice ages reviewed here feature a phenomenon of synchronization between internal climate dynamics and astronomical forcing. However, these theories differ in their bifurcation structure and this has an effect on the way the ice age phenomenon could grow 3 Ma ago. All theories on rapid events reviewed here rely on the concept of a limit cycle excited by changes in the surface freshwater balance of the ocean. The article also reviews basic effects of stochastic fluctuations on these models, including the phenomenon of phase dispersion, shortening of the limit cycle and stochastic resonance. It concludes with a more personal statement about the potential for inference with simple stochastic dynamical systems in palaeoclimate science. PMID:22291227

Market Orientation within University Schools of Business: Can a Dynamical Systems Viewpoint Applied to a Non-Temporal Data Set Yield Valuable Insights for University Managers?

ERIC Educational Resources Information Center

Cox, John C.; Webster, Robert L.; Hammond, Kevin L.

2009-01-01

This study investigates the use of using complexity theory--the study of nonlinear dynamical systems of which chaos and catastrophe theory are subsets--in the analysis of a non temporal data set to derive valuable insights into the functioning of university schools of business. The approach is unusual in that studies of nonlinearity in complex…

Where neuroscience and dynamic system theory meet autonomous robotics: a contracting basal ganglia model for action selection.

PubMed

Girard, B; Tabareau, N; Pham, Q C; Berthoz, A; Slotine, J-J

2008-05-01

Action selection, the problem of choosing what to do next, is central to any autonomous agent architecture. We use here a multi-disciplinary approach at the convergence of neuroscience, dynamical system theory and autonomous robotics, in order to propose an efficient action selection mechanism based on a new model of the basal ganglia. We first describe new developments of contraction theory regarding locally projected dynamical systems. We exploit these results to design a stable computational model of the cortico-baso-thalamo-cortical loops. Based on recent anatomical data, we include usually neglected neural projections, which participate in performing accurate selection. Finally, the efficiency of this model as an autonomous robot action selection mechanism is assessed in a standard survival task. The model exhibits valuable dithering avoidance and energy-saving properties, when compared with a simple if-then-else decision rule.

Patterns of gender development.

PubMed

Martin, Carol Lynn; Ruble, Diane N

2010-01-01

A comprehensive theory of gender development must describe and explain long-term developmental patterning and changes and how gender is experienced in the short term. This review considers multiple views on gender patterning, illustrated with contemporary research. First, because developmental research involves understanding normative patterns of change with age, several theoretically important topics illustrate gender development: how children come to recognize gender distinctions and understand stereotypes, and the emergence of prejudice and sexism. Second, developmental researchers study the stability of individual differences over time, which elucidates developmental processes. We review stability in two domains-sex segregation and activities/interests. Finally, a new approach advances understanding of developmental patterns, based on dynamic systems theory. Dynamic systems theory is a metatheoretical framework for studying stability and change, which developed from the study of complex and nonlinear systems in physics and mathematics. Some major features and examples show how dynamic approaches have been and could be applied in studying gender development.

Patterns of Gender Development

PubMed Central

Martin, Carol Lynn; Ruble, Diane N.

2013-01-01

A comprehensive theory of gender development must describe and explain long-term developmental patterning and changes and how gender is experienced in the short term. This review considers multiple views on gender patterning, illustrated with contemporary research. First, because developmental research involves understanding normative patterns of change with age, several theoretically important topics illustrate gender development: how children come to recognize gender distinctions and understand stereotypes, and the emergence of prejudice and sexism. Second, developmental researchers study the stability of individual differences over time, which elucidates developmental processes. We review stability in two domains—sex segregation and activities/interests. Finally, a new approach advances understanding of developmental patterns, based on dynamic systems theory. Dynamic systems theory is a metatheoretical framework for studying stability and change, which developed from the study of complex and nonlinear systems in physics and mathematics. Some major features and examples show how dynamic approaches have been and could be applied in studying gender development. PMID:19575615

Response Functions for the Two-Dimensional Ultracold Fermi Gas: Dynamical BCS Theory and Beyond

NASA Astrophysics Data System (ADS)

Vitali, Ettore; Shi, Hao; Qin, Mingpu; Zhang, Shiwei

2017-12-01

Response functions are central objects in physics. They provide crucial information about the behavior of physical systems, and they can be directly compared with scattering experiments involving particles such as neutrons or photons. Calculations of such functions starting from the many-body Hamiltonian of a physical system are challenging and extremely valuable. In this paper, we focus on the two-dimensional (2D) ultracold Fermi atomic gas which has been realized experimentally. We present an application of the dynamical BCS theory to obtain response functions for different regimes of interaction strengths in the 2D gas with zero-range attractive interaction. We also discuss auxiliary-field quantum Monte Carlo (AFQMC) methods for the calculation of imaginary time correlations in these dilute Fermi gas systems. Illustrative results are given and comparisons are made between AFQMC and dynamical BCS theory results to assess the accuracy of the latter.

From phase transitions to the topological renaissance. Comment on "Topodynamics of metastable brains" by Arturo Tozzi et al.

NASA Astrophysics Data System (ADS)

Somogyvári, Zoltán; Érdi, Péter

2017-07-01

The neural topodynamics theory of Tozzi et al. [13] has two main foci: metastable brain dynamics and the topological approach based on the Borsuk-Ulam theorem (BUT). Briefly, metastable brain dynamics theory hypothesizes that temporary stable synchronization and desynchronization of large number of individual dynamical systems, formed by local neural circuits, are responsible for coding of complex concepts in the brain and sudden changes of these synchronization patterns correspond to operational steps. But what dynamical network could form the substrate for this metastable dynamics, capable of entering into a combinatorially high number of metastable synchronization patterns and exhibit rapid transient changes between them? The general problem is related to the discrimination between ;Black Swans; and ;Dragon Kings;. While BSs are related to the theory of self-organized criticality, and suggests that high-impact extreme events are unpredictable, Dragon-kings are associated with the occurrence of a phase transition, whose emergent organization is based on intermittent criticality [9]. Widening the limits of predictability is one of the big open problems in the theory and practice of complex systems (Sect. 9.3 of Érdi [2]).

Algorithm for Overcoming the Curse of Dimensionality for Certain Non-convex Hamilton-Jacobi Equations, Projections and Differential Games

DTIC Science & Technology

2016-05-01

Algorithm for Overcoming the Curse of Dimensionality for Certain Non-convex Hamilton-Jacobi Equations, Projections and Differential Games Yat Tin...subproblems. Our approach is expected to have wide applications in continuous dynamic games , control theory problems, and elsewhere. Mathematics...differential dynamic games , control theory problems, and dynamical systems coming from the physical world, e.g. [11]. An important application is to

Dynamic phase transitions and dynamic phase diagrams of the Blume-Emery-Griffiths model in an oscillating field: the effective-field theory based on the Glauber-type stochastic dynamics

NASA Astrophysics Data System (ADS)

Ertaş, Mehmet; Keskin, Mustafa

2015-06-01

Using the effective-field theory based on the Glauber-type stochastic dynamics (DEFT), we investigate dynamic phase transitions and dynamic phase diagrams of the Blume-Emery-Griffiths model under an oscillating magnetic field. We presented the dynamic phase diagrams in (T/J, h0/J), (D/J, T/J) and (K/J, T/J) planes, where T, h0, D, K and z are the temperature, magnetic field amplitude, crystal-field interaction, biquadratic interaction and the coordination number. The dynamic phase diagrams exhibit several ordered phases, coexistence phase regions and special critical points, as well as re-entrant behavior depending on interaction parameters. We also compare and discuss the results with the results of the same system within the mean-field theory based on the Glauber-type stochastic dynamics and find that some of the dynamic first-order phase lines and special dynamic critical points disappeared in the DEFT calculation.

Dynamical systems, attractors, and neural circuits.

PubMed

Miller, Paul

2016-01-01

Biology is the study of dynamical systems. Yet most of us working in biology have limited pedagogical training in the theory of dynamical systems, an unfortunate historical fact that can be remedied for future generations of life scientists. In my particular field of systems neuroscience, neural circuits are rife with nonlinearities at all levels of description, rendering simple methodologies and our own intuition unreliable. Therefore, our ideas are likely to be wrong unless informed by good models. These models should be based on the mathematical theories of dynamical systems since functioning neurons are dynamic-they change their membrane potential and firing rates with time. Thus, selecting the appropriate type of dynamical system upon which to base a model is an important first step in the modeling process. This step all too easily goes awry, in part because there are many frameworks to choose from, in part because the sparsely sampled data can be consistent with a variety of dynamical processes, and in part because each modeler has a preferred modeling approach that is difficult to move away from. This brief review summarizes some of the main dynamical paradigms that can arise in neural circuits, with comments on what they can achieve computationally and what signatures might reveal their presence within empirical data. I provide examples of different dynamical systems using simple circuits of two or three cells, emphasizing that any one connectivity pattern is compatible with multiple, diverse functions.

Nonequilibrium magnetic properties in a two-dimensional kinetic mixed Ising system within the effective-field theory and Glauber-type stochastic dynamics approach.

PubMed

Ertaş, Mehmet; Deviren, Bayram; Keskin, Mustafa

2012-11-01

Nonequilibrium magnetic properties in a two-dimensional kinetic mixed spin-2 and spin-5/2 Ising system in the presence of a time-varying (sinusoidal) magnetic field are studied within the effective-field theory (EFT) with correlations. The time evolution of the system is described by using Glauber-type stochastic dynamics. The dynamic EFT equations are derived by employing the Glauber transition rates for two interpenetrating square lattices. We investigate the time dependence of the magnetizations for different interaction parameter values in order to find the phases in the system. We also study the thermal behavior of the dynamic magnetizations, the hysteresis loop area, and dynamic correlation. The dynamic phase diagrams are presented in the reduced magnetic field amplitude and reduced temperature plane and we observe that the system exhibits dynamic tricritical and reentrant behaviors. Moreover, the system also displays a double critical end point (B), a zero-temperature critical point (Z), a critical end point (E), and a triple point (TP). We also performed a comparison with the mean-field prediction in order to point out the effects of correlations and found that some of the dynamic first-order phase lines, which are artifacts of the mean-field approach, disappeared.

Consequences of nonclassical measurement for the algorithmic description of continuous dynamical systems

NASA Technical Reports Server (NTRS)

Fields, Chris

1989-01-01

Continuous dynamical systems intuitively seem capable of more complex behavior than discrete systems. If analyzed in the framework of the traditional theory of computation, a continuous dynamical system with countably many quasistable states has at least the computational power of a universal Turing machine. Such an analysis assumes, however, the classical notion of measurement. If measurement is viewed nonclassically, a continuous dynamical system cannot, even in principle, exhibit behavior that cannot be simulated by a universal Turing machine.

Consequences of nonclassical measurement for the algorithmic description of continuous dynamical systems

NASA Technical Reports Server (NTRS)

Fields, Chris

1989-01-01

Continuous dynamical systems intuitively seem capable of more complex behavior than discrete systems. If analyzed in the framework of the traditional theory of computation, a continuous dynamical system with countablely many quasistable states has at least the computational power of a universal Turing machine. Such an analyses assumes, however, the classical notion of measurement. If measurement is viewed nonclassically, a continuous dynamical system cannot, even in principle, exhibit behavior that cannot be simulated by a universal Turing machine.

Density-functional theory simulation of large quantum dots

NASA Astrophysics Data System (ADS)

Jiang, Hong; Baranger, Harold U.; Yang, Weitao

2003-10-01

Kohn-Sham spin-density functional theory provides an efficient and accurate model to study electron-electron interaction effects in quantum dots, but its application to large systems is a challenge. Here an efficient method for the simulation of quantum dots using density-function theory is developed; it includes the particle-in-the-box representation of the Kohn-Sham orbitals, an efficient conjugate-gradient method to directly minimize the total energy, a Fourier convolution approach for the calculation of the Hartree potential, and a simplified multigrid technique to accelerate the convergence. We test the methodology in a two-dimensional model system and show that numerical studies of large quantum dots with several hundred electrons become computationally affordable. In the noninteracting limit, the classical dynamics of the system we study can be continuously varied from integrable to fully chaotic. The qualitative difference in the noninteracting classical dynamics has an effect on the quantum properties of the interacting system: integrable classical dynamics leads to higher-spin states and a broader distribution of spacing between Coulomb blockade peaks.

Non-equilibrium magnetic interactions in strongly correlated systems

NASA Astrophysics Data System (ADS)

Secchi, A.; Brener, S.; Lichtenstein, A. I.; Katsnelson, M. I.

2013-06-01

We formulate a low-energy theory for the magnetic interactions between electrons in the multi-band Hubbard model under non-equilibrium conditions determined by an external time-dependent electric field which simulates laser-induced spin dynamics. We derive expressions for dynamical exchange parameters in terms of non-equilibrium electronic Green functions and self-energies, which can be computed, e.g., with the methods of time-dependent dynamical mean-field theory. Moreover, we find that a correct description of the system requires, in addition to exchange, a new kind of magnetic interaction, that we name twist exchange, which formally resembles Dzyaloshinskii-Moriya coupling, but is not due to spin-orbit, and is actually due to an effective three-spin interaction. Our theory allows the evaluation of the related time-dependent parameters as well.

Modelling and Simulation of the Dynamics of the Antigen-Specific T Cell Response Using Variable Structure Control Theory.

PubMed

Anelone, Anet J N; Spurgeon, Sarah K

2016-01-01

Experimental and mathematical studies in immunology have revealed that the dynamics of the programmed T cell response to vigorous infection can be conveniently modelled using a sigmoidal or a discontinuous immune response function. This paper hypothesizes strong synergies between this existing work and the dynamical behaviour of engineering systems with a variable structure control (VSC) law. These findings motivate the interpretation of the immune system as a variable structure control system. It is shown that dynamical properties as well as conditions to analytically assess the transition from health to disease can be developed for the specific T cell response from the theory of variable structure control. In particular, it is shown that the robustness properties of the specific T cell response as observed in experiments can be explained analytically using a VSC perspective. Further, the predictive capacity of the VSC framework to determine the T cell help required to overcome chronic Lymphocytic Choriomeningitis Virus (LCMV) infection is demonstrated. The findings demonstrate that studying the immune system using variable structure control theory provides a new framework for evaluating immunological dynamics and experimental observations. A modelling and simulation tool results with predictive capacity to determine how to modify the immune response to achieve healthy outcomes which may have application in drug development and vaccine design.

Dynamics with a Nonstandard Inertia-Acceleration Relation: An Alternative to Dark Matter in Galactic Systems

NASA Astrophysics Data System (ADS)

Milgrom, M.

1994-02-01

We investigate particle dynamics that is governed by a nonstandard kinetic action of a special form. We are guided by a phenomenological scheme-the modified dynamics (MOND)-that imputes the mass discrepancy, observed in galactic systems, not to the presence of dark matter, but to a departure from Newtonian dynamics below a certain scale of accelerations, a0. The particle's equation of motion in a potential φ is derived from an action, S, of the form S ~ Sk[r(t), a0] - ∫ φ dt. The limit a0 --> 0 corresponds to Newtonian dynamics, and there the kinetic action Sk must take the standard form. In the opposite limit, a0 --> ∞ we require Sk --> 0-and more specifically, for circular orbits Sk ~ a-10-in order to attain the phenomenological success of MOND. Galilei-invariant such theories must be strongly nonlocal. This is a blessing, as such theories need not suffer from the illnesses that are endemic to higher-derivative theories. We comment on the possibility that such a modified law of motion is an effective theory resulting from the elimination of degrees of freedom pertaining to the universe at large (the near equality a0 ≍ cH0 being a trace of that connection). We derive a general virial relation for bounded trajectories. Exact solutions are obtained for circular orbits, which pertain to rotation curves of disk galaxies. We also explore, in passing, theories that depart from the conventional Newtonian dynamics for very low frequencies.

Quantum dynamics of hydrogen atoms on graphene. I. System-bath modeling.

PubMed

Bonfanti, Matteo; Jackson, Bret; Hughes, Keith H; Burghardt, Irene; Martinazzo, Rocco

2015-09-28

An accurate system-bath model to investigate the quantum dynamics of hydrogen atoms chemisorbed on graphene is presented. The system comprises a hydrogen atom and the carbon atom from graphene that forms the covalent bond, and it is described by a previously developed 4D potential energy surface based on density functional theory ab initio data. The bath describes the rest of the carbon lattice and is obtained from an empirical force field through inversion of a classical equilibrium correlation function describing the hydrogen motion. By construction, model building easily accommodates improvements coming from the use of higher level electronic structure theory for the system. Further, it is well suited to a determination of the system-environment coupling by means of ab initio molecular dynamics. This paper details the system-bath modeling and shows its application to the quantum dynamics of vibrational relaxation of a chemisorbed hydrogen atom, which is here investigated at T = 0 K with the help of the multi-configuration time-dependent Hartree method. Paper II deals with the sticking dynamics.

Slow dynamics in glasses: A comparison between theory and experiment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Phillips, J. C.

Minimalist theories of complex systems are broadly of two kinds: mean field and axiomatic. So far, all theories of complex properties absent from simple systems and intrinsic to glasses are axiomatic. Stretched Exponential Relaxation (SER) is the prototypical complex temporal property of glasses, discovered by Kohlrausch 150 years ago, and now observed almost universally in microscopically homogeneous, complex nonequilibrium materials, including luminescent electronic Coulomb glasses. A critical comparison of alternative axiomatic theories with both numerical simulations and experiments strongly favors channeled dynamical trap models over static percolative or energy landscape models. The topics discussed cover those reported since the author'smore » review article in 1996, with an emphasis on parallels between channel bifurcation in electronic and molecular relaxation.« less

Complex double-mass dynamic model of rotor on thrust foil gas dynamic bearings

NASA Astrophysics Data System (ADS)

Sytin, A.; Babin, A.; Vasin, S.

2017-08-01

The present paper considers simulation of a rotor’s dynamics behaviour on thrust foil gas dynamic bearings based on simultaneous solution of gas dynamics differential equations, equations of theory of elasticity, motion equations and some additional equations. A double-mass dynamic system was considered during the rotor’s motion simulation which allows not only evaluation of rotor’s dynamic behaviour, but also to evaluate the influence of operational and load parameters on the dynamics of the rotor-bearing system.

Construction of Rational Maps on the Projective Line with Given Dynamical Structure

DTIC Science & Technology

2016-05-11

References 42 4 1. Introduction The is a paper in arithmetic dynamics, a relatively young field at the intersection of the older studies of number theory...computers became available. The exponentially increased computational power and access to larger data sets rocketed the field forward, allowing...theory and dy- 5 namical systems, have come together to create a new field : arithmetic dynamics. Relative to the study of mathematics as a whole

Complexity theory and physical unification: From microscopic to oscopic level

NASA Astrophysics Data System (ADS)

Pavlos, G. P.; Iliopoulos, A. C.; Karakatsanis, L. P.; Tsoutsouras, V. G.; Pavlos, E. G.

During the last two decades, low dimensional chaotic or self-organized criticality (SOC) processes have been observed by our group in many different physical systems such as space plasmas, the solar or the magnetospheric dynamics, the atmosphere, earthquakes, the brain activity as well as in informational systems. All these systems are complex systems living far from equilibrium with strong self-organization and phase transition character. The theoretical interpretation of these natural phenomena needs a deeper insight into the fundamentals of complexity theory. In this study, we try to give a synoptic description of complexity theory both at the microscopic and at the oscopic level of the physical reality. Also, we propose that the self-organization observed oscopically is a phenomenon that reveals the strong unifying character of the complex dynamics which includes thermodynamical and dynamical characteristics in all levels of the physical reality. From this point of view, oscopical deterministic and stochastic processes are closely related to the microscopical chaos and self-organization. In this study the scientific work of scientists such as Wilson, Nicolis, Prigogine, Hooft, Nottale, El Naschie, Castro, Tsallis, Chang and others is used for the development of a unified physical comprehension of complex dynamics from the microscopic to the oscopic level.

Longitudinal magnetization dynamics in Heisenberg magnets: Spin Green functions approach (Review Article)

NASA Astrophysics Data System (ADS)

Krivoruchko, V. N.

2017-11-01

In spite of the fact that dynamical properties of magnets have been extensively studied over the past years, the longitudinal magnetization dynamics is still much less understood than transverse one even in the equilibrium state of a system. In this paper, we give a review of existing, based on quantum-mechanical approach, theoretical descriptions of the longitudinal magnetization dynamics for ferro-, ferri- and antiferromagnetic dielectrics. The aim is to reveal specific features of this type of magnetization vibrations under description a system within the framework of one of the basic model theory of magnetism—the Heisenberg model. Related experimental investigations as well as open questions are also briefly discussed. We hope that understanding of the longitudinal magnetization dynamics distinctive features in the equilibrium state have to be a reference point for a theory uncovering the physical mechanisms that govern ultrafast spin dynamics after femtosecond laser pulse demagnetization when a system is far beyond an equilibrium state.

The Emergence of Land Use as a Global Force in the Earth System

NASA Astrophysics Data System (ADS)

Ellis, E. C.

2015-12-01

Human societies have emerged as a global force capable of transforming the biosphere, hydrosphere, lithosphere, atmosphere and climate. As a result, the long-term dynamics of the Earth system can no longer be understood or predicted without understanding their coupling with human societal dynamics. Here, a general causal theory is presented to explain why behaviorally modern humans, unlike any prior multicellular species, gained this unprecedented capacity to reshape the Earth system and how this societal capacity has changed from the Pleistocene to the present and future. Sociocultural niche construction theory, building on existing theories of ecosystem engineering, niche construction, the extended evolutionary synthesis, cultural evolution, ultrasociality and social change, can explain both the long-term upscaling of human societies and their unprecedented capacity to transform the Earth system. Regime shifts in human sociocultural niche construction, from the clearing of land using fire, to shifting cultivation, to intensive agriculture, to global food systems dependent on fossil fuel combustion, have enabled human societies to scale up while gaining the capacity to reshape the global patterns and processes of biogeography, ecosystems, landscapes, biomes, the biosphere, and ultimately the functioning of the Earth system. Just as Earth's geophysical climate system shapes the long-term dynamics of energy and material flow across the "spheres" of the Earth system, human societies, interacting at global scale to form "human systems", are increasingly shaping the global dynamics of energy, material, biotic and information flow across the spheres of the Earth system, including a newly emerged anthroposphere comprised of human societies and their material cultures. Human systems and the anthroposphere are strongly coupled with climate and other Earth systems and are dynamic in response to evolutionary changes in human social organization, cooperative ecosystem engineering, non-kin exchange relationships, and energy systems. It is hoped that intentional societal efforts to alter the dynamics of human systems can ultimately move Earth systems towards more beneficial and less detrimental outcomes for both human societies and nonhuman species.

Quantum theory for the dynamic structure factor in correlated two-component systems in nonequilibrium: Application to x-ray scattering.

PubMed

Vorberger, J; Chapman, D A

2018-01-01

We present a quantum theory for the dynamic structure factors in nonequilibrium, correlated, two-component systems such as plasmas or warm dense matter. The polarization function, which is needed as the input for the calculation of the structure factors, is calculated in nonequilibrium based on a perturbation expansion in the interaction strength. To make our theory applicable for x-ray scattering, a generalized Chihara decomposition for the total electron structure factor in nonequilibrium is derived. Examples are given and the influence of correlations and exchange on the structure and the x-ray-scattering spectrum are discussed for a model nonequilibrium distribution, as often encountered during laser heating of materials, as well as for two-temperature systems.

Quantum theory for the dynamic structure factor in correlated two-component systems in nonequilibrium: Application to x-ray scattering

NASA Astrophysics Data System (ADS)

Vorberger, J.; Chapman, D. A.

2018-01-01

We present a quantum theory for the dynamic structure factors in nonequilibrium, correlated, two-component systems such as plasmas or warm dense matter. The polarization function, which is needed as the input for the calculation of the structure factors, is calculated in nonequilibrium based on a perturbation expansion in the interaction strength. To make our theory applicable for x-ray scattering, a generalized Chihara decomposition for the total electron structure factor in nonequilibrium is derived. Examples are given and the influence of correlations and exchange on the structure and the x-ray-scattering spectrum are discussed for a model nonequilibrium distribution, as often encountered during laser heating of materials, as well as for two-temperature systems.

In Situ Probe Science at Saturn

NASA Technical Reports Server (NTRS)

Atkinson, D.H.; Lunine, J.I.; Simon-Miller, A. A.; Atreya, S. K.; Brinckerhoff, W.; Colaprete, A.; Coustenis, A.; Fletcher, L. N.; Guillot, T.; Lebreton, J.-P.;

Structural Stability of Mathematical Models of National Economy

NASA Astrophysics Data System (ADS)

Ashimov, Abdykappar A.; Sultanov, Bahyt T.; Borovskiy, Yuriy V.; Adilov, Zheksenbek M.; Ashimov, Askar A.

2011-12-01

In the paper we test robustness of particular dynamic systems in a compact regions of a plane and a weak structural stability of one dynamic system of high order in a compact region of its phase space. The test was carried out based on the fundamental theory of dynamical systems on a plane and based on the conditions for weak structural stability of high order dynamic systems. A numerical algorithm for testing the weak structural stability of high order dynamic systems has been proposed. Based on this algorithm we assess the weak structural stability of one computable general equilibrium model.

Ab initio molecular dynamics with nuclear quantum effects at classical cost: Ring polymer contraction for density functional theory.

PubMed

Marsalek, Ondrej; Markland, Thomas E

2016-02-07

Path integral molecular dynamics simulations, combined with an ab initio evaluation of interactions using electronic structure theory, incorporate the quantum mechanical nature of both the electrons and nuclei, which are essential to accurately describe systems containing light nuclei. However, path integral simulations have traditionally required a computational cost around two orders of magnitude greater than treating the nuclei classically, making them prohibitively costly for most applications. Here we show that the cost of path integral simulations can be dramatically reduced by extending our ring polymer contraction approach to ab initio molecular dynamics simulations. By using density functional tight binding as a reference system, we show that our ring polymer contraction scheme gives rapid and systematic convergence to the full path integral density functional theory result. We demonstrate the efficiency of this approach in ab initio simulations of liquid water and the reactive protonated and deprotonated water dimer systems. We find that the vast majority of the nuclear quantum effects are accurately captured using contraction to just the ring polymer centroid, which requires the same number of density functional theory calculations as a classical simulation. Combined with a multiple time step scheme using the same reference system, which allows the time step to be increased, this approach is as fast as a typical classical ab initio molecular dynamics simulation and 35× faster than a full path integral calculation, while still exactly including the quantum sampling of nuclei. This development thus offers a route to routinely include nuclear quantum effects in ab initio molecular dynamics simulations at negligible computational cost.

Theory and computation of non-RRKM lifetime distributions and rates in chemical systems with three or more degrees of freedom

NASA Astrophysics Data System (ADS)

Gabern, Frederic; Koon, Wang S.; Marsden, Jerrold E.; Ross, Shane D.

2005-11-01

The computation, starting from basic principles, of chemical reaction rates in realistic systems (with three or more degrees of freedom) has been a longstanding goal of the chemistry community. Our current work, which merges tube dynamics with Monte Carlo methods provides some key theoretical and computational tools for achieving this goal. We use basic tools of dynamical systems theory, merging the ideas of Koon et al. [W.S. Koon, M.W. Lo, J.E. Marsden, S.D. Ross, Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics, Chaos 10 (2000) 427-469.] and De Leon et al. [N. De Leon, M.A. Mehta, R.Q. Topper, Cylindrical manifolds in phase space as mediators of chemical reaction dynamics and kinetics. I. Theory, J. Chem. Phys. 94 (1991) 8310-8328.], particularly the use of invariant manifold tubes that mediate the reaction, into a tool for the computation of lifetime distributions and rates of chemical reactions and scattering phenomena, even in systems that exhibit non-statistical behavior. Previously, the main problem with the application of tube dynamics has been with the computation of volumes in phase spaces of high dimension. The present work provides a starting point for overcoming this hurdle with some new ideas and implements them numerically. Specifically, an algorithm that uses tube dynamics to provide the initial bounding box for a Monte Carlo volume determination is used. The combination of a fine scale method for determining the phase space structure (invariant manifold theory) with statistical methods for volume computations (Monte Carlo) is the main contribution of this paper. The methodology is applied here to a three degree of freedom model problem and may be useful for higher degree of freedom systems as well.

Neural dynamic optimization for control systems.II. Theory.

PubMed

Seong, C Y; Widrow, B

2001-01-01

The paper presents neural dynamic optimization (NDO) as a method of optimal feedback control for nonlinear multi-input-multi-output (MIMO) systems. The main feature of NDO is that it enables neural networks to approximate the optimal feedback solution whose existence dynamic programming (DP) justifies, thereby reducing the complexities of computation and storage problems of the classical methods such as DP. This paper mainly describes the theory of NDO, while the two other companion papers of this topic explain the background for the development of NDO and demonstrate the method with several applications including control of autonomous vehicles and of a robot arm, respectively.

Representing and reasoning about program in situation calculus

NASA Astrophysics Data System (ADS)

Yang, Bo; Zhang, Ming-yi; Wu, Mao-nian; Xie, Gang

2011-12-01

Situation calculus is an expressive tool for modeling dynamical system in artificial intelligence, changes in a dynamical world is represented naturally by the notions of action, situation and fluent in situation calculus. Program can be viewed as a discrete dynamical system, so it is possible to model program with situation calculus. To model program written in a smaller core programming language CL, notion of fluent is expanded for representing value of expression. Together with some functions returning concerned objects from expressions, a basic action theory of CL programming is constructed. Under such a theory, some properties of program, such as correctness and termination can be reasoned about.

A practical application of the geometrical theory on fibered manifolds to an autonomous bicycle motion in mechanical system with nonholonomic constraints

NASA Astrophysics Data System (ADS)

Haddout, Soufiane

2018-01-01

The equations of motion of a bicycle are highly nonlinear and rolling of wheels without slipping can only be expressed by nonholonomic constraint equations. A geometrical theory of general nonholonomic constrained systems on fibered manifolds and their jet prolongations, based on so-called Chetaev-type constraint forces, was proposed and developed in the last decade by O. Krupková (Rossi) in 1990's. Her approach is suitable for study of all kinds of mechanical systems-without restricting to Lagrangian, time-independent, or regular ones, and is applicable to arbitrary constraints (holonomic, semiholonomic, linear, nonlinear or general nonholonomic). The goal of this paper is to apply Krupková's geometric theory of nonholonomic mechanical systems to study a concrete problem in nonlinear nonholonomic dynamics, i.e., autonomous bicycle. The dynamical model is preserved in simulations in its original nonlinear form without any simplifying. The results of numerical solutions of constrained equations of motion, derived within the theory, are in good agreement with measurements and thus they open the possibility of direct application of the theory to practical situations.

Optimal control theory investigation of proprotor/wing response to vertical gust

NASA Technical Reports Server (NTRS)

Frick, J. K. D.; Johnson, W.

1974-01-01

Optimal control theory is used to design linear state variable feedback to improve the dynamic characteristics of a rotor and cantilever wing representing the tilting proprotor aircraft in cruise flight. The response to a vertical gust and system damping are used as criteria for the open and closed loop performance. The improvement in the dynamic characteristics achievable is examined for a gimballed rotor and for a hingeless rotor design. Several features of the design process are examined, including: (1) using only the wing or only the rotor dynamics in the control system design; (2) the use of a wing flap as well as the rotor controls for inputs; (3) and the performance of the system designed for one velocity at other forward speeds.

Thermospheric dynamics - A system theory approach

NASA Technical Reports Server (NTRS)

Codrescu, M.; Forbes, J. M.; Roble, R. G.

1990-01-01

A system theory approach to thermospheric modeling is developed, based upon a linearization method which is capable of preserving nonlinear features of a dynamical system. The method is tested using a large, nonlinear, time-varying system, namely the thermospheric general circulation model (TGCM) of the National Center for Atmospheric Research. In the linearized version an equivalent system, defined for one of the desired TGCM output variables, is characterized by a set of response functions that is constructed from corresponding quasi-steady state and unit sample response functions. The linearized version of the system runs on a personal computer and produces an approximation of the desired TGCM output field height profile at a given geographic location.

Cooperative Networked Control of Dynamical Peer-to-Peer Vehicle Systems

DTIC Science & Technology

2007-12-28

dynamic deployment and task allocation;verification and hybrid systems; and information management for cooperative control. The activity of the...32 5.3 Decidability Results on Discrete and Hybrid Systems ...... .................. 33 5.4 Switched Systems...solved. Verification and hybrid systems. The program has produced significant advances in the theory of hybrid input-output automata, (HIOA) and the

A Fast Algorithm for Massively Parallel, Long-Term, Simulation of Complex Molecular Dynamics Systems

NASA Technical Reports Server (NTRS)

Jaramillo-Botero, Andres; Goddard, William A, III; Fijany, Amir

1997-01-01

The advances in theory and computing technology over the last decade have led to enormous progress in applying atomistic molecular dynamics (MD) methods to the characterization, prediction, and design of chemical, biological, and material systems,.

Thermalization dynamics of two correlated bosonic quantum wires after a split

NASA Astrophysics Data System (ADS)

Huber, Sebastian; Buchhold, Michael; Schmiedmayer, Jörg; Diehl, Sebastian

2018-04-01

Cherently splitting a one-dimensional Bose gas provides an attractive, experimentally established platform to investigate many-body quantum dynamics. At short enough times, the dynamics is dominated by the dephasing of single quasiparticles, and well described by the relaxation towards a generalized Gibbs ensemble corresponding to the free Luttinger theory. At later times on the other hand, the approach to a thermal Gibbs ensemble is expected for a generic, interacting quantum system. Here, we go one step beyond the quadratic Luttinger theory and include the leading phonon-phonon interactions. By applying kinetic theory and nonequilibrium Dyson-Schwinger equations, we analyze the full relaxation dynamics beyond dephasing and determine the asymptotic thermalization process in the two-wire system for a symmetric splitting protocol. The major observables are the different phonon occupation functions and the experimentally accessible coherence factor, as well as the phase correlations between the two wires. We demonstrate that, depending on the splitting protocol, the presence of phonon collisions can have significant influence on the asymptotic evolution of these observables, which makes the corresponding thermalization dynamics experimentally accessible.

Statistical Mechanical Theory of Coupled Slow Dynamics in Glassy Polymer-Molecule Mixtures

NASA Astrophysics Data System (ADS)

Zhang, Rui; Schweizer, Kenneth

The microscopic Elastically Collective Nonlinear Langevin Equation theory of activated relaxation in one-component supercooled liquids and glasses is generalized to polymer-molecule mixtures. The key idea is to account for dynamic coupling between molecule and polymer segment motion. For describing the molecule hopping event, a temporal casuality condition is formulated to self-consistently determine a dimensionless degree of matrix distortion relative to the molecule jump distance based on the concept of coupled dynamic free energies. Implementation for real materials employs an established Kuhn sphere model of the polymer liquid and a quantitative mapping to a hard particle reference system guided by the experimental equation-of-state. The theory makes predictions for the mixture dynamic shear modulus, activated relaxation time and diffusivity of both species, and mixture glass transition temperature as a function of molecule-Kuhn segment size ratio and attraction strength, composition and temperature. Model calculations illustrate the dynamical behavior in three distinct mixture regimes (fully miscible, bridging, clustering) controlled by the molecule-polymer interaction or chi-parameter. Applications to specific experimental systems will be discussed.

Nonlinear problems in flight dynamics

NASA Technical Reports Server (NTRS)

Chapman, G. T.; Tobak, M.

1984-01-01

A comprehensive framework is proposed for the description and analysis of nonlinear problems in flight dynamics. Emphasis is placed on the aerodynamic component as the major source of nonlinearities in the flight dynamic system. Four aerodynamic flows are examined to illustrate the richness and regularity of the flow structures and the nature of the flow structures and the nature of the resulting nonlinear aerodynamic forces and moments. A framework to facilitate the study of the aerodynamic system is proposed having parallel observational and mathematical components. The observational component, structure is described in the language of topology. Changes in flow structure are described via bifurcation theory. Chaos or turbulence is related to the analogous chaotic behavior of nonlinear dynamical systems characterized by the existence of strange attractors having fractal dimensionality. Scales of the flow are considered in the light of ideas from group theory. Several one and two degree of freedom dynamical systems with various mathematical models of the nonlinear aerodynamic forces and moments are examined to illustrate the resulting types of dynamical behavior. The mathematical ideas that proved useful in the description of fluid flows are shown to be similarly useful in the description of flight dynamic behavior.

Complex, Dynamic Systems: A New Transdisciplinary Theme for Applied Linguistics?

ERIC Educational Resources Information Center

Larsen-Freeman, Diane

2012-01-01

In this plenary address, I suggest that Complexity Theory has the potential to contribute a transdisciplinary theme to applied linguistics. Transdisciplinary themes supersede disciplines and spur new kinds of creative activity (Halliday 2001 [1990]). Investigating complex systems requires researchers to pay attention to system dynamics. Since…

Introduction: Second Language Development as a Dynamic Process

ERIC Educational Resources Information Center

De Bot, Kees

2008-01-01

In this contribution, some of the basic characteristics of complex adaptive systems, collectively labeled Dynamic Systems Theory (DST), are discussed. Such systems are self-organizing, dependent on initial conditions, sometimes chaotic, and they show emergent properties. The focus in DST is on development over time. Language is seen as a dynamic…

Phase reduction approach to synchronisation of nonlinear oscillators

NASA Astrophysics Data System (ADS)

Nakao, Hiroya

2016-04-01

Systems of dynamical elements exhibiting spontaneous rhythms are found in various fields of science and engineering, including physics, chemistry, biology, physiology, and mechanical and electrical engineering. Such dynamical elements are often modelled as nonlinear limit-cycle oscillators. In this article, we briefly review phase reduction theory, which is a simple and powerful method for analysing the synchronisation properties of limit-cycle oscillators exhibiting rhythmic dynamics. Through phase reduction theory, we can systematically simplify the nonlinear multi-dimensional differential equations describing a limit-cycle oscillator to a one-dimensional phase equation, which is much easier to analyse. Classical applications of this theory, i.e. the phase locking of an oscillator to a periodic external forcing and the mutual synchronisation of interacting oscillators, are explained. Further, more recent applications of this theory to the synchronisation of non-interacting oscillators induced by common noise and the dynamics of coupled oscillators on complex networks are discussed. We also comment on some recent advances in phase reduction theory for noise-driven oscillators and rhythmic spatiotemporal patterns.

Theory of time-resolved photoelectron imaging. Comparison of a density functional with a time-dependent density functional approach

NASA Astrophysics Data System (ADS)

Suzuki, Yoshi-ichi; Seideman, Tamar; Stener, Mauro

2004-01-01

Time-resolved photoelectron differential cross sections are computed within a quantum dynamical theory that combines a formally exact solution of the nuclear dynamics with density functional theory (DFT)-based approximations of the electronic dynamics. Various observables of time-resolved photoelectron imaging techniques are computed at the Kohn-Sham and at the time-dependent DFT levels. Comparison of the results serves to assess the reliability of the former method and hence its usefulness as an economic approach for time-domain photoelectron cross section calculations, that is applicable to complex polyatomic systems. Analysis of the matrix elements that contain the electronic dynamics provides insight into a previously unexplored aspect of femtosecond-resolved photoelectron imaging.

Sedimentation of a two-dimensional colloidal mixture exhibiting liquid-liquid and gas-liquid phase separation: a dynamical density functional theory study.

PubMed

Malijevský, Alexandr; Archer, Andrew J

2013-10-14

We present dynamical density functional theory results for the time evolution of the density distribution of a sedimenting model two-dimensional binary mixture of colloids. The interplay between the bulk phase behaviour of the mixture, its interfacial properties at the confining walls, and the gravitational field gives rise to a rich variety of equilibrium and non-equilibrium morphologies. In the fluid state, the system exhibits both liquid-liquid and gas-liquid phase separation. As the system sediments, the phase separation significantly affects the dynamics and we explore situations where the final state is a coexistence of up to three different phases. Solving the dynamical equations in two-dimensions, we find that in certain situations the final density profiles of the two species have a symmetry that is different from that of the external potentials, which is perhaps surprising, given the statistical mechanics origin of the theory. The paper concludes with a discussion on this.

GDSCalc: A Web-Based Application for Evaluating Discrete Graph Dynamical Systems

PubMed Central

Elmeligy Abdelhamid, Sherif H.; Kuhlman, Chris J.; Marathe, Madhav V.; Mortveit, Henning S.; Ravi, S. S.

2015-01-01

Discrete dynamical systems are used to model various realistic systems in network science, from social unrest in human populations to regulation in biological networks. A common approach is to model the agents of a system as vertices of a graph, and the pairwise interactions between agents as edges. Agents are in one of a finite set of states at each discrete time step and are assigned functions that describe how their states change based on neighborhood relations. Full characterization of state transitions of one system can give insights into fundamental behaviors of other dynamical systems. In this paper, we describe a discrete graph dynamical systems (GDSs) application called GDSCalc for computing and characterizing system dynamics. It is an open access system that is used through a web interface. We provide an overview of GDS theory. This theory is the basis of the web application; i.e., an understanding of GDS provides an understanding of the software features, while abstracting away implementation details. We present a set of illustrative examples to demonstrate its use in education and research. Finally, we compare GDSCalc with other discrete dynamical system software tools. Our perspective is that no single software tool will perform all computations that may be required by all users; tools typically have particular features that are more suitable for some tasks. We situate GDSCalc within this space of software tools. PMID:26263006

GDSCalc: A Web-Based Application for Evaluating Discrete Graph Dynamical Systems.

PubMed

Elmeligy Abdelhamid, Sherif H; Kuhlman, Chris J; Marathe, Madhav V; Mortveit, Henning S; Ravi, S S

2015-01-01

Discrete dynamical systems are used to model various realistic systems in network science, from social unrest in human populations to regulation in biological networks. A common approach is to model the agents of a system as vertices of a graph, and the pairwise interactions between agents as edges. Agents are in one of a finite set of states at each discrete time step and are assigned functions that describe how their states change based on neighborhood relations. Full characterization of state transitions of one system can give insights into fundamental behaviors of other dynamical systems. In this paper, we describe a discrete graph dynamical systems (GDSs) application called GDSCalc for computing and characterizing system dynamics. It is an open access system that is used through a web interface. We provide an overview of GDS theory. This theory is the basis of the web application; i.e., an understanding of GDS provides an understanding of the software features, while abstracting away implementation details. We present a set of illustrative examples to demonstrate its use in education and research. Finally, we compare GDSCalc with other discrete dynamical system software tools. Our perspective is that no single software tool will perform all computations that may be required by all users; tools typically have particular features that are more suitable for some tasks. We situate GDSCalc within this space of software tools.

An introduction to chaos theory in CFD

NASA Technical Reports Server (NTRS)

Pulliam, Thomas H.

1990-01-01

The popular subject 'chaos theory' has captured the imagination of a wide variety of scientists and engineers. CFD has always been faced with nonlinear systems and it is natural to assume that nonlinear dynamics will play a role at sometime in such work. This paper will attempt to introduce some of the concepts and analysis procedures associated with nonlinear dynamics theory. In particular, results from computations of an airfoil at high angle of attack which exhibits a sequence of bifurcations for single frequency unsteady shedding through period doublings cascading into low dimensional chaos are used to present and demonstrate various aspects of nonlinear dynamics in CFD.

Dynamics of Complexity and Accuracy: A Longitudinal Case Study of Advanced Untutored Development

ERIC Educational Resources Information Center

Polat, Brittany; Kim, Youjin

2014-01-01

This longitudinal case study follows a dynamic systems approach to investigate an under-studied research area in second language acquisition, the development of complexity and accuracy for an advanced untutored learner of English. Using the analytical tools of dynamic systems theory (Verspoor et al. 2011) within the framework of complexity,…

A Thermodynamic Approach to Soil-Plant-Atmosphere Modeling: From Metabolic Biochemical Processes to Water-Carbon-Nitrogen Balance

NASA Astrophysics Data System (ADS)

Clavijo, H. W.

2016-12-01

Modeling the soil-plant-atmosphere continuum has been central part of understanding interrelationships among biogeochemical and hydrological processes. Theory behind of couplings Land Surface Models (LSM) and Dynamical Global Vegetation Models (DGVM) are based on physical and physiological processes connected by input-output interactions mainly. This modeling framework could be improved by the application of non-equilibrium thermodynamic basis that could encompass the majority of biophysical processes in a standard fashion. This study presents an alternative model for plant-water-atmosphere based on energy-mass thermodynamics. The system of dynamic equations derived is based on the total entropy, the total energy balance for the plant, the biomass dynamics at metabolic level and the water-carbon-nitrogen fluxes and balances. One advantage of this formulation is the capability to describe adaptation and evolution of dynamics of plant as a bio-system coupled to the environment. Second, it opens a window for applications on specific conditions from individual plant scale, to watershed scale, to global scale. Third, it enhances the possibility of analyzing anthropogenic impacts on the system, benefiting from the mathematical formulation and its non-linearity. This non-linear model formulation is analyzed under the concepts of qualitative system dynamics theory, for different state-space phase portraits. The attractors and sources are pointed out with its stability analysis. Possibility of bifurcations are explored and reported. Simulations for the system dynamics under different conditions are presented. These results show strong consistency and applicability that validates the use of the non-equilibrium thermodynamic theory.

Discontinuities reveal panarchy in socio-ecological system

EPA Science Inventory

Debates on the organization, structure and dynamics of ecosystems across scales of space and time have waxed and waned in the literature for a century. From successional theory to ecosystem theories of resilience and robustness, from hierarchy to ascendency to panarchy theory, e...

Multireference quantum chemistry through a joint density matrix renormalization group and canonical transformation theory.

PubMed

Yanai, Takeshi; Kurashige, Yuki; Neuscamman, Eric; Chan, Garnet Kin-Lic

2010-01-14

We describe the joint application of the density matrix renormalization group and canonical transformation theory to multireference quantum chemistry. The density matrix renormalization group provides the ability to describe static correlation in large active spaces, while the canonical transformation theory provides a high-order description of the dynamic correlation effects. We demonstrate the joint theory in two benchmark systems designed to test the dynamic and static correlation capabilities of the methods, namely, (i) total correlation energies in long polyenes and (ii) the isomerization curve of the [Cu(2)O(2)](2+) core. The largest complete active spaces and atomic orbital basis sets treated by the joint DMRG-CT theory in these systems correspond to a (24e,24o) active space and 268 atomic orbitals in the polyenes and a (28e,32o) active space and 278 atomic orbitals in [Cu(2)O(2)](2+).

Invasive advance of an advantageous mutation: nucleation theory.

PubMed

O'Malley, Lauren; Basham, James; Yasi, Joseph A; Korniss, G; Allstadt, Andrew; Caraco, Thomas

2006-12-01

For sedentary organisms with localized reproduction, spatially clustered growth drives the invasive advance of a favorable mutation. We model competition between two alleles where recurrent mutation introduces a genotype with a rate of local propagation exceeding the resident's rate. We capture ecologically important properties of the rare invader's stochastic dynamics by assuming discrete individuals and local neighborhood interactions. To understand how individual-level processes may govern population patterns, we invoke the physical theory for nucleation of spatial systems. Nucleation theory discriminates between single-cluster and multi-cluster dynamics. A sufficiently low mutation rate, or a sufficiently small environment, generates single-cluster dynamics, an inherently stochastic process; a favorable mutation advances only if the invader cluster reaches a critical radius. For this mode of invasion, we identify the probability distribution of waiting times until the favored allele advances to competitive dominance, and we ask how the critical cluster size varies as propagation or mortality rates vary. Increasing the mutation rate or system size generates multi-cluster invasion, where spatial averaging produces nearly deterministic global dynamics. For this process, an analytical approximation from nucleation theory, called Avrami's Law, describes the time-dependent behavior of the genotype densities with remarkable accuracy.

Continuation Methods for Qualitative Analysis of Aircraft Dynamics

NASA Technical Reports Server (NTRS)

Cummings, Peter A.

2004-01-01

A class of numerical methods for constructing bifurcation curves for systems of coupled, non-linear ordinary differential equations is presented. Foundations are discussed, and several variations are outlined along with their respective capabilities. Appropriate background material from dynamical systems theory is presented.

Self-consistent Green's function embedding for advanced electronic structure methods based on a dynamical mean-field concept

NASA Astrophysics Data System (ADS)

Chibani, Wael; Ren, Xinguo; Scheffler, Matthias; Rinke, Patrick

2016-04-01

We present an embedding scheme for periodic systems that facilitates the treatment of the physically important part (here a unit cell or a supercell) with advanced electronic structure methods, that are computationally too expensive for periodic systems. The rest of the periodic system is treated with computationally less demanding approaches, e.g., Kohn-Sham density-functional theory, in a self-consistent manner. Our scheme is based on the concept of dynamical mean-field theory formulated in terms of Green's functions. Our real-space dynamical mean-field embedding scheme features two nested Dyson equations, one for the embedded cluster and another for the periodic surrounding. The total energy is computed from the resulting Green's functions. The performance of our scheme is demonstrated by treating the embedded region with hybrid functionals and many-body perturbation theory in the GW approach for simple bulk systems. The total energy and the density of states converge rapidly with respect to the computational parameters and approach their bulk limit with increasing cluster (i.e., computational supercell) size.

Time-dependent density functional theory for open systems with a positivity-preserving decomposition scheme for environment spectral functions

NASA Astrophysics Data System (ADS)

Wang, RuLin; Zheng, Xiao; Kwok, YanHo; Xie, Hang; Chen, GuanHua; Yam, ChiYung

2015-04-01

Understanding electronic dynamics on material surfaces is fundamentally important for applications including nanoelectronics, inhomogeneous catalysis, and photovoltaics. Practical approaches based on time-dependent density functional theory for open systems have been developed to characterize the dissipative dynamics of electrons in bulk materials. The accuracy and reliability of such approaches depend critically on how the electronic structure and memory effects of surrounding material environment are accounted for. In this work, we develop a novel squared-Lorentzian decomposition scheme, which preserves the positive semi-definiteness of the environment spectral matrix. The resulting electronic dynamics is guaranteed to be both accurate and convergent even in the long-time limit. The long-time stability of electronic dynamics simulation is thus greatly improved within the current decomposition scheme. The validity and usefulness of our new approach are exemplified via two prototypical model systems: quasi-one-dimensional atomic chains and two-dimensional bilayer graphene.

Non-Markovian generalization of the Lindblad theory of open quantum systems

NASA Astrophysics Data System (ADS)

Breuer, Heinz-Peter

2007-02-01

A systematic approach to the non-Markovian quantum dynamics of open systems is given by the projection operator techniques of nonequilibrium statistical mechanics. Combining these methods with concepts from quantum information theory and from the theory of positive maps, we derive a class of correlated projection superoperators that take into account in an efficient way statistical correlations between the open system and its environment. The result is used to develop a generalization of the Lindblad theory to the regime of highly non-Markovian quantum processes in structured environments.

Emergent "Quantum" Theory in Complex Adaptive Systems.

PubMed

Minic, Djordje; Pajevic, Sinisa

2016-04-30

Motivated by the question of stability, in this letter we argue that an effective quantum-like theory can emerge in complex adaptive systems. In the concrete example of stochastic Lotka-Volterra dynamics, the relevant effective "Planck constant" associated with such emergent "quantum" theory has the dimensions of the square of the unit of time. Such an emergent quantum-like theory has inherently non-classical stability as well as coherent properties that are not, in principle, endangered by thermal fluctuations and therefore might be of crucial importance in complex adaptive systems.

Emergent “Quantum” Theory in Complex Adaptive Systems

PubMed Central

Minic, Djordje; Pajevic, Sinisa

2017-01-01

Motivated by the question of stability, in this letter we argue that an effective quantum-like theory can emerge in complex adaptive systems. In the concrete example of stochastic Lotka-Volterra dynamics, the relevant effective “Planck constant” associated with such emergent “quantum” theory has the dimensions of the square of the unit of time. Such an emergent quantum-like theory has inherently non-classical stability as well as coherent properties that are not, in principle, endangered by thermal fluctuations and therefore might be of crucial importance in complex adaptive systems. PMID:28890591

Dynamics of Numerics & Spurious Behaviors in CFD Computations. Revised

NASA Technical Reports Server (NTRS)

Yee, Helen C.; Sweby, Peter K.

1997-01-01

The global nonlinear behavior of finite discretizations for constant time steps and fixed or adaptive grid spacings is studied using tools from dynamical systems theory. Detailed analysis of commonly used temporal and spatial discretizations for simple model problems is presented. The role of dynamics in the understanding of long time behavior of numerical integration and the nonlinear stability, convergence, and reliability of using time-marching approaches for obtaining steady-state numerical solutions in computational fluid dynamics (CFD) is explored. The study is complemented with examples of spurious behavior observed in steady and unsteady CFD computations. The CFD examples were chosen to illustrate non-apparent spurious behavior that was difficult to detect without extensive grid and temporal refinement studies and some knowledge from dynamical systems theory. Studies revealed the various possible dangers of misinterpreting numerical simulation of realistic complex flows that are constrained by available computing power. In large scale computations where the physics of the problem under study is not well understood and numerical simulations are the only viable means of solution, extreme care must be taken in both computation and interpretation of the numerical data. The goal of this paper is to explore the important role that dynamical systems theory can play in the understanding of the global nonlinear behavior of numerical algorithms and to aid the identification of the sources of numerical uncertainties in CFD.

Dynamical entropy via entropy of non-random matrices: application to stability and complexity in modelling ecosystems.

PubMed

Chakrabarti, C G; Ghosh, Koyel

2013-10-01

In the present paper we have first introduced a measure of dynamical entropy of an ecosystem on the basis of the dynamical model of the system. The dynamical entropy which depends on the eigenvalues of the community matrix of the system leads to a consistent measure of complexity of the ecosystem to characterize the dynamical behaviours such as the stability, instability and periodicity around the stationary states of the system. We have illustrated the theory with some model ecosystems. Copyright © 2013 Elsevier Inc. All rights reserved.

A state-of-the-art review of transportation systems evaluation techniques relevant to air transportation, volume 1. [urban planning and urban transportation using decision theory

NASA Technical Reports Server (NTRS)

Haefner, L. E.

1975-01-01

Mathematical and philosophical approaches are presented for evaluation and implementation of ground and air transportation systems. Basic decision processes are examined that are used for cost analyses and planning (i.e, statistical decision theory, linear and dynamic programming, optimization, game theory). The effects on the environment and the community that a transportation system may have are discussed and modelled. Algorithmic structures are examined and selected bibliographic annotations are included. Transportation dynamic models were developed. Citizen participation in transportation projects (i.e, in Maryland and Massachusetts) is discussed. The relevance of the modelling and evaluation approaches to air transportation (i.e, airport planning) is examined in a case study in St. Louis, Missouri.

Application of non-linear dynamics to the characterization of cardiac electrical instability

NASA Technical Reports Server (NTRS)

Kaplan, D. T.; Cohen, R. J.

1987-01-01

Beat-to-beat alternation in the morphology of the ECG has been previously observed in hearts susceptible to fibrillation. In addition, fibrillation has been characterized by some as a chaotic state. Period doubling phenomena, such as alternation, and the onset of chaos have been connected by non-linear dynamical systems theory. In this paper, we describe the use of a technique from nonlinear dynamics theory, the construction of a first return nap, to assess the susceptibility to fibrillation threshhold in canine experiments.

Stability and dynamical properties of material flow systems on random networks

NASA Astrophysics Data System (ADS)

Anand, K.; Galla, T.

2009-04-01

The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are characteristic of flow networks in economic, ecological and biological systems. Based on results from random matrix theory, we work out the phase diagram of such systems defined on extensively connected random graphs, and study in detail how the choice of control policies and the network structure affects stability. We also present results for more complex topologies of the underlying graph, focussing on finitely connected Erdös-Réyni graphs, Small-World Networks and Barabási-Albert scale-free networks. Results indicate that variability of input-output matrix elements, and random structures of the underlying graph tend to make the system less stable, while fast price dynamics or strong responsiveness to stock accumulation promote stability.

Dissipative controller designs for second-order dynamic systems

NASA Technical Reports Server (NTRS)

Morris, K. A.; Juang, J. N.

1990-01-01

The passivity theorem may be used to design robust controllers for structures with positive transfer functions. This result is extended to more general configurations using dissipative system theory. A stability theorem for robust, model-independent controllers of structures which lack collocated rate sensors and actuators is given. The theory is illustrated for non-square systems and systems with displacement sensors.

Introduction to Fuzzy Set Theory

NASA Technical Reports Server (NTRS)

Kosko, Bart

1990-01-01

An introduction to fuzzy set theory is described. Topics covered include: neural networks and fuzzy systems; the dynamical systems approach to machine intelligence; intelligent behavior as adaptive model-free estimation; fuzziness versus probability; fuzzy sets; the entropy-subsethood theorem; adaptive fuzzy systems for backing up a truck-and-trailer; product-space clustering with differential competitive learning; and adaptive fuzzy system for target tracking.

Graph-based linear scaling electronic structure theory.

PubMed

Niklasson, Anders M N; Mniszewski, Susan M; Negre, Christian F A; Cawkwell, Marc J; Swart, Pieter J; Mohd-Yusof, Jamal; Germann, Timothy C; Wall, Michael E; Bock, Nicolas; Rubensson, Emanuel H; Djidjev, Hristo

2016-06-21

We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials, including challenging systems such as biomolecules. The methodology combines well-controlled accuracy, low computational cost, and natural low-communication parallelism. This combination addresses substantial shortcomings of linear scaling electronic structure theory, in particular with respect to quantum-based molecular dynamics simulations.

Graph-based linear scaling electronic structure theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Niklasson, Anders M. N., E-mail: amn@lanl.gov; Negre, Christian F. A.; Cawkwell, Marc J.

2016-06-21

We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials, including challenging systems such as biomolecules. The methodology combines well-controlled accuracy, low computational cost, and natural low-communication parallelism. This combination addresses substantial shortcomings of linear scaling electronic structure theory, in particular with respect to quantum-based molecular dynamics simulations.

The birth of gravitational evolutionary dynamics of stellar systems (from Th. Wright to W. Herschel).

NASA Astrophysics Data System (ADS)

Eremeeva, A. J.

1995-05-01

Th. Wright, I. Kant and I. H. Lambert used well-known ideas about the structure and dynamics of the Solar system as a basis of their concepts of the stellar Universe. W. Herschel discovered the main features of the true, non-hierarchical large-scale structure of the Universe. He was also a pioneer of stellar dynamics with its new statistical laws and also of the theory of dynamical evolution in stellar systems at different scales.

Approximated Stable Inversion for Nonlinear Systems with Nonhyperbolic Internal Dynamics. Revised

NASA Technical Reports Server (NTRS)

Devasia, Santosh

1999-01-01

A technique to achieve output tracking for nonminimum phase nonlinear systems with non- hyperbolic internal dynamics is presented. The present paper integrates stable inversion techniques (that achieve exact-tracking) with approximation techniques (that modify the internal dynamics) to circumvent the nonhyperbolicity of the internal dynamics - this nonhyperbolicity is an obstruction to applying presently available stable inversion techniques. The theory is developed for nonlinear systems and the method is applied to a two-cart with inverted-pendulum example.

Chaos in World Politics: A Reflection

NASA Astrophysics Data System (ADS)

Ferreira, Manuel Alberto Martins; Filipe, José António Candeias Bonito; Coelho, Manuel F. P.; Pedro, Isabel C.

Chaos theory results from natural scientists' findings in the area of non-linear dynamics. The importance of related models has increased in the last decades, by studying the temporal evolution of non-linear systems. In consequence, chaos is one of the concepts that most rapidly have been expanded in what research topics respects. Considering that relationships in non-linear systems are unstable, chaos theory aims to understand and to explain this kind of unpredictable aspects of nature, social life, the uncertainties, the nonlinearities, the disorders and confusion, scientifically it represents a disarray connection, but basically it involves much more than that. The existing close relationship between change and time seems essential to understand what happens in the basics of chaos theory. In fact, this theory got a crucial role in the explanation of many phenomena. The relevance of this kind of theories has been well recognized to explain social phenomena and has permitted new advances in the study of social systems. Chaos theory has also been applied, particularly in the context of politics, in this area. The goal of this chapter is to make a reflection on chaos theory - and dynamical systems such as the theories of complexity - in terms of the interpretation of political issues, considering some kind of events in the political context and also considering the macro-strategic ideas of states positioning in the international stage.

Using Systems Theory to Understand and Respond to Family Influences on Children's Bullying Behavior: Friendly Schools Friendly Families Program

ERIC Educational Resources Information Center

Cross, Donna; Barnes, Amy

2014-01-01

This article addresses Systems Theory as it applies to school-age children's bullying behavior. It focuses on the interrelationships, mutual influences, and dynamics of relationships within the family, and how these may affect children's behavior toward their peers. The theory helps to explain the ways family patterns are reflected in…

Neptune - Unexpected and predicted: Prognosis of theory and Voyager-2 observations

NASA Astrophysics Data System (ADS)

Chechel'Nitskii, A. M.

1992-08-01

The impact of the Voyager-2 discoveries at Neptune on theory are reviewed. The theories of the shell structure of astronomical systems, shell hierarchy, the multicomponent cosmic medium, weak and power elite orbits, quantization of dynamic parameters, and transspheres are summarized and their relevance to the Neptune system, particularly the rings, is considered in the context of the findings of Voyager-2.

Gravity

NASA Astrophysics Data System (ADS)

Poisson, Eric; Will, Clifford M.

2014-05-01

Preface; 1. Foundations of Newtonian gravity; 2. Structure of self-gravitating bodies; 3. Newtonian orbital dynamics; 4. Minkowski spacetime; 5. Curved spacetime; 6. Post-Minkowskian theory: formulation; 7. Post-Minkowskian theory: implementation; 8. Post-Newtonian theory: fundamentals; 9. Post-Newtonian theory: system of isolated bodies; 10. Post-Newtonian celestial mechanics, astrometry and navigation; 11. Gravitational waves; 12. Radiative losses and radiation reaction; 13. Alternative theories of gravity; References; Index.

Toward a Conceptual Pattern in Librarianship: A Model.

ERIC Educational Resources Information Center

Nitecki, Joseph Z.

1970-01-01

In an attempt to import some concepts from general systems theory to the theory of librarianship, basic elements in the theory of librarianship were identified, interrelated in a form of a static model, and projected into a possible, dynamic pattern of change. (Author/LS)

Dynamic stability of maglev systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cai, Y.; Chen, S.S.; Mulcahy, T.M.

1994-05-01

Because dynamic instabilities are not acceptable in any commercial maglev system, it is important to consider dynamic instability in the development of all maglev systems. This study considers the stability of maglev systems based on experimental data, scoping calculations, and simple mathematical models. Divergence and flutter are obtained for coupled vibration of a three-degree-of-freedom maglev vehicle on a guideway consisting of double L-shaped aluminum segments. The theory and analysis developed in this study provides basic stability characteristics and identifies future research needs for maglev systems.

Social judgment theory based model on opinion formation, polarization and evolution

NASA Astrophysics Data System (ADS)

Chau, H. F.; Wong, C. Y.; Chow, F. K.; Fung, Chi-Hang Fred

2014-12-01

The dynamical origin of opinion polarization in the real world is an interesting topic that physical scientists may help to understand. To properly model the dynamics, the theory must be fully compatible with findings by social psychologists on microscopic opinion change. Here we introduce a generic model of opinion formation with homogeneous agents based on the well-known social judgment theory in social psychology by extending a similar model proposed by Jager and Amblard. The agents’ opinions will eventually cluster around extreme and/or moderate opinions forming three phases in a two-dimensional parameter space that describes the microscopic opinion response of the agents. The dynamics of this model can be qualitatively understood by mean-field analysis. More importantly, first-order phase transition in opinion distribution is observed by evolving the system under a slow change in the system parameters, showing that punctuated equilibria in public opinion can occur even in a fully connected social network.

Barrierless association of CF2 and dissociation of C2F4 by variational transition-state theory and system-specific quantum Rice–Ramsperger–Kassel theory

PubMed Central

Bao, Junwei Lucas; Zhang, Xin

2016-01-01

Bond dissociation is a fundamental chemical reaction, and the first principles modeling of the kinetics of dissociation reactions with a monotonically increasing potential energy along the dissociation coordinate presents a challenge not only for modern electronic structure methods but also for kinetics theory. In this work, we use multifaceted variable-reaction-coordinate variational transition-state theory (VRC-VTST) to compute the high-pressure limit dissociation rate constant of tetrafluoroethylene (C2F4), in which the potential energies are computed by direct dynamics with the M08-HX exchange correlation functional. To treat the pressure dependence of the unimolecular rate constants, we use the recently developed system-specific quantum Rice–Ramsperger–Kassel theory. The calculations are carried out by direct dynamics using an exchange correlation functional validated against calculations that go beyond coupled-cluster theory with single, double, and triple excitations. Our computed dissociation rate constants agree well with the recent experimental measurements. PMID:27834727

Barrierless association of CF2 and dissociation of C2F4 by variational transition-state theory and system-specific quantum Rice-Ramsperger-Kassel theory.

PubMed

Bao, Junwei Lucas; Zhang, Xin; Truhlar, Donald G

2016-11-29

Bond dissociation is a fundamental chemical reaction, and the first principles modeling of the kinetics of dissociation reactions with a monotonically increasing potential energy along the dissociation coordinate presents a challenge not only for modern electronic structure methods but also for kinetics theory. In this work, we use multifaceted variable-reaction-coordinate variational transition-state theory (VRC-VTST) to compute the high-pressure limit dissociation rate constant of tetrafluoroethylene (C 2 F 4 ), in which the potential energies are computed by direct dynamics with the M08-HX exchange correlation functional. To treat the pressure dependence of the unimolecular rate constants, we use the recently developed system-specific quantum Rice-Ramsperger-Kassel theory. The calculations are carried out by direct dynamics using an exchange correlation functional validated against calculations that go beyond coupled-cluster theory with single, double, and triple excitations. Our computed dissociation rate constants agree well with the recent experimental measurements.

The dynamic opponent relativity model: an integration and extension of capacity theory and existing theoretical perspectives on the neuropsychology of arousal and emotion.

PubMed

Comer, Clinton S; Harrison, Patti Kelly; Harrison, David W

2015-01-01

Arousal theory as discussed within the present paper refers to those mechanisms and neural systems involved in central nervous system activation and more specifically the systems involved in cortical activation. Historical progress in the evolution of arousal theory has led to a better understanding of the functional neural systems involved in arousal or activation processes and ultimately contributed much to our current theories of emotion. Despite evidence for the dynamic interplay between the left and right cerebral hemispheres, the concepts of cerebral balance and dynamic activation have been emphasized in the neuropsychological literature. A conceptual model is proposed herein that incorporates the unique contributions from multiple neuropsychological theories of arousal and emotion. It is argued that the cerebral hemispheres may play oppositional roles in emotion partially due to the differences in their functional specializations and in their persistence upon activation. In the presence of a threat or provocation, the right hemisphere may activate survival relevant responses partially derived from hemispheric specializations in arousal and emotional processing, including the mobilization of sympathetic drive to promote heightened blood pressure, heart rate, glucose mobilization and respiratory support necessary for the challenge. Oppositional processes and mechanisms are discussed, which may be relevant to the regulatory control over the survival response; however, the capacity of these systems is necessarily limited. A limited capacity mechanism is proposed, which is familiar within other physiological systems, including that providing for the prevention of muscular damage under exceptional demand. This capacity theory is proposed, wherein a link may be expected between exceptional stress within a neural system and damage to the neural system. These mechanisms are proposed to be relevant to emotion and emotional disorders. Discussion is provided on the possible role of currently applied therapeutic interventions for emotional disorders.

Application of dynamical systems theory to global weather phenomena revealed by satellite imagery

NASA Technical Reports Server (NTRS)

Saltzman, Barry; Ebisuzaki, Wesley; Maasch, Kirk A.; Oglesby, Robert; Pandolfo, Lionel; Tang, Chung-Muh

1989-01-01

Theoretical studies of low frequency and seasonal weather variability; dynamical properties of observational and general circulation model (GCM)-generated records; effects of the hydrologic cycle and latent heat release on extratropical weather; and Earth-system science studies are summarized.

Connection dynamics of a gauge theory of gravity coupled with matter

NASA Astrophysics Data System (ADS)

Yang, Jian; Banerjee, Kinjal; Ma, Yongge

2013-10-01

We study the coupling of the gravitational action, which is a linear combination of the Hilbert-Palatini term and the quadratic torsion term, to the action of Dirac fermions. The system possesses local Poincare invariance and hence belongs to Poincare gauge theory (PGT) with matter. The complete Hamiltonian analysis of the theory is carried out without gauge fixing but under certain ansatz on the coupling parameters, which leads to a consistent connection dynamics with second-class constraints and torsion. After performing a partial gauge fixing, all second-class constraints can be solved, and a SU(2)-connection dynamical formalism of the theory can be obtained. Hence, the techniques of loop quantum gravity (LQG) can be employed to quantize this PGT with non-zero torsion. Moreover, the Barbero-Immirzi parameter in LQG acquires its physical meaning as the coupling parameter between the Hilbert-Palatini term and the quadratic torsion term in this gauge theory of gravity.

Social Ecology of Asthma: Engaging Stakeholders in Integrating Health Behavior Theories and Practice-Based Evidence through Systems Mapping

ERIC Educational Resources Information Center

Gillen, Emily M.; Hassmiller Lich, Kristen; Yeatts, Karin B.; Hernandez, Michelle L.; Smith, Timothy W.; Lewis, Megan A.

2014-01-01

This article describes a process for integrating health behavior and social science theories with practice-based insights using participatory systems thinking and diagramming methods largely inspired by system dynamics methods. This integration can help close the gap between research and practice in health education and health behavior by offering…

Ab initio molecular dynamics with nuclear quantum effects at classical cost: Ring polymer contraction for density functional theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marsalek, Ondrej; Markland, Thomas E., E-mail: tmarkland@stanford.edu

Path integral molecular dynamics simulations, combined with an ab initio evaluation of interactions using electronic structure theory, incorporate the quantum mechanical nature of both the electrons and nuclei, which are essential to accurately describe systems containing light nuclei. However, path integral simulations have traditionally required a computational cost around two orders of magnitude greater than treating the nuclei classically, making them prohibitively costly for most applications. Here we show that the cost of path integral simulations can be dramatically reduced by extending our ring polymer contraction approach to ab initio molecular dynamics simulations. By using density functional tight binding asmore » a reference system, we show that our ring polymer contraction scheme gives rapid and systematic convergence to the full path integral density functional theory result. We demonstrate the efficiency of this approach in ab initio simulations of liquid water and the reactive protonated and deprotonated water dimer systems. We find that the vast majority of the nuclear quantum effects are accurately captured using contraction to just the ring polymer centroid, which requires the same number of density functional theory calculations as a classical simulation. Combined with a multiple time step scheme using the same reference system, which allows the time step to be increased, this approach is as fast as a typical classical ab initio molecular dynamics simulation and 35× faster than a full path integral calculation, while still exactly including the quantum sampling of nuclei. This development thus offers a route to routinely include nuclear quantum effects in ab initio molecular dynamics simulations at negligible computational cost.« less

Collective intelligence for control of distributed dynamical systems

NASA Astrophysics Data System (ADS)

Wolpert, D. H.; Wheeler, K. R.; Tumer, K.

2000-03-01

We consider the El Farol bar problem, also known as the minority game (W. B. Arthur, The American Economic Review, 84 (1994) 406; D. Challet and Y. C. Zhang, Physica A, 256 (1998) 514). We view it as an instance of the general problem of how to configure the nodal elements of a distributed dynamical system so that they do not "work at cross purposes", in that their collective dynamics avoids frustration and thereby achieves a provided global goal. We summarize a mathematical theory for such configuration applicable when (as in the bar problem) the global goal can be expressed as minimizing a global energy function and the nodes can be expressed as minimizers of local free energy functions. We show that a system designed with that theory performs nearly optimally for the bar problem.

Unified formalism for the generalized kth-order Hamilton-Jacobi problem

NASA Astrophysics Data System (ADS)

Colombo, Leonardo; de Léon, Manuel; Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso

2014-08-01

The geometric formulation of the Hamilton-Jacobi theory enables us to generalize it to systems of higher-order ordinary differential equations. In this work we introduce the unified Lagrangian-Hamiltonian formalism for the geometric Hamilton-Jacobi theory on higher-order autonomous dynamical systems described by regular Lagrangian functions.

The Chaos Theory of Careers

ERIC Educational Resources Information Center

Bright, Jim E. H.; Pryor, Robert G. L.

2011-01-01

The Chaos Theory of Careers (CTC; Pryor & Bright, 2011) construes both individuals and the contexts in which they develop their careers in terms of complex dynamical systems. Such systems perpetually operate under influences of stability and change both internally and in relation to each other. The CTC introduces new concepts to account for…

Recruitment dynamics in adaptive social networks

NASA Astrophysics Data System (ADS)

Shkarayev, Maxim; Shaw, Leah; Schwartz, Ira

2011-03-01

We model recruitment in social networks in the presence of birth and death processes. The recruitment is characterized by nodes changing their status to that of the recruiting class as a result of contact with recruiting nodes. The recruiting nodes may adapt their connections in order to improve recruitment capabilities, thus changing the network structure. We develop a mean-field theory describing the system dynamics. Using mean-field theory we characterize the dependence of the growth threshold of the recruiting class on the adaptation parameter. Furthermore, we investigate the effect of adaptation on the recruitment dynamics, as well as on network topology. The theoretical predictions are confirmed by the direct simulations of the full system.

Some empirical evidence for ecological dissonance theory.

PubMed

Miller, D I; Verhoek-Miller, N; Giesen, J M; Wells-Parker, E

2000-04-01

Using Festinger's cognitive dissonance theory as a model, the extension to Barker's ecological theory, referred to as ecological dissonance theory, was developed. Designed to examine the motivational dynamics involved when environmental systems are in conflict with each other or with cognitive systems, ecological dissonance theory yielded five propositions which were tested in 10 studies. This summary of the studies suggests operationally defined measures of ecological dissonance may correlate with workers' satisfaction with their jobs, involvement with their jobs, alienation from their work, and to a lesser extent, workers' conflict resolution behavior and communication style.

Fixing extensions to general relativity in the nonlinear regime

NASA Astrophysics Data System (ADS)

Cayuso, Juan; Ortiz, Néstor; Lehner, Luis

2017-10-01

The question of what gravitational theory could supersede General Relativity has been central in theoretical physics for decades. Many disparate alternatives have been proposed motivated by cosmology, quantum gravity and phenomenological angles, and have been subjected to tests derived from cosmological, solar system and pulsar observations typically restricted to linearized regimes. Gravitational waves from compact binaries provide new opportunities to probe these theories in the strongly gravitating/highly dynamical regimes. To this end however, a reliable understanding of the dynamics in such a regime is required. Unfortunately, most of these theories fail to define well posed initial value problems, which prevents at face value from meeting such challenge. In this work, we introduce a consistent program able to remedy this situation. This program is inspired in the approach to "fixing" viscous relativistic hydrodynamics introduced by Israel and Stewart in the late 70's. We illustrate how to implement this approach to control undesirable effects of higher order derivatives in gravity theories and argue how the modified system still captures the true dynamics of the putative underlying theories in 3 +1 dimensions. We sketch the implementation of this idea in a couple of effective theories of gravity, one in the context of Noncommutative Geometry, and one in the context of Chern-Simons modified General Relativity.

Modelling home televisiting services using systems dynamic theory.

PubMed

Valero, M A; Arredondo, M T; del Nogal, F; Gallar, P; Insausti, J; Del Pozo, F

2001-01-01

A quantitative model was developed to study the provision of a home televisiting service. Systems dynamic theory was used to describe the relationships between quality of care, accessibility and cost-effectiveness. Input information was gathered from the telemedicine literature, as well as from over 75 sessions of a televisiting service provided by the Severo Ochoa Hospital to 18 housebound patients from three different medical specialties. The model allowed the Severo Ochoa Hospital to estimate the equipment needed to support increased medical contacts for intensive cardiac and other patients.

Using a Complexity Approach to Study the Interpersonal Dynamics in Teacher-­Student Interactions: A Case Study of Two Teachers

ERIC Educational Resources Information Center

Pennings, Helena J. M.

2017-01-01

In the present study, complex dynamic systems theory and interpersonal theory are combined to describe the teacher-student interactions of two teachers with different interpersonal styles. The aim was to show and explain the added value of looking at different steps in the analysis of behavioral time-series data (i.e., observations of teacher and…

Nonadiabatic dynamics of electron transfer in solution: Explicit and implicit solvent treatments that include multiple relaxation time scales

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schwerdtfeger, Christine A.; Soudackov, Alexander V.; Hammes-Schiffer, Sharon, E-mail: shs3@illinois.edu

2014-01-21

The development of efficient theoretical methods for describing electron transfer (ET) reactions in condensed phases is important for a variety of chemical and biological applications. Previously, dynamical dielectric continuum theory was used to derive Langevin equations for a single collective solvent coordinate describing ET in a polar solvent. In this theory, the parameters are directly related to the physical properties of the system and can be determined from experimental data or explicit molecular dynamics simulations. Herein, we combine these Langevin equations with surface hopping nonadiabatic dynamics methods to calculate the rate constants for thermal ET reactions in polar solvents formore » a wide range of electronic couplings and reaction free energies. Comparison of explicit and implicit solvent calculations illustrates that the mapping from explicit to implicit solvent models is valid even for solvents exhibiting complex relaxation behavior with multiple relaxation time scales and a short-time inertial response. The rate constants calculated for implicit solvent models with a single solvent relaxation time scale corresponding to water, acetonitrile, and methanol agree well with analytical theories in the Golden rule and solvent-controlled regimes, as well as in the intermediate regime. The implicit solvent models with two relaxation time scales are in qualitative agreement with the analytical theories but quantitatively overestimate the rate constants compared to these theories. Analysis of these simulations elucidates the importance of multiple relaxation time scales and the inertial component of the solvent response, as well as potential shortcomings of the analytical theories based on single time scale solvent relaxation models. This implicit solvent approach will enable the simulation of a wide range of ET reactions via the stochastic dynamics of a single collective solvent coordinate with parameters that are relevant to experimentally accessible systems.« less

Numerical methods for solving moment equations in kinetic theory of neuronal network dynamics

NASA Astrophysics Data System (ADS)

Rangan, Aaditya V.; Cai, David; Tao, Louis

2007-02-01

Recently developed kinetic theory and related closures for neuronal network dynamics have been demonstrated to be a powerful theoretical framework for investigating coarse-grained dynamical properties of neuronal networks. The moment equations arising from the kinetic theory are a system of (1 + 1)-dimensional nonlinear partial differential equations (PDE) on a bounded domain with nonlinear boundary conditions. The PDEs themselves are self-consistently specified by parameters which are functions of the boundary values of the solution. The moment equations can be stiff in space and time. Numerical methods are presented here for efficiently and accurately solving these moment equations. The essential ingredients in our numerical methods include: (i) the system is discretized in time with an implicit Euler method within a spectral deferred correction framework, therefore, the PDEs of the kinetic theory are reduced to a sequence, in time, of boundary value problems (BVPs) with nonlinear boundary conditions; (ii) a set of auxiliary parameters is introduced to recast the original BVP with nonlinear boundary conditions as BVPs with linear boundary conditions - with additional algebraic constraints on the auxiliary parameters; (iii) a careful combination of two Newton's iterates for the nonlinear BVP with linear boundary condition, interlaced with a Newton's iterate for solving the associated algebraic constraints is constructed to achieve quadratic convergence for obtaining the solutions with self-consistent parameters. It is shown that a simple fixed-point iteration can only achieve a linear convergence for the self-consistent parameters. The practicability and efficiency of our numerical methods for solving the moment equations of the kinetic theory are illustrated with numerical examples. It is further demonstrated that the moment equations derived from the kinetic theory of neuronal network dynamics can very well capture the coarse-grained dynamical properties of integrate-and-fire neuronal networks.

Modeling transonic aerodynamic response using nonlinear systems theory for use with modern control theory

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1993-01-01

The presentation begins with a brief description of the motivation and approach that has been taken for this research. This will be followed by a description of the Volterra Theory of Nonlinear Systems and the CAP-TSD code which is an aeroelastic, transonic CFD (Computational Fluid Dynamics) code. The application of the Volterra theory to a CFD model and, more specifically, to a CAP-TSD model of a rectangular wing with a NACA 0012 airfoil section will be presented.

The Feldenkrais Method: A Dynamic Approach to Changing Motor Behavior.

ERIC Educational Resources Information Center

Buchanan, Patricia A.; Ulrich, Beverly D.

2001-01-01

Describes the Feldenkrais Method of somatic education, noting parallels with a dynamic systems theory (DST) approach to motor behavior. Feldenkrais uses movement and perception to foster individualized improvement in function. DST explains that a human-environment system continually adapts to changing conditions and assembles behaviors…

Strongly contracted canonical transformation theory

NASA Astrophysics Data System (ADS)

Neuscamman, Eric; Yanai, Takeshi; Chan, Garnet Kin-Lic

2010-01-01

Canonical transformation (CT) theory describes dynamic correlation in multireference systems with large active spaces. Here we discuss CT theory's intruder state problem and why our previous approach of overlap matrix truncation becomes infeasible for sufficiently large active spaces. We propose the use of strongly and weakly contracted excitation operators as alternatives for dealing with intruder states in CT theory. The performance of these operators is evaluated for the H2O, N2, and NiO molecules, with comparisons made to complete active space second order perturbation theory and Davidson-corrected multireference configuration interaction theory. Finally, using a combination of strongly contracted CT theory and orbital-optimized density matrix renormalization group theory, we evaluate the singlet-triplet gap of free base porphin using an active space containing all 24 out-of-plane 2p orbitals. Modeling dynamic correlation with an active space of this size is currently only possible using CT theory.

Proton-driven spin diffusion in rotating solids via reversible and irreversible quantum dynamics

PubMed Central

Veshtort, Mikhail; Griffin, Robert G.

2011-01-01

Proton-driven spin diffusion (PDSD) experiments in rotating solids have received a great deal of attention as a potential source of distance constraints in large biomolecules. However, the quantitative relationship between the molecular structure and observed spin diffusion has remained obscure due to the lack of an accurate theoretical description of the spin dynamics in these experiments. We start with presenting a detailed relaxation theory of PDSD in rotating solids that provides such a description. The theory applies to both conventional and radio-frequency-assisted PDSD experiments and extends to the non-Markovian regime to include such phenomena as rotational resonance (R2). The basic kinetic equation of the theory in the non-Markovian regime has the form of a memory function equation, with the role of the memory function played by the correlation function. The key assumption used in the derivation of this equation expresses the intuitive notion of the irreversible dissipation of coherences in macroscopic systems. Accurate expressions for the correlation functions and for the spin diffusion constants are given. The theory predicts that the spin diffusion constants governing the multi-site PDSD can be approximated by the constants observed in the two-site diffusion. Direct numerical simulations of PDSD dynamics via reversible Liouville-von Neumann equation are presented to support and compliment the theory. Remarkably, an exponential decay of the difference magnetization can be observed in such simulations in systems consisting of only 12 spins. This is a unique example of a real physical system whose typically macroscopic and apparently irreversible behavior can be traced via reversible microscopic dynamics. An accurate value for the spin diffusion constant can be usually obtained through direct simulations of PDSD in systems consisting of two 13C nuclei and about ten 1H nuclei from their nearest environment. Spin diffusion constants computed by this method are in excellent agreement with the spin diffusion constants obtained through equations given by the relaxation theory of PDSD. The constants resulting from these two approaches were also in excellent agreement with the results of 2D rotary resonance recoupling proton-driven spin diffusion (R3-PDSD) experiments performed in three model compounds, where magnetization exchange occurred over distances up to 4.9 Å. With the methodology presented, highly accurate internuclear distances can be extracted from such data. Relayed transfer of magnetization between distant nuclei appears to be the main (and apparently resolvable) source of uncertainty in such measurements. The non-Markovian kinetic equation was applied to the analysis of the R2 spin dynamics. The conventional semi-phenomenological treatment of relxation in R2 has been shown to be equivalent to the assumption of the Lorentzian spectral density function in the relaxatoin theory of PDSD. As this assumption is a poor approximation in real physical systems, the conventional R2 treatment is likely to carry a significant model error that has not been recognized previously. The relaxation theory of PDSD appears to provide an accurate, parameter-free alternative. Predictions of this theory agreed well with the full quantum mechanical simulations of the R2 dynamics in the few simple model systems we considered. PMID:21992326

Chain representations of Open Quantum Systems and Lieb-Robinson like bounds for the dynamics

NASA Astrophysics Data System (ADS)

Woods, Mischa

2013-03-01

This talk is concerned with the mapping of the Hamiltonian of open quantum systems onto chain representations, which forms the basis for a rigorous theory of the interaction of a system with its environment. This mapping progresses as an interaction which gives rise to a sequence of residual spectral densities of the system. The rigorous mathematical properties of this mapping have been unknown so far. Here we develop the theory of secondary measures to derive an analytic, expression for the sequence solely in terms of the initial measure and its associated orthogonal polynomials of the first and second kind. These mappings can be thought of as taking a highly nonlocal Hamiltonian to a local Hamiltonian. In the latter, a Lieb-Robinson like bound for the dynamics of the open quantum system makes sense. We develop analytical bounds on the error to observables of the system as a function of time when the semi-infinite chain in truncated at some finite length. The fact that this is possible shows that there is a finite ``Speed of sound'' in these chain representations. This has many implications of the simulatability of open quantum systems of this type and demonstrates that a truncated chain can faithfully reproduce the dynamics at shorter times. These results make a significant and mathematically rigorous contribution to the understanding of the theory of open quantum systems; and pave the way towards the efficient simulation of these systems, which within the standard methods, is often an intractable problem. EPSRC CDT in Controlled Quantum Dynamics, EU STREP project and Alexander von Humboldt Foundation

Applications of Density Functional Theory in Soft Condensed Matter

NASA Astrophysics Data System (ADS)

Löwen, Hartmut

Applications of classical density functional theory (DFT) to soft matter systems like colloids, liquid crystals and polymer solutions are discussed with a focus on the freezing transition and on nonequilibrium Brownian dynamics. First, after a brief reminder of equilibrium density functional theory, DFT is applied to the freezing transition of liquids into crystalline lattices. In particular, spherical particles with radially symmetric pair potentials will be treated (like hard spheres, the classical one-component plasma or Gaussian-core particles). Second, the DFT will be generalized towards Brownian dynamics in order to tackle nonequilibrium problems. After a general introduction to Brownian dynamics using the complementary Smoluchowski and Langevin pictures appropriate for the dynamics of colloidal suspensions, the dynamical density functional theory (DDFT) will be derived from the Smoluchowski equation. This will be done first for spherical particles (e.g. hard spheres or Gaussian-cores) without hydrodynamic interactions. Then we show how to incorporate hydrodynamic interactions between the colloidal particles into the DDFT framework and compare to Brownian dynamics computer simulations. Third orientational degrees of freedom (rod-like particles) will be considered as well. In the latter case, the stability of intermediate liquid crystalline phases (isotropic, nematic, smectic-A, plastic crystals etc) can be predicted. Finally, the corresponding dynamical extension of density functional theory towards orientational degrees of freedom is proposed and the collective behaviour of "active" (self-propelled) Brownian particles is briefly discussed.

Multiple dynamics in a single predator-prey system: experimental effects of food quality.

PubMed Central

Nelson, W A; McCauley, E; Wrona, F J

2001-01-01

Recent work with the freshwater zooplankton Daphnia has suggested that the quality of its algal prey can have a significant effect on its demographic rates and life-history patterns. Predator-prey theory linking food quantity and food quality predicts that a single system should be able to display two distinct patterns of population dynamics. One pattern is predicted to have high herbivore and low algal biomass dynamics (high HBD), whereas the other is predicted to have low herbivore and high algal biomass dynamics (low HBD). Despite these predictions and the stoichiometric evidence that many phytoplankton communities may have poor access to food of quality, there have been few tests of whether a dynamic predator-prey system can display both of these distinct patterns. Here we report, to the authors' knowledge, the first evidence for two dynamical patterns, as predicted by theory, in a single predator-prey system. We show that the high HBD is a result of food quantity effects and that the low HBD is a result of food quality effects, which are maintained by phosphorus limitation in the predator. These results provide an important link between the known effects of nutrient limitation in herbivores and the significance of prey quality in predator-prey population dynamics in natural zooplankton communities. PMID:11410147

Nuclear Fission: from more phenomenology and adjusted parameters to more fundamental theory and increased predictive power

NASA Astrophysics Data System (ADS)

Bulgac, Aurel; Jin, Shi; Magierski, Piotr; Roche, Kenneth; Schunck, Nicolas; Stetcu, Ionel

2017-11-01

Two major recent developments in theory and computational resources created the favorable conditions for achieving a microscopic description of fission dynamics in classically allowed regions of the collective potential energy surface, almost eighty years after its discovery in 1939 by Hahn and Strassmann [1]. The first major development was in theory, the extension of the Time-Dependent Density Functional Theory (TDDFT) [2-5] to superfluid fermion systems [6]. The second development was in computing, the emergence of powerful enough supercomputers capable of solving the complex systems of equations describing the time evolution in three dimensions without any restrictions of hundreds of strongly interacting nucleons. Thus the conditions have been created to renounce phenomenological models and incomplete microscopic treatments with uncontrollable approximations and/or assumptions in the description of the complex dynamics of fission. Even though the available nuclear energy density functionals (NEDFs) are phenomenological still, their accuracy is improving steadily and the prospects of being able to perform calculations of the nuclear fission dynamics and to predict many properties of the fission fragments, otherwise not possible to extract from experiments.

Reconstruction of the dynamics of the climatic system from time-series data

PubMed Central

Nicolis, C.; Nicolis, G.

1986-01-01

The oxygen isotope record of the last million years, as provided by a deep sea core sediment, is analyzed by a method recently developed in the theory of dynamical systems. The analysis suggests that climatic variability is the manifestation of a chaotic dynamics described by an attractor of fractal dimensionality. A quantitative measure of the limited predictability of the climatic system is provided by the evaluation of the time-correlation function and the largest positive Lyapounov exponent of the system. PMID:16593650

Rotation in vibration, optimization, and aeroelastic stability problems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Kaza, K. R. V.

1974-01-01

The effects of rotation in the areas of vibrations, dynamic stability, optimization, and aeroelasticity were studied. The governing equations of motion for the study of vibration and dynamic stability of a rapidly rotating deformable body were developed starting from the nonlinear theory of elasticity. Some common features such as the limitations of the classical theory of elasticity, the choice of axis system, the property of self-adjointness, the phenomenon of frequency splitting, shortcomings of stability methods as applied to gyroscopic systems, and the effect of internal and external damping on stability in gyroscopic systems are identified and discussed, and are then applied to three specific problems.

Adiabatic invariants in stellar dynamics. 2: Gravitational shocking

NASA Technical Reports Server (NTRS)

Weinberg, Martin D.

1994-01-01

A new theory of gravitational shocking based on time-dependent perturbation theory shows that the changes in energy and angular momentum due to a slowly varying disturbance are not exponentially small for stellar dynamical systems in general. It predicts significant shock heating by slowly varying perturbations previously thought to be negligible according to the adiabatic criterion. The theory extends the scenarios traditionally computed only with the impulse approximation and is applicable to a wide class of disturbances. The approach is applied specifically to the problem of disk shocking of star clusters.

Neurodynamic system theory: scope and limits.

PubMed

Erdi, P

1993-06-01

This paper proposes that neurodynamic system theory may be used to connect structural and functional aspects of neural organization. The paper claims that generalized causal dynamic models are proper tools for describing the self-organizing mechanism of the nervous system. In particular, it is pointed out that ontogeny, development, normal performance, learning, and plasticity, can be treated by coherent concepts and formalism. Taking into account the self-referential character of the brain, autopoiesis, endophysics and hermeneutics are offered as elements of a poststructuralist brain (-mind-computer) theory.

Electro-osmotic flow of a model electrolyte

NASA Astrophysics Data System (ADS)

Zhu, Wei; Singer, Sherwin J.; Zheng, Zhi; Conlisk, A. T.

2005-04-01

Electro-osmotic flow is studied by nonequilibrium molecular dynamics simulations in a model system chosen to elucidate various factors affecting the velocity profile and facilitate comparison with existing continuum theories. The model system consists of spherical ions and solvent, with stationary, uniformly charged walls that make a channel with a height of 20 particle diameters. We find that hydrodynamic theory adequately describes simple pressure-driven (Poiseuille) flow in this model. However, Poisson-Boltzmann theory fails to describe the ion distribution in important situations, and therefore continuum fluid dynamics based on the Poisson-Boltzmann ion distribution disagrees with simulation results in those situations. The failure of Poisson-Boltzmann theory is traced to the exclusion of ions near the channel walls resulting from reduced solvation of the ions in that region. When a corrected ion distribution is used as input for hydrodynamic theory, agreement with numerical simulations is restored. An analytic theory is presented that demonstrates that repulsion of the ions from the channel walls increases the flow rate, and attraction to the walls has the opposite effect. A recent numerical study of electro-osmotic flow is reanalyzed in the light of our findings, and the results conform well to our conclusions for the model system.

A tutorial on dynamical systems concepts applied to Lagrangian transport in oceanic flows defined as finite time data sets: Theoretical and computational issues

NASA Astrophysics Data System (ADS)

Mancho, Ana M.; Small, Des; Wiggins, Stephen

2006-12-01

In the past 15 years the framework and ideas from dynamical systems theory have been applied to a variety of transport and mixing problems in oceanic flows. The motivation for this approach comes directly from advances in observational capabilities in oceanography (e.g., drifter deployments, remote sensing capabilities, satellite imagery, etc.) which reveal space-time structures that are highly suggestive of the structures one visualizes in the global, geometrical study of dynamical systems theory. In this tutorial, we motivate this approach by showing the relationship between fluid transport in two-dimensional time-periodic incompressible flows and the geometrical structures that exist for two-dimensional area-preserving maps, such as hyperbolic periodic orbits, their stable and unstable manifolds and KAM (Kolmogorov-Arnold-Moser) tori. This serves to set the stage for the attempt to “transfer” this approach to more realistic flows modelling the ocean. However, in order to accomplish this several difficulties must be overcome. The first difficulty that confronts us that any attempt to carry out a dynamical systems approach to transport requires us to obtain the appropriate “dynamical system”, which is the velocity field describing the fluid flow. In general, adequate model velocity fields are obtained by numerical solution of appropriate partial differential equations describing the dynamical evolution of the velocity field. Numerical solution of the partial differential equations can only be done for a finite time interval, and since the ocean is generally not time-periodic, this leads to a new type of dynamical system: a finite-time, aperiodically time-dependent velocity field defined as a data set on a space-time grid. The global, geometrical analysis of transport in such dynamical systems requires both new concepts and new analytical and computational tools, as well as the necessity to discard some of the standard ideas and results from dynamical systems theory. The purpose of this tutorial is to describe these new concepts and analytical tools first using simple dynamical systems where quantities can be computed exactly. We then discuss their computational implications and implementation in the context of a model geophysical flow: a turbulent wind-driven double-gyre in the quasigeostrophic approximation.

Interdisciplinary and physics challenges of network theory

NASA Astrophysics Data System (ADS)

Bianconi, Ginestra

2015-09-01

Network theory has unveiled the underlying structure of complex systems such as the Internet or the biological networks in the cell. It has identified universal properties of complex networks, and the interplay between their structure and dynamics. After almost twenty years of the field, new challenges lie ahead. These challenges concern the multilayer structure of most of the networks, the formulation of a network geometry and topology, and the development of a quantum theory of networks. Making progress on these aspects of network theory can open new venues to address interdisciplinary and physics challenges including progress on brain dynamics, new insights into quantum technologies, and quantum gravity.

Flory-Stockmayer analysis on reprocessable polymer networks

NASA Astrophysics Data System (ADS)

Li, Lingqiao; Chen, Xi; Jin, Kailong; Torkelson, John

Reprocessable polymer networks can undergo structure rearrangement through dynamic chemistries under proper conditions, making them a promising candidate for recyclable crosslinked materials, e.g. tires. This research field has been focusing on various chemistries. However, there has been lacking of an essential physical theory explaining the relationship between abundancy of dynamic linkages and reprocessability. Based on the classical Flory-Stockmayer analysis on network gelation, we developed a similar analysis on reprocessable polymer networks to quantitatively predict the critical condition for reprocessability. Our theory indicates that it is unnecessary for all bonds to be dynamic to make the resulting network reprocessable. As long as there is no percolated permanent network in the system, the material can fully rearrange. To experimentally validate our theory, we used a thiol-epoxy network model system with various dynamic linkage compositions. The stress relaxation behavior of resulting materials supports our theoretical prediction: only 50 % of linkages between crosslinks need to be dynamic for a tri-arm network to be reprocessable. Therefore, this analysis provides the first fundamental theoretical platform for designing and evaluating reprocessable polymer networks. We thank McCormick Research Catalyst Award Fund and ISEN cluster fellowship (L. L.) for funding support.

Quantum learning of classical stochastic processes: The completely positive realization problem

NASA Astrophysics Data System (ADS)

Monràs, Alex; Winter, Andreas

2016-01-01

Among several tasks in Machine Learning, a specially important one is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of this is the task of inferring the hidden Markov model underlying a given stochastic process. This is known as the positive realization problem (PRP), [L. Benvenuti and L. Farina, IEEE Trans. Autom. Control 49(5), 651-664 (2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece in the broad field of positive systems theory. We consider the scenario where the latent variables are quantum (i.e., quantum states of a finite-dimensional system) and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument — if any — yields the process at hand by iterative application. We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the hidden Markov model, or the iterated quantum instrument, is however devoid of any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The completely positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine learning, device-independent characterization and reverse-engineering of stochastic processes and quantum processors, and more generally, of dynamical processes with quantum memory [M. Guţă, Phys. Rev. A 83(6), 062324 (2011); M. Guţă and N. Yamamoto, e-print arXiv:1303.3771(2013)].

Colloquium: Non-Markovian dynamics in open quantum systems

NASA Astrophysics Data System (ADS)

Breuer, Heinz-Peter; Laine, Elsi-Mari; Piilo, Jyrki; Vacchini, Bassano

2016-04-01

The dynamical behavior of open quantum systems plays a key role in many applications of quantum mechanics, examples ranging from fundamental problems, such as the environment-induced decay of quantum coherence and relaxation in many-body systems, to applications in condensed matter theory, quantum transport, quantum chemistry, and quantum information. In close analogy to a classical Markovian stochastic process, the interaction of an open quantum system with a noisy environment is often modeled phenomenologically by means of a dynamical semigroup with a corresponding time-independent generator in Lindblad form, which describes a memoryless dynamics of the open system typically leading to an irreversible loss of characteristic quantum features. However, in many applications open systems exhibit pronounced memory effects and a revival of genuine quantum properties such as quantum coherence, correlations, and entanglement. Here recent theoretical results on the rich non-Markovian quantum dynamics of open systems are discussed, paying particular attention to the rigorous mathematical definition, to the physical interpretation and classification, as well as to the quantification of quantum memory effects. The general theory is illustrated by a series of physical examples. The analysis reveals that memory effects of the open system dynamics reflect characteristic features of the environment which opens a new perspective for applications, namely, to exploit a small open system as a quantum probe signifying nontrivial features of the environment it is interacting with. This Colloquium further explores the various physical sources of non-Markovian quantum dynamics, such as structured environmental spectral densities, nonlocal correlations between environmental degrees of freedom, and correlations in the initial system-environment state, in addition to developing schemes for their local detection. Recent experiments addressing the detection, quantification, and control of non-Markovian quantum dynamics are also briefly discussed.

Modal interaction in linear dynamic systems near degenerate modes

NASA Technical Reports Server (NTRS)

Afolabi, D.

1991-01-01

In various problems in structural dynamics, the eigenvalues of a linear system depend on a characteristic parameter of the system. Under certain conditions, two eigenvalues of the system approach each other as the characteristic parameter is varied, leading to modal interaction. In a system with conservative coupling, the two eigenvalues eventually repel each other, leading to the curve veering effect. In a system with nonconservative coupling, the eigenvalues continue to attract each other, eventually colliding, leading to eigenvalue degeneracy. Modal interaction is studied in linear systems with conservative and nonconservative coupling using singularity theory, sometimes known as catastrophe theory. The main result is this: eigenvalue degeneracy is a cause of instability; in systems with conservative coupling, it induces only geometric instability, whereas in systems with nonconservative coupling, eigenvalue degeneracy induces both geometric and elastic instability. Illustrative examples of mechanical systems are given.

Dynamical Analyses for Developmental Science: A Primer for Intrigued Scientists

ERIC Educational Resources Information Center

DiDonato, M. D.; England, D.; Martin, C. L.; Amazeen, P. G.

2013-01-01

Dynamical systems theory is becoming more popular in social and developmental science. However, unfamiliarity with dynamical analysis techniques remains an obstacle for developmentalists who would like to quantitatively apply dynamics in their own research. The goal of this article is to address this issue by clearly and simply presenting several…

Bridging Developmental Systems Theory and Evolutionary Psychology Using Dynamic Optimization

ERIC Educational Resources Information Center

Frankenhuis, Willem E.; Panchanathan, Karthik; Clark Barrett, H.

2013-01-01

Interactions between evolutionary psychologists and developmental systems theorists have been largely antagonistic. This is unfortunate because potential synergies between the two approaches remain unexplored. This article presents a method that may help to bridge the divide, and that has proven fruitful in biology: dynamic optimization. Dynamic…

The Self as a Complex Dynamic System

ERIC Educational Resources Information Center

Mercer, Sarah

2011-01-01

This article explores the potential offered by complexity theories for understanding language learners' sense of self and attempts to show how the self might usefully be conceived of as a complex dynamic system. Rather than presenting empirical findings, the article discusses existent research on the self and aims at outlining a conceptual…

Closed Loop Vibrational Control: Theory and Applications

DTIC Science & Technology

1993-10-01

the open loop system dynamics will be close to that of Bit. However, in general, in a closed loop system with a specified feedback co-’ - oller , for...Juang, and G. Rodriguez , "Formulations and Applications of Large Structure Actuator and Sensor Placements," Second VPI & SU/AIAA Symposium on Dynamics

Dynamics of global supply chain and electric power networks: Models, pricing analysis, and computations

NASA Astrophysics Data System (ADS)

Matsypura, Dmytro

In this dissertation, I develop a new theoretical framework for the modeling, pricing analysis, and computation of solutions to electric power supply chains with power generators, suppliers, transmission service providers, and the inclusion of consumer demands. In particular, I advocate the application of finite-dimensional variational inequality theory, projected dynamical systems theory, game theory, network theory, and other tools that have been recently proposed for the modeling and analysis of supply chain networks (cf. Nagurney (2006)) to electric power markets. This dissertation contributes to the extant literature on the modeling, analysis, and solution of supply chain networks, including global supply chains, in general, and electric power supply chains, in particular, in the following ways. It develops a theoretical framework for modeling, pricing analysis, and computation of electric power flows/transactions in electric power systems using the rationale for supply chain analysis. The models developed include both static and dynamic ones. The dissertation also adds a new dimension to the methodology of the theory of projected dynamical systems by proving that, irrespective of the speeds of adjustment, the equilibrium of the system remains the same. Finally, I include alternative fuel suppliers, along with their behavior into the supply chain modeling and analysis framework. This dissertation has strong practical implications. In an era in which technology and globalization, coupled with increasing risk and uncertainty, complicate electricity demand and supply within and between nations, the successful management of electric power systems and pricing become increasingly pressing topics with relevance not only for economic prosperity but also national security. This dissertation addresses such related topics by providing models, pricing tools, and algorithms for decentralized electric power supply chains. This dissertation is based heavily on the following coauthored papers: Nagurney, Cruz, and Matsypura (2003), Nagurney and Matsypura (2004, 2005, 2006), Matsypura and Nagurney (2005), Matsypura, Nagurney, and Liu (2006).

Nonlinear dynamics and predictability in the atmospheric sciences

NASA Technical Reports Server (NTRS)

Ghil, M.; Kimoto, M.; Neelin, J. D.

1991-01-01

Systematic applications of nonlinear dynamics to studies of the atmosphere and climate are reviewed for the period 1987-1990. Problems discussed include paleoclimatic applications, low-frequency atmospheric variability, and interannual variability of the ocean-atmosphere system. Emphasis is placed on applications of the successive bifurcation approach and the ergodic theory of dynamical systems to understanding and prediction of intraseasonal, interannual, and Quaternary climate changes.

Quantum electron-vibrational dynamics at finite temperature: Thermo field dynamics approach

NASA Astrophysics Data System (ADS)

Borrelli, Raffaele; Gelin, Maxim F.

2016-12-01

Quantum electron-vibrational dynamics in molecular systems at finite temperature is described using an approach based on the thermo field dynamics theory. This formulation treats temperature effects in the Hilbert space without introducing the Liouville space. A comparison with the theoretically equivalent density matrix formulation shows the key numerical advantages of the present approach. The solution of thermo field dynamics equations with a novel technique for the propagation of tensor trains (matrix product states) is discussed. Numerical applications to model spin-boson systems show that the present approach is a promising tool for the description of quantum dynamics of complex molecular systems at finite temperature.

Random Matrix Theory in molecular dynamics analysis.

PubMed

Palese, Luigi Leonardo

2015-01-01

It is well known that, in some situations, principal component analysis (PCA) carried out on molecular dynamics data results in the appearance of cosine-shaped low index projections. Because this is reminiscent of the results obtained by performing PCA on a multidimensional Brownian dynamics, it has been suggested that short-time protein dynamics is essentially nothing more than a noisy signal. Here we use Random Matrix Theory to analyze a series of short-time molecular dynamics experiments which are specifically designed to be simulations with high cosine content. We use as a model system the protein apoCox17, a mitochondrial copper chaperone. Spectral analysis on correlation matrices allows to easily differentiate random correlations, simply deriving from the finite length of the process, from non-random signals reflecting the intrinsic system properties. Our results clearly show that protein dynamics is not really Brownian also in presence of the cosine-shaped low index projections on principal axes. Copyright © 2014 Elsevier B.V. All rights reserved.

Dynamical influence processes on networks: general theory and applications to social contagion.

PubMed

Harris, Kameron Decker; Danforth, Christopher M; Dodds, Peter Sheridan

2013-08-01

We study binary state dynamics on a network where each node acts in response to the average state of its neighborhood. By allowing varying amounts of stochasticity in both the network and node responses, we find different outcomes in random and deterministic versions of the model. In the limit of a large, dense network, however, we show that these dynamics coincide. We construct a general mean-field theory for random networks and show this predicts that the dynamics on the network is a smoothed version of the average response function dynamics. Thus, the behavior of the system can range from steady state to chaotic depending on the response functions, network connectivity, and update synchronicity. As a specific example, we model the competing tendencies of imitation and nonconformity by incorporating an off-threshold into standard threshold models of social contagion. In this way, we attempt to capture important aspects of fashions and societal trends. We compare our theory to extensive simulations of this "limited imitation contagion" model on Poisson random graphs, finding agreement between the mean-field theory and stochastic simulations.

Direct Observation of Dynamical Quantum Phase Transitions in an Interacting Many-Body System

NASA Astrophysics Data System (ADS)

Jurcevic, P.; Shen, H.; Hauke, P.; Maier, C.; Brydges, T.; Hempel, C.; Lanyon, B. P.; Heyl, M.; Blatt, R.; Roos, C. F.

2017-08-01

The theory of phase transitions represents a central concept for the characterization of equilibrium matter. In this work we study experimentally an extension of this theory to the nonequilibrium dynamical regime termed dynamical quantum phase transitions (DQPTs). We investigate and measure DQPTs in a string of ions simulating interacting transverse-field Ising models. During the nonequilibrium dynamics induced by a quantum quench we show for strings of up to 10 ions the direct detection of DQPTs by revealing nonanalytic behavior in time. Moreover, we provide a link between DQPTs and the dynamics of other quantities such as the magnetization, and we establish a connection between DQPTs and entanglement production.

Direct Observation of Dynamical Quantum Phase Transitions in an Interacting Many-Body System.

PubMed

Jurcevic, P; Shen, H; Hauke, P; Maier, C; Brydges, T; Hempel, C; Lanyon, B P; Heyl, M; Blatt, R; Roos, C F

2017-08-25

The theory of phase transitions represents a central concept for the characterization of equilibrium matter. In this work we study experimentally an extension of this theory to the nonequilibrium dynamical regime termed dynamical quantum phase transitions (DQPTs). We investigate and measure DQPTs in a string of ions simulating interacting transverse-field Ising models. During the nonequilibrium dynamics induced by a quantum quench we show for strings of up to 10 ions the direct detection of DQPTs by revealing nonanalytic behavior in time. Moreover, we provide a link between DQPTs and the dynamics of other quantities such as the magnetization, and we establish a connection between DQPTs and entanglement production.

Information processing and dynamics in minimally cognitive agents.

PubMed

Beer, Randall D; Williams, Paul L

2015-01-01

There has been considerable debate in the literature about the relative merits of information processing versus dynamical approaches to understanding cognitive processes. In this article, we explore the relationship between these two styles of explanation using a model agent evolved to solve a relational categorization task. Specifically, we separately analyze the operation of this agent using the mathematical tools of information theory and dynamical systems theory. Information-theoretic analysis reveals how task-relevant information flows through the system to be combined into a categorization decision. Dynamical analysis reveals the key geometrical and temporal interrelationships underlying the categorization decision. Finally, we propose a framework for directly relating these two different styles of explanation and discuss the possible implications of our analysis for some of the ongoing debates in cognitive science. Copyright © 2014 Cognitive Science Society, Inc.

SIAM conference on applications of dynamical systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

1992-01-01

A conference (Oct.15--19, 1992, Snowbird, Utah; sponsored by SIAM (Society for Industrial and Applied Mathematics) Activity Group on Dynamical Systems) was held that highlighted recent developments in applied dynamical systems. The main lectures and minisymposia covered theory about chaotic motion, applications in high energy physics and heart fibrillations, turbulent motion, Henon map and attractor, integrable problems in classical physics, pattern formation in chemical reactions, etc. The conference fostered an exchange between mathematicians working on theoretical issues of modern dynamical systems and applied scientists. This two-part document contains abstracts, conference program, and an author index.

SIAM conference on applications of dynamical systems. Abstracts and author index

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

1992-12-31

A conference (Oct.15--19, 1992, Snowbird, Utah; sponsored by SIAM (Society for Industrial and Applied Mathematics) Activity Group on Dynamical Systems) was held that highlighted recent developments in applied dynamical systems. The main lectures and minisymposia covered theory about chaotic motion, applications in high energy physics and heart fibrillations, turbulent motion, Henon map and attractor, integrable problems in classical physics, pattern formation in chemical reactions, etc. The conference fostered an exchange between mathematicians working on theoretical issues of modern dynamical systems and applied scientists. This two-part document contains abstracts, conference program, and an author index.

A Complex Systems Framework for Research on Leadership and Organizational Dynamics in Academic Libraries

ERIC Educational Resources Information Center

Gilstrap, Donald L.

2009-01-01

This article provides a historiographical analysis of major leadership and organizational development theories that have shaped our thinking about how we lead and administrate academic libraries. Drawing from behavioral, cognitive, systems, and complexity theories, this article discusses major theorists and research studies appearing over the past…

Generalized-active-space pair-density functional theory: an efficient method to study large, strongly correlated, conjugated systems.

PubMed

Ghosh, Soumen; Cramer, Christopher J; Truhlar, Donald G; Gagliardi, Laura

2017-04-01

Predicting ground- and excited-state properties of open-shell organic molecules by electronic structure theory can be challenging because an accurate treatment has to correctly describe both static and dynamic electron correlation. Strongly correlated systems, i.e. , systems with near-degeneracy correlation effects, are particularly troublesome. Multiconfigurational wave function methods based on an active space are adequate in principle, but it is impractical to capture most of the dynamic correlation in these methods for systems characterized by many active electrons. We recently developed a new method called multiconfiguration pair-density functional theory (MC-PDFT), that combines the advantages of wave function theory and density functional theory to provide a more practical treatment of strongly correlated systems. Here we present calculations of the singlet-triplet gaps in oligoacenes ranging from naphthalene to dodecacene. Calculations were performed for unprecedently large orbitally optimized active spaces of 50 electrons in 50 orbitals, and we test a range of active spaces and active space partitions, including four kinds of frontier orbital partitions. We show that MC-PDFT can predict the singlet-triplet splittings for oligoacenes consistent with the best available and much more expensive methods, and indeed MC-PDFT may constitute the benchmark against which those other models should be compared, given the absence of experimental data.

Theory of few photon dynamics in light emitting quantum dot devices

NASA Astrophysics Data System (ADS)

Carmele, Alexander; Richter, Marten; Sitek, Anna; Knorr, Andreas

2009-10-01

We present a modified cluster expansion to describe single-photon emitters in a semiconductor environment. We calculate microscopically to what extent semiconductor features in quantum dot-wetting layer systems alter the exciton and photon dynamics in comparison to the atom-like emission dynamics. We access these systems by the photon-probability-cluster-expansion: a reliable approach for few photon dynamics in many body electron systems. As a first application, we show that the amplitude of vacuum Rabi flops determines the number of electrons in the quantum dot.

In-Flight Aeroelastic Stability of the Thermal Protection System on the NASA HIAD, Part II: Nonlinear Theory and Extended Aerodynamics

NASA Technical Reports Server (NTRS)

Goldman, Benjamin D.; Dowell, Earl H.; Scott, Robert C.

2015-01-01

Conical shell theory and a supersonic potential flow aerodynamic theory are used to study the nonlinear pressure buckling and aeroelastic limit cycle behavior of the thermal protection system for NASA's Hypersonic Inflatable Aerodynamic Decelerator. The structural model of the thermal protection system consists of an orthotropic conical shell of the Donnell type, resting on several circumferential elastic supports. Classical Piston Theory is used initially for the aerodynamic pressure, but was found to be insufficient at low supersonic Mach numbers. Transform methods are applied to the convected wave equation for potential flow, and a time-dependent aerodynamic pressure correction factor is obtained. The Lagrangian of the shell system is formulated in terms of the generalized coordinates for all displacements and the Rayleigh-Ritz method is used to derive the governing differential-algebraic equations of motion. Aeroelastic limit cycle oscillations and buckling deformations are calculated in the time domain using a Runge-Kutta method in MATLAB. Three conical shell geometries were considered in the present analysis: a 3-meter diameter 70 deg. cone, a 3.7-meter 70 deg. cone, and a 6-meter diameter 70 deg. cone. The 6-meter configuration was loaded statically and the results were compared with an experimental load test of a 6-meter HIAD. Though agreement between theoretical and experimental strains was poor, the circumferential wrinkling phenomena observed during the experiments was captured by the theory and axial deformations were qualitatively similar in shape. With Piston Theory aerodynamics, the nonlinear flutter dynamic pressures of the 3-meter configuration were in agreement with the values calculated using linear theory, and the limit cycle amplitudes were generally on the order of the shell thickness. The effect of axial tension was studied for this configuration, and increasing tension was found to decrease the limit cycle amplitudes when the circumferential elastic supports were neglected, but resulted in more complex behavior when the supports were included. The nominal flutter dynamic pressure of the 3.7-meter configuration was significantly lower than that of the 3-meter, and it was found that two sets of natural modes coalesce to flutter modes near the same dynamic pressure. This resulted in a significant drop in the limit cycle frequencies at higher dynamic pressures, where the flutter mode with the lower frequency becomes more critical. Pre-buckling pressure loads and the aerodynamic pressure correction factor were studied for all geometries, and these effects resulted in significantly lower flutter boundaries compared with Piston Theory alone. The maximum dynamic pressure predicted by aerodynamic simulations of a proposed 3.7-meter HIAD vehicle was still lower than any of the calculated flutter dynamic pressures, suggesting that aeroelastic effects for this vehicle are of little concern.

Survival and weak chaos.

PubMed

Nee, Sean

2018-05-01

Survival analysis in biology and reliability theory in engineering concern the dynamical functioning of bio/electro/mechanical units. Here we incorporate effects of chaotic dynamics into the classical theory. Dynamical systems theory now distinguishes strong and weak chaos. Strong chaos generates Type II survivorship curves entirely as a result of the internal operation of the system, without any age-independent, external, random forces of mortality. Weak chaos exhibits (a) intermittency and (b) Type III survivorship, defined as a decreasing per capita mortality rate: engineering explicitly defines this pattern of decreasing hazard as 'infant mortality'. Weak chaos generates two phenomena from the normal functioning of the same system. First, infant mortality- sensu engineering-without any external explanatory factors, such as manufacturing defects, which is followed by increased average longevity of survivors. Second, sudden failure of units during their normal period of operation, before the onset of age-dependent mortality arising from senescence. The relevance of these phenomena encompasses, for example: no-fault-found failure of electronic devices; high rates of human early spontaneous miscarriage/abortion; runaway pacemakers; sudden cardiac death in young adults; bipolar disorder; and epilepsy.

Survival and weak chaos

PubMed Central

2018-01-01

Survival analysis in biology and reliability theory in engineering concern the dynamical functioning of bio/electro/mechanical units. Here we incorporate effects of chaotic dynamics into the classical theory. Dynamical systems theory now distinguishes strong and weak chaos. Strong chaos generates Type II survivorship curves entirely as a result of the internal operation of the system, without any age-independent, external, random forces of mortality. Weak chaos exhibits (a) intermittency and (b) Type III survivorship, defined as a decreasing per capita mortality rate: engineering explicitly defines this pattern of decreasing hazard as ‘infant mortality’. Weak chaos generates two phenomena from the normal functioning of the same system. First, infant mortality—sensu engineering—without any external explanatory factors, such as manufacturing defects, which is followed by increased average longevity of survivors. Second, sudden failure of units during their normal period of operation, before the onset of age-dependent mortality arising from senescence. The relevance of these phenomena encompasses, for example: no-fault-found failure of electronic devices; high rates of human early spontaneous miscarriage/abortion; runaway pacemakers; sudden cardiac death in young adults; bipolar disorder; and epilepsy. PMID:29892407

Quantization of systems with temporally varying discretization. II. Local evolution moves

NASA Astrophysics Data System (ADS)

Höhn, Philipp A.

2014-10-01

Several quantum gravity approaches and field theory on an evolving lattice involve a discretization changing dynamics generated by evolution moves. Local evolution moves in variational discrete systems (1) are a generalization of the Pachner evolution moves of simplicial gravity models, (2) update only a small subset of the dynamical data, (3) change the number of kinematical and physical degrees of freedom, and (4) generate a dynamical (or canonical) coarse graining or refining of the underlying discretization. To systematically explore such local moves and their implications in the quantum theory, this article suitably expands the quantum formalism for global evolution moves, constructed in Paper I [P. A. Höhn, "Quantization of systems with temporally varying discretization. I. Evolving Hilbert spaces," J. Math. Phys. 55, 083508 (2014); e-print arXiv:1401.6062 [gr-qc

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

PubMed

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.

Application of Tube Dynamics to Non-Statistical Reaction Processes

NASA Astrophysics Data System (ADS)

Gabern, F.; Koon, W. S.; Marsden, J. E.; Ross, S. D.; Yanao, T.

2006-06-01

A technique based on dynamical systems theory is introduced for the computation of lifetime distributions and rates of chemical reactions and scattering phenomena, even in systems that exhibit non-statistical behavior. In particular, we merge invariant manifold tube dynamics with Monte Carlo volume determination for accurate rate calculations. This methodology is applied to a three-degree-of-freedom model problem and some ideas on how it might be extended to higher-degree-of-freedom systems are presented.

Dynamic stability of electrodynamic maglev systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cai, Y.; Chen, S.S.; Mulcahy, T.M.

1997-01-01

Because dynamic instabilities are not acceptable in any commercial maglev system, it is important to consider dynamic instability in the development of all maglev systems. This study considers the stability of maglev systems based on mathematical models and experimental data. Divergence and flutter are obtained for coupled vibration of a three-degree-of-freedom maglev vehicle on a guideway consisting of double L-shaped aluminum segments. The theory and analysis for motion-dependent magnetic-force-induced instability developed in this study provides basic stability characteristics and identifies future research needs for maglev systems.

The solar nebula and the planetesimal disk

NASA Technical Reports Server (NTRS)

Ward, W. R.

1984-01-01

Two popular theories of solar system formation are briefly reviewed, then used as background in an examination of several new developments related to planetary ring dynamics that promise to have great impact on future research. Most important are the incorporation of accretion disk and density wave theories into cosmogonic theory. A successful integration of these mechanisms may significantly constrain evolutionary models of the early solar system and also provide new insight into the mechanisms themselves.

The solar nebula and the planetesimal disk

NASA Astrophysics Data System (ADS)

Ward, W. R.

Two popular theories of solar system formation are briefly reviewed, then used as background in an examination of several new developments related to planetary ring dynamics that promise to have great impact on future research. Most important are the incorporation of accretion disk and density wave theories into cosmogonic theory. A successful integration of these mechanisms may significantly constrain evolutionary models of the early solar system and also provide new insight into the mechanisms themselves.

Space-Group Symmetries Generate Chaotic Fluid Advection in Crystalline Granular Media

NASA Astrophysics Data System (ADS)

Turuban, R.; Lester, D. R.; Le Borgne, T.; Méheust, Y.

2018-01-01

The classical connection between symmetry breaking and the onset of chaos in dynamical systems harks back to the seminal theory of Noether [Transp. Theory Statist. Phys. 1, 186 (1918), 10.1080/00411457108231446]. We study the Lagrangian kinematics of steady 3D Stokes flow through simple cubic and body-centered cubic (bcc) crystalline lattices of close-packed spheres, and uncover an important exception. While breaking of point-group symmetries is a necessary condition for chaotic mixing in both lattices, a further space-group (glide) symmetry of the bcc lattice generates a transition from globally regular to globally chaotic dynamics. This finding provides new insights into chaotic mixing in porous media and has significant implications for understanding the impact of symmetries upon generic dynamical systems.

Emotions are emergent processes: they require a dynamic computational architecture

PubMed Central

Scherer, Klaus R.

2009-01-01

Emotion is a cultural and psychobiological adaptation mechanism which allows each individual to react flexibly and dynamically to environmental contingencies. From this claim flows a description of the elements theoretically needed to construct a virtual agent with the ability to display human-like emotions and to respond appropriately to human emotional expression. This article offers a brief survey of the desirable features of emotion theories that make them ideal blueprints for agent models. In particular, the component process model of emotion is described, a theory which postulates emotion-antecedent appraisal on different levels of processing that drive response system patterning predictions. In conclusion, investing seriously in emergent computational modelling of emotion using a nonlinear dynamic systems approach is suggested. PMID:19884141

1985 Particle Accelerator Conference: Accelerator Engineering and Technology, 11th, Vancouver, Canada, May 13-16, 1985, Proceedings

NASA Astrophysics Data System (ADS)

Strathdee, A.

1985-10-01

The topics discussed are related to high-energy accelerators and colliders, particle sources and electrostatic accelerators, controls, instrumentation and feedback, beam dynamics, low- and intermediate-energy circular accelerators and rings, RF and other acceleration systems, beam injection, extraction and transport, operations and safety, linear accelerators, applications of accelerators, radiation sources, superconducting supercolliders, new acceleration techniques, superconducting components, cryogenics, and vacuum. Accelerator and storage ring control systems are considered along with linear and nonlinear orbit theory, transverse and longitudinal instabilities and cures, beam cooling, injection and extraction orbit theory, high current dynamics, general beam dynamics, and medical and radioisotope applications. Attention is given to superconducting RF structures, magnet technology, superconducting magnets, and physics opportunities with relativistic heavy ion accelerators.

A real-time extension of density matrix embedding theory for non-equilibrium electron dynamics

NASA Astrophysics Data System (ADS)

Kretchmer, Joshua S.; Chan, Garnet Kin-Lic

2018-02-01

We introduce real-time density matrix embedding theory (DMET), a dynamical quantum embedding theory for computing non-equilibrium electron dynamics in strongly correlated systems. As in the previously developed static DMET, real-time DMET partitions the system into an impurity corresponding to the region of interest coupled to the surrounding environment, which is efficiently represented by a quantum bath of the same size as the impurity. In this work, we focus on a simplified single-impurity time-dependent formulation as a first step toward a multi-impurity theory. The equations of motion of the coupled impurity and bath embedding problem are derived using the time-dependent variational principle. The accuracy of real-time DMET is compared to that of time-dependent complete active space self-consistent field (TD-CASSCF) theory and time-dependent Hartree-Fock (TDHF) theory for a variety of quantum quenches in the single impurity Anderson model (SIAM), in which the Hamiltonian is suddenly changed (quenched) to induce a non-equilibrium state. Real-time DMET shows a marked improvement over the mean-field TDHF, converging to the exact answer even in the non-trivial Kondo regime of the SIAM. However, as expected from analogous behavior in static DMET, the constrained structure of the real-time DMET wavefunction leads to a slower convergence with respect to active space size, in the single-impurity formulation, relative to TD-CASSCF. Our initial results suggest that real-time DMET provides a promising framework to simulate non-equilibrium electron dynamics in which strong electron correlation plays an important role, and lays the groundwork for future multi-impurity formulations.

A real-time extension of density matrix embedding theory for non-equilibrium electron dynamics.

PubMed

Kretchmer, Joshua S; Chan, Garnet Kin-Lic

2018-02-07

We introduce real-time density matrix embedding theory (DMET), a dynamical quantum embedding theory for computing non-equilibrium electron dynamics in strongly correlated systems. As in the previously developed static DMET, real-time DMET partitions the system into an impurity corresponding to the region of interest coupled to the surrounding environment, which is efficiently represented by a quantum bath of the same size as the impurity. In this work, we focus on a simplified single-impurity time-dependent formulation as a first step toward a multi-impurity theory. The equations of motion of the coupled impurity and bath embedding problem are derived using the time-dependent variational principle. The accuracy of real-time DMET is compared to that of time-dependent complete active space self-consistent field (TD-CASSCF) theory and time-dependent Hartree-Fock (TDHF) theory for a variety of quantum quenches in the single impurity Anderson model (SIAM), in which the Hamiltonian is suddenly changed (quenched) to induce a non-equilibrium state. Real-time DMET shows a marked improvement over the mean-field TDHF, converging to the exact answer even in the non-trivial Kondo regime of the SIAM. However, as expected from analogous behavior in static DMET, the constrained structure of the real-time DMET wavefunction leads to a slower convergence with respect to active space size, in the single-impurity formulation, relative to TD-CASSCF. Our initial results suggest that real-time DMET provides a promising framework to simulate non-equilibrium electron dynamics in which strong electron correlation plays an important role, and lays the groundwork for future multi-impurity formulations.

Generating functionals and Gaussian approximations for interruptible delay reactions

NASA Astrophysics Data System (ADS)

Brett, Tobias; Galla, Tobias

2015-10-01

We develop a generating functional description of the dynamics of non-Markovian individual-based systems in which delay reactions can be terminated before completion. This generalizes previous work in which a path-integral approach was applied to dynamics in which delay reactions complete with certainty. We construct a more widely applicable theory, and from it we derive Gaussian approximations of the dynamics, valid in the limit of large, but finite, population sizes. As an application of our theory we study predator-prey models with delay dynamics due to gestation or lag periods to reach the reproductive age. In particular, we focus on the effects of delay on noise-induced cycles.

Tests of Theories of Crime in Female Prisoners.

PubMed

Lindberg, Marc A; Fugett, April; Adkins, Ashtin; Cook, Kelsey

2017-02-01

Several general theories of crime were tested with path models on 293 female prisoners in a U.S. State prison. The theories tested included Social Bond and Control, Thrill/Risk Seeking, and a new attachment-based Developmental Dynamic Systems model. A large battery of different instruments ranging from measures of risk taking, to a crime addiction scale, to Childhood Adverse Events, to attachments and clinical issues were used. The older general theories of crime did not hold up well under the rigor of path modeling. The new dynamic systems model was supported that incorporated adverse childhood events leading to (a) peer crime, (b) crime addiction, and (c) a measure derived from the Attachment and Clinical Issues Questionnaire (ACIQ) that takes individual differences in attachments and clinical issues into account. The results were discussed in terms of new approaches to Research Defined Criteria of Diagnosis (RDoC) and new approaches to intervention.

An Analytical Dynamics Approach to the Control of Mechanical Systems

NASA Astrophysics Data System (ADS)

Mylapilli, Harshavardhan

A new and novel approach to the control of nonlinear mechanical systems is presented in this study. The approach is inspired by recent results in analytical dynamics that deal with the theory of constrained motion. The control requirements on the dynamical system are viewed from an analytical dynamics perspective and the theory of constrained motion is used to recast these control requirements as constraints on the dynamical system. Explicit closed form expressions for the generalized nonlinear control forces are obtained by using the fundamental equation of mechanics. The control so obtained is optimal at each instant of time and causes the constraints to be exactly satisfied. No linearizations and/or approximations of the nonlinear dynamical system are made, and no a priori structure is imposed on the nature of nonlinear controller. Three examples dealing with highly nonlinear complex dynamical systems that are chosen from diverse areas of discrete and continuum mechanics are presented to demonstrate the control approach. The first example deals with the energy control of underactuated inhomogeneous nonlinear lattices (or chains), the second example deals with the synchronization of the motion of multiple coupled slave gyros with that of a master gyro, and the final example deals with the control of incompressible hyperelastic rubber-like thin cantilever beams. Numerical simulations accompanying these examples show the ease, simplicity and the efficacy with which the control methodology can be applied and the accuracy with which the desired control objectives can be met.

Modeling the relaxation dynamics of fluids in nanoporous materials

NASA Astrophysics Data System (ADS)

Edison, John R.

Mesoporous materials are being widely used in the chemical industry in various environmentally friendly separation processes and as catalysts. Our research can be broadly described as an effort to understand the behavior of fluids confined in such materials. More specifically we try to understand the influence of state variables like temperature and pore variables like size, shape, connectivity and structural heterogeneity on both the dynamic and equilibrium behavior of confined fluids. The dynamic processes associated with the approach to equilibrium are largely unexplored. It is important to look into the dynamic behavior for two reasons. First, confined fluids experience enhanced metastabilities and large equilibration times in certain classes of mesoporous materials, and the approach to the metastable/stable equilibrium is of tremendous interest. Secondly, understanding the transport resistances in a microscopic scale will help better engineer heterogeneous catalysts and separation processes. Here we present some of our preliminary studies on dynamics of fluids in ideal pore geometries. The tool that we have used extensively to investigate the relaxation dynamics of fluids in pores is the dynamic mean field theory (DMFT) as developed by Monson [P. A. Monson, J. Chem. Phys., 128, 084701 (2008)]. The theory is based on a lattice gas model of the system and can be viewed as a highly computationally efficient approximation to the dynamics averaged over an ensemble of Kawasaki dynamics Monte Carlo trajectories of the system. It provides a theory of the dynamics of the system consistent with the thermodynamics in mean field theory. The nucleation mechanisms associated with confined fluid phase transitions are emergent features in the calculations. We begin by describing the details of the theory and then present several applications of DMFT. First we present applications to three model pore networks (a) a network of slit pores with a single pore width; (b) a network of slit pores with two pore widths arranged in intersecting channels with a single pore width in each channel; (c) a network of slit pores with two pore widths forming an array of ink-bottles. The results illustrate the effects of pore connectivity upon the dynamics of vapor liquid phase transformations as well as on the mass transfer resistances to equilibration. We then present an application to a case where the solid-fluid interactions lead to partial wetting on a planar surface. The pore filling process in such systems features an asymmetric density distribution where a liquid droplet appears on one of the walls. We also present studies on systems where there is partial drying or drying associated with weakly attractive or repulsive interactions between the fluid and the pore walls. We describe the symmetries exhibited by the lattice model between pore filling for wetting states and pore emptying for drying states, for both the thermodynamics and dynamics. We then present an extension of DMFT to mixtures and present some examples that illustrate the utility of the approach. Finally we present an assessment the accuracy of the DMFT through comparisons with a higher order approximation based on the path probability method as well as Kawasaki dynamics.

A Lagrangian Formulation of Neural Networks I: Theory and Analog Dynamics

NASA Technical Reports Server (NTRS)

Mjolsness, Eric; Miranker, Willard L.

1997-01-01

We expand the mathematicla apparatus for relaxation networks, which conventionally consists of an objective function E and a dynamics given by a system of differenctial equations along whose trajectories E is diminished.

Chaos as an intermittently forced linear system.

PubMed

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kaiser, Eurika; Kutz, J Nathan

2017-05-30

Understanding the interplay of order and disorder in chaos is a central challenge in modern quantitative science. Approximate linear representations of nonlinear dynamics have long been sought, driving considerable interest in Koopman theory. We present a universal, data-driven decomposition of chaos as an intermittently forced linear system. This work combines delay embedding and Koopman theory to decompose chaotic dynamics into a linear model in the leading delay coordinates with forcing by low-energy delay coordinates; this is called the Hankel alternative view of Koopman (HAVOK) analysis. This analysis is applied to the Lorenz system and real-world examples including Earth's magnetic field reversal and measles outbreaks. In each case, forcing statistics are non-Gaussian, with long tails corresponding to rare intermittent forcing that precedes switching and bursting phenomena. The forcing activity demarcates coherent phase space regions where the dynamics are approximately linear from those that are strongly nonlinear.The huge amount of data generated in fields like neuroscience or finance calls for effective strategies that mine data to reveal underlying dynamics. Here Brunton et al.develop a data-driven technique to analyze chaotic systems and predict their dynamics in terms of a forced linear model.

A Navier-Stokes phase-field crystal model for colloidal suspensions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Praetorius, Simon, E-mail: simon.praetorius@tu-dresden.de; Voigt, Axel, E-mail: axel.voigt@tu-dresden.de

2015-04-21

We develop a fully continuous model for colloidal suspensions with hydrodynamic interactions. The Navier-Stokes Phase-Field Crystal model combines ideas of dynamic density functional theory with particulate flow approaches and is derived in detail and related to other dynamic density functional theory approaches with hydrodynamic interactions. The derived system is numerically solved using adaptive finite elements and is used to analyze colloidal crystallization in flowing environments demonstrating a strong coupling in both directions between the crystal shape and the flow field. We further validate the model against other computational approaches for particulate flow systems for various colloidal sedimentation problems.

A Navier-Stokes phase-field crystal model for colloidal suspensions.

PubMed

Praetorius, Simon; Voigt, Axel

2015-04-21

We develop a fully continuous model for colloidal suspensions with hydrodynamic interactions. The Navier-Stokes Phase-Field Crystal model combines ideas of dynamic density functional theory with particulate flow approaches and is derived in detail and related to other dynamic density functional theory approaches with hydrodynamic interactions. The derived system is numerically solved using adaptive finite elements and is used to analyze colloidal crystallization in flowing environments demonstrating a strong coupling in both directions between the crystal shape and the flow field. We further validate the model against other computational approaches for particulate flow systems for various colloidal sedimentation problems.

Spin and orbital exchange interactions from Dynamical Mean Field Theory

NASA Astrophysics Data System (ADS)

Secchi, A.; Lichtenstein, A. I.; Katsnelson, M. I.

2016-02-01

We derive a set of equations expressing the parameters of the magnetic interactions characterizing a strongly correlated electronic system in terms of single-electron Green's functions and self-energies. This allows to establish a mapping between the initial electronic system and a spin model including up to quadratic interactions between the effective spins, with a general interaction (exchange) tensor that accounts for anisotropic exchange, Dzyaloshinskii-Moriya interaction and other symmetric terms such as dipole-dipole interaction. We present the formulas in a format that can be used for computations via Dynamical Mean Field Theory algorithms.

Sliding mode control for generalized robust synchronization of mismatched fractional order dynamical systems and its application to secure transmission of voice messages.

PubMed

Muthukumar, P; Balasubramaniam, P; Ratnavelu, K

2017-07-26

This paper proposes a generalized robust synchronization method for different dimensional fractional order dynamical systems with mismatched fractional derivatives in the presence of function uncertainty and external disturbance by a designing sliding mode controller. Based on the proposed theory of generalized robust synchronization criterion, a novel audio cryptosystem is proposed for sending or sharing voice messages secretly via insecure channel. Numerical examples are given to verify the potency of the proposed theories. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Reduction and reconstruction of the dynamics of nonholonomic systems

NASA Astrophysics Data System (ADS)

Cortés, Jorge; de León, Manuel

1999-12-01

The reduction and reconstruction of the dynamics of nonholonomic mechanical systems with symmetry are investigated. We have considered a more general framework of constrained Hamiltonian systems since they appear in the reduction procedure. A reduction scheme in terms of the nonholonomic momentum mapping is developed. The reduction of the nonholonomic brackets is also discussed. The theory is illustrated with several examples.

Using a Card Trick to Illustrate Fixed Points and Stability

ERIC Educational Resources Information Center

Champanerkar, Jyoti; Jani, Mahendra

2015-01-01

Mathematical ideas from number theory, group theory, dynamical systems, and computer science have often been used to explain card tricks. Conversely, playing cards have been often used to illustrate the mathematical concepts of probability distributions and group theory. In this paper, we describe how the 21-card trick may be used to illustrate…

Formulation and closure of compressible turbulence equations in the light of kinetic theory

NASA Technical Reports Server (NTRS)

Tsuge, S.; Sagara, K.

1976-01-01

Fluid-dynamic moment equations, based on a kinetic hierarchy system, are derived governing the interaction between turbulent and thermal fluctuations. The kinetic theory is shown to reduce the inherent complexity of the conventional formalism of compressible turbulence theory and to minimize arbitrariness in formulating the closure condition.

Mode coupling theory for nonequilibrium glassy dynamics of thermal self-propelled particles.

PubMed

Feng, Mengkai; Hou, Zhonghuai

2017-06-28

We present a mode coupling theory study for the relaxation and glassy dynamics of a system of strongly interacting self-propelled particles, wherein the self-propulsion force is described by Ornstein-Uhlenbeck colored noise and thermal noises are included. Our starting point is an effective Smoluchowski equation governing the distribution function of particle positions, from which we derive a memory function equation for the time dependence of density fluctuations in nonequilibrium steady states. With the basic assumption of the absence of macroscopic currents and standard mode coupling approximation, we can obtain expressions for the irreducible memory function and other relevant dynamic terms, wherein the nonequilibrium character of the active system is manifested through an averaged diffusion coefficient D[combining macron] and a nontrivial structural function S 2 (q) with q being the magnitude of wave vector q. D[combining macron] and S 2 (q) enter the frequency term and the vertex term for the memory function, and thus influence both the short time and the long time dynamics of the system. With these equations obtained, we study the glassy dynamics of this thermal self-propelled particle system by investigating the Debye-Waller factor f q and relaxation time τ α as functions of the persistence time τ p of self-propulsion, the single particle effective temperature T eff as well as the number density ρ. Consequently, we find the critical density ρ c for given τ p shifts to larger values with increasing magnitude of propulsion force or effective temperature, in good accordance with previously reported simulation work. In addition, the theory facilitates us to study the critical effective temperature T for fixed ρ as well as its dependence on τ p . We find that T increases with τ p and in the limit τ p → 0, it approaches the value for a simple passive Brownian system as expected. Our theory also well recovers the results for passive systems and can be easily extended to more complex systems such as active-passive mixtures.

Modeling Stochastic Complexity in Complex Adaptive Systems: Non-Kolmogorov Probability and the Process Algebra Approach.

PubMed

Sulis, William H

2017-10-01

Walter Freeman III pioneered the application of nonlinear dynamical systems theories and methodologies in his work on mesoscopic brain dynamics.Sadly, mainstream psychology and psychiatry still cling to linear correlation based data analysis techniques, which threaten to subvert the process of experimentation and theory building. In order to progress, it is necessary to develop tools capable of managing the stochastic complexity of complex biopsychosocial systems, which includes multilevel feedback relationships, nonlinear interactions, chaotic dynamics and adaptability. In addition, however, these systems exhibit intrinsic randomness, non-Gaussian probability distributions, non-stationarity, contextuality, and non-Kolmogorov probabilities, as well as the absence of mean and/or variance and conditional probabilities. These properties and their implications for statistical analysis are discussed. An alternative approach, the Process Algebra approach, is described. It is a generative model, capable of generating non-Kolmogorov probabilities. It has proven useful in addressing fundamental problems in quantum mechanics and in the modeling of developing psychosocial systems.

Nonadiabatic Dynamics for Electrons at Second-Order: Real-Time TDDFT and OSCF2.

PubMed

Nguyen, Triet S; Parkhill, John

2015-07-14

We develop a new model to simulate nonradiative relaxation and dephasing by combining real-time Hartree-Fock and density functional theory (DFT) with our recent open-systems theory of electronic dynamics. The approach has some key advantages: it has been systematically derived and properly relaxes noninteracting electrons to a Fermi-Dirac distribution. This paper combines the new dissipation theory with an atomistic, all-electron quantum chemistry code and an atom-centered model of the thermal environment. The environment is represented nonempirically and is dependent on molecular structure in a nonlocal way. A production quality, O(N(3)) closed-shell implementation of our theory applicable to realistic molecular systems is presented, including timing information. This scaling implies that the added cost of our nonadiabatic relaxation model, time-dependent open self-consistent field at second order (OSCF2), is computationally inexpensive, relative to adiabatic propagation of real-time time-dependent Hartree-Fock (TDHF) or time-dependent density functional theory (TDDFT). Details of the implementation and numerical algorithm, including factorization and efficiency, are discussed. We demonstrate that OSCF2 approaches the stationary self-consistent field (SCF) ground state when the gap is large relative to k(b)T. The code is used to calculate linear-response spectra including the effects of bath dynamics. Finally, we show how our theory of finite-temperature relaxation can be used to correct ground-state DFT calculations.

Energy Current Cumulants in One-Dimensional Systems in Equilibrium

NASA Astrophysics Data System (ADS)

Dhar, Abhishek; Saito, Keiji; Roy, Anjan

2018-06-01

A recent theory based on fluctuating hydrodynamics predicts that one-dimensional interacting systems with particle, momentum, and energy conservation exhibit anomalous transport that falls into two main universality classes. The classification is based on behavior of equilibrium dynamical correlations of the conserved quantities. One class is characterized by sound modes with Kardar-Parisi-Zhang scaling, while the second class has diffusive sound modes. The heat mode follows Lévy statistics, with different exponents for the two classes. Here we consider heat current fluctuations in two specific systems, which are expected to be in the above two universality classes, namely, a hard particle gas with Hamiltonian dynamics and a harmonic chain with momentum conserving stochastic dynamics. Numerical simulations show completely different system-size dependence of current cumulants in these two systems. We explain this numerical observation using a phenomenological model of Lévy walkers with inputs from fluctuating hydrodynamics. This consistently explains the system-size dependence of heat current fluctuations. For the latter system, we derive the cumulant-generating function from a more microscopic theory, which also gives the same system-size dependence of cumulants.

Post-Newtonian celestial dynamics in cosmology: Field equations

NASA Astrophysics Data System (ADS)

Kopeikin, Sergei M.; Petrov, Alexander N.

2013-02-01

Post-Newtonian celestial dynamics is a relativistic theory of motion of massive bodies and test particles under the influence of relatively weak gravitational forces. The standard approach for development of this theory relies upon the key concept of the isolated astronomical system supplemented by the assumption that the background spacetime is flat. The standard post-Newtonian theory of motion was instrumental in the explanation of the existing experimental data on binary pulsars, satellite, and lunar laser ranging, and in building precise ephemerides of planets in the Solar System. Recent studies of the formation of large-scale structures in our Universe indicate that the standard post-Newtonian mechanics fails to describe more subtle dynamical effects in motion of the bodies comprising the astronomical systems of larger size—galaxies and clusters of galaxies—where the Riemann curvature of the expanding Friedmann-Lemaître-Robertson-Walker universe interacts with the local gravitational field of the astronomical system and, as such, cannot be ignored. The present paper outlines theoretical principles of the post-Newtonian mechanics in the expanding Universe. It is based upon the gauge-invariant theory of the Lagrangian perturbations of cosmological manifold caused by an isolated astronomical N-body system (the Solar System, a binary star, a galaxy, and a cluster of galaxies). We postulate that the geometric properties of the background manifold are described by a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker metric governed by two primary components—the dark matter and the dark energy. The dark matter is treated as an ideal fluid with the Lagrangian taken in the form of pressure along with the scalar Clebsch potential as a dynamic variable. The dark energy is associated with a single scalar field with a potential which is hold unspecified as long as the theory permits. Both the Lagrangians of the dark matter and the scalar field are 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 gravitational waves emitted by coalescing binaries and/or merging galactic nuclei.

Pseudo paths towards minimum energy states in network dynamics

NASA Astrophysics Data System (ADS)

Hedayatifar, L.; Hassanibesheli, F.; Shirazi, A. H.; Vasheghani Farahani, S.; Jafari, G. R.

2017-10-01

The dynamics of networks forming on Heider balance theory moves towards lower tension states. The condition derived from this theory enforces agents to reevaluate and modify their interactions to achieve equilibrium. These possible changes in network's topology can be considered as various paths that guide systems to minimum energy states. Based on this theory the final destination of a system could reside on a local minimum energy, ;jammed state;, or the global minimum energy, balanced states. The question we would like to address is whether jammed states just appear by chance? Or there exist some pseudo paths that bound a system towards a jammed state. We introduce an indicator to suspect the location of a jammed state based on the Inverse Participation Ratio method (IPR). We provide a margin before a local minimum where the number of possible paths dramatically drastically decreases. This is a condition that proves adequate for ending up on a jammed states.

Data-Driven Model Reduction and Transfer Operator Approximation

NASA Astrophysics Data System (ADS)

Klus, Stefan; Nüske, Feliks; Koltai, Péter; Wu, Hao; Kevrekidis, Ioannis; Schütte, Christof; Noé, Frank

2018-06-01

In this review paper, we will present different data-driven dimension reduction techniques for dynamical systems that are based on transfer operator theory as well as methods to approximate transfer operators and their eigenvalues, eigenfunctions, and eigenmodes. The goal is to point out similarities and differences between methods developed independently by the dynamical systems, fluid dynamics, and molecular dynamics communities such as time-lagged independent component analysis, dynamic mode decomposition, and their respective generalizations. As a result, extensions and best practices developed for one particular method can be carried over to other related methods.

Note on transmitted complexity for quantum dynamical systems

NASA Astrophysics Data System (ADS)

Watanabe, Noboru; Muto, Masahiro

2017-10-01

Transmitted complexity (mutual entropy) is one of the important measures for quantum information theory developed recently in several ways. We will review the fundamental concepts of the Kossakowski, Ohya and Watanabe entropy and define a transmitted complexity for quantum dynamical systems. This article is part of the themed issue `Second quantum revolution: foundational questions'.

A DST Model of Multilingualism and the Role of Metalinguistic Awareness

ERIC Educational Resources Information Center

Jessner, Ulrike

2008-01-01

This paper suggests that a dynamic systems theory (DST) provides an adequate conceptual metaphor for discussing multilingual development. Multilingual acquisition is a nonlinear and complex dynamic process depending on a number of interacting factors. Variability plays a crucial role in the multilingual system as it changes over time (Herdina &…

Embracing Connectedness and Change: A Complex Dynamic Systems Perspective for Applied Linguistic Research

ERIC Educational Resources Information Center

Cameron, Lynne

2015-01-01

Complex dynamic systems (CDS) theory offers a powerful metaphorical model of applied linguistic processes, allowing holistic descriptions of situated phenomena, and addressing the connectedness and change that often characterise issues in our field. A recent study of Kenyan conflict transformation illustrates application of a CDS perspective. Key…

Collisional and dynamical processes in moon and planet formation

NASA Technical Reports Server (NTRS)

Chapman, C. R.; Davis, D. R.; Weidenschilling, S. J.; Hartmann, W. K.; Spaute, D.

1987-01-01

Research on a variety of dynamical processes relevant to the formation of planets, satellites and ring systems is discussed. The main focus is on studies of accretionary formation of early protoplanets using a numerical model, structures and evolution of ring systems and individual bodies within planetary rings, and theories of lunar origin.

Toward a Comprehensive Model of Antisocial Development: A Dynamic Systems Approach

ERIC Educational Resources Information Center

Granic, Isabela; Patterson, Gerald R.

2006-01-01

The purpose of this article is to develop a preliminary comprehensive model of antisocial development based on dynamic systems principles. The model is built on the foundations of behavioral research on coercion theory. First, the authors focus on the principles of multistability, feedback, and nonlinear causality to reconceptualize real-time…

Careers in Academe: The Academic Labour Market as an Eco-System

ERIC Educational Resources Information Center

Baruch, Yehuda

2013-01-01

Purpose: This paper aims to explore the contrast between stable and dynamic labour markets in academe in light of career theories that were originally developed for business environments. Design/methodology/approach: A conceptual design, offering the eco-system as a framework. Findings: It evaluates their relevance and applicability to dynamic and…

Focusing on the Complexity of Emotion Issues in Academic Learning: A Dynamical Component Systems Approach

ERIC Educational Resources Information Center

Eynde, Peter Op 't; Turner, Jeannine E.

2006-01-01

Understanding the interrelations among students' cognitive, emotional, motivational, and volitional processes is an emergening focus in educational psychology. A dynamical, component systems theory of emotions is presented as a promising framework to further unravel these complex interrelations. This framework considers emotions to be a process…

Modeling of thin-walled structures interacting with acoustic media as constrained two-dimensional continua

NASA Astrophysics Data System (ADS)

Rabinskiy, L. N.; Zhavoronok, S. I.

2018-04-01

The transient interaction of acoustic media and elastic shells is considered on the basis of the transition function approach. The three-dimensional hyperbolic initial boundary-value problem is reduced to a two-dimensional problem of shell theory with integral operators approximating the acoustic medium effect on the shell dynamics. The kernels of these integral operators are determined by the elementary solution of the problem of acoustic waves diffraction at a rigid obstacle with the same boundary shape as the wetted shell surface. The closed-form elementary solution for arbitrary convex obstacles can be obtained at the initial interaction stages on the background of the so-called “thin layer hypothesis”. Thus, the shell–wave interaction model defined by integro-differential dynamic equations with analytically determined kernels of integral operators becomes hence two-dimensional but nonlocal in time. On the other hand, the initial interaction stage results in localized dynamic loadings and consequently in complex strain and stress states that require higher-order shell theories. Here the modified theory of I.N.Vekua–A.A.Amosov-type is formulated in terms of analytical continuum dynamics. The shell model is constructed on a two-dimensional manifold within a set of field variables, Lagrangian density, and constraint equations following from the boundary conditions “shifted” from the shell faces to its base surface. Such an approach allows one to construct consistent low-order shell models within a unified formal hierarchy. The equations of the N th-order shell theory are singularly perturbed and contain second-order partial derivatives with respect to time and surface coordinates whereas the numerical integration of systems of first-order equations is more efficient. Such systems can be obtained as Hamilton–de Donder–Weyl-type equations for the Lagrangian dynamical system. The Hamiltonian formulation of the elementary N th-order shell theory is here briefly described.

Dissipative open systems theory as a foundation for the thermodynamics of linear systems.

PubMed

Delvenne, Jean-Charles; Sandberg, Henrik

2017-03-06

In this paper, we advocate the use of open dynamical systems, i.e. systems sharing input and output variables with their environment, and the dissipativity theory initiated by Jan Willems as models of thermodynamical systems, at the microscopic and macroscopic level alike. We take linear systems as a study case, where we show how to derive a global Lyapunov function to analyse networks of interconnected systems. We define a suitable notion of dynamic non-equilibrium temperature that allows us to derive a discrete Fourier law ruling the exchange of heat between lumped, discrete-space systems, enriched with the Maxwell-Cattaneo correction. We complete these results by a brief recall of the steps that allow complete derivation of the dissipation and fluctuation in macroscopic systems (i.e. at the level of probability distributions) from lossless and deterministic systems.This article is part of the themed issue 'Horizons of cybernetical physics'. © 2017 The Author(s).

Risk assessment and adaptive runoff utilization in water resource system considering the complex relationship among water supply, electricity generation and environment

NASA Astrophysics Data System (ADS)

Zhou, J.; Zeng, X.; Mo, L.; Chen, L.; Jiang, Z.; Feng, Z.; Yuan, L.; He, Z.

2017-12-01

Generally, the adaptive utilization and regulation of runoff in the source region of China's southwest rivers is classified as a typical multi-objective collaborative optimization problem. There are grim competitions and incidence relation in the subsystems of water supply, electricity generation and environment, which leads to a series of complex problems represented by hydrological process variation, blocked electricity output and water environment risk. Mathematically, the difficulties of multi-objective collaborative optimization focus on the description of reciprocal relationships and the establishment of evolving model of adaptive systems. Thus, based on the theory of complex systems science, this project tries to carry out the research from the following aspects: the changing trend of coupled water resource, the covariant factor and driving mechanism, the dynamic evolution law of mutual feedback dynamic process in the supply-generation-environment coupled system, the environmental response and influence mechanism of coupled mutual feedback water resource system, the relationship between leading risk factor and multiple risk based on evolutionary stability and dynamic balance, the transfer mechanism of multiple risk response with the variation of the leading risk factor, the multidimensional coupled feedback system of multiple risk assessment index system and optimized decision theory. Based on the above-mentioned research results, the dynamic method balancing the efficiency of multiple objectives in the coupled feedback system and optimized regulation model of water resources is proposed, and the adaptive scheduling mode considering the internal characteristics and external response of coupled mutual feedback system of water resource is established. In this way, the project can make a contribution to the optimal scheduling theory and methodology of water resource management under uncertainty in the source region of Southwest River.

Universal self-similar dynamics of relativistic and nonrelativistic field theories near nonthermal fixed points

NASA Astrophysics Data System (ADS)

Piñeiro Orioli, Asier; Boguslavski, Kirill; Berges, Jürgen

2015-07-01

We investigate universal behavior of isolated many-body systems far from equilibrium, which is relevant for a wide range of applications from ultracold quantum gases to high-energy particle physics. The universality is based on the existence of nonthermal fixed points, which represent nonequilibrium attractor solutions with self-similar scaling behavior. The corresponding dynamic universality classes turn out to be remarkably large, encompassing both relativistic as well as nonrelativistic quantum and classical systems. For the examples of nonrelativistic (Gross-Pitaevskii) and relativistic scalar field theory with quartic self-interactions, we demonstrate that infrared scaling exponents as well as scaling functions agree. We perform two independent nonperturbative calculations, first by using classical-statistical lattice simulation techniques and second by applying a vertex-resummed kinetic theory. The latter extends kinetic descriptions to the nonperturbative regime of overoccupied modes. Our results open new perspectives to learn from experiments with cold atoms aspects about the dynamics during the early stages of our universe.

The study of micro-inextensible piezoelectric cantilever plate

NASA Astrophysics Data System (ADS)

Chen, L. H.; Xu, J. W.; Zhang, W.

2018-06-01

In this paper, a micro-inextensible piezoelectric cantilever plate is analyzed and its nonlinear dynamic behaviour is studied. The nonlinear oscillation differential equation is established by using Hamilton’s principle with the application of strain gradient theory to consider the size effect, and inextensible theory to consider the large deformation and rotation effect of cantilever plate. Based on MATLAB software, using the Runge-Kuta method, we can obtain the response of the nonlinear oscillation differential equation. The influences of the strain gradient length scale parameter and voltage on the dynamic response of micro piezoelectric cantilever plate are investigated separately. The results confirmed an increase of the stiffness of the system by using the strain gradient theory and the amplitude of the vibration is reduced. The vibration of the system can be controlled by applying an active voltage. The effect of external excitation frequency on nonlinear dynamic behaviour is considered by using Poincare surface of section and diagrams of waveforms, phase and bifurcation.

The Conduit and Whirlpooling: A New Theory of Knowledge Constitution and Dispersion

ERIC Educational Resources Information Center

Nzegwu, Azuka

2010-01-01

There is a new epistemological approach for exploring knowledge constitution and dispersal in a dynamic Web ecosystem. The approach has three pivots. The first presents virtual whirlpools as knowledge systems. The second introduces the creator of the system as the Conduit. The third formulates a theory of knowledge that involves the collective…

Integrating Program Theory and Systems-Based Procedures in Program Evaluation: A Dynamic Approach to Evaluate Educational Programs

ERIC Educational Resources Information Center

Grammatikopoulos, Vasilis

2012-01-01

The current study attempts to integrate parts of program theory and systems-based procedures in educational program evaluation. The educational program that was implemented, called the "Early Steps" project, proposed that physical education can contribute to various educational goals apart from the usual motor skills improvement. Basic…

The Einstein-Vlasov System/Kinetic Theory.

PubMed

Andréasson, Håkan

2011-01-01

The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on non-relativistic and special relativistic physics, i.e., to model the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. This paper gives introductions to kinetic theory in non-curved spacetimes and then the Einstein-Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental to a good comprehension of kinetic theory in general relativity.

The dynamic development of gender variability.

PubMed

Fausto-Sterling, Anne

2012-01-01

We diagram and discuss theories of gender identity development espoused by the clinical groups represented in this special issue. We contend that theories of origin relate importantly to clinical practice, and argue that the existing clinical theories are under-developed. Therefore, we develop a dynamic systems framework for gender identity development. Specifically, we suggest that critical aspects of presymbolic gender embodiment occur during infancy as part of the synchronous interplay of caregiver-infant dyads. By 18 months, a transition to symbolic representation and the beginning of an internalization of a sense of gender can be detected and consolidation is quite evident by 3 years of age. We conclude by suggesting empirical studies that could expand and test this framework. With the belief that better, more explicit developmental theory can improve clinical practice, we urge that clinicians take a dynamic developmental view of gender identity formation into account.

Bounds on the power of proofs and advice in general physical theories.

PubMed

Lee, Ciarán M; Hoban, Matty J

2016-06-01

Quantum theory presents us with the tools for computational and communication advantages over classical theory. One approach to uncovering the source of these advantages is to determine how computation and communication power vary as quantum theory is replaced by other operationally defined theories from a broad framework of such theories. Such investigations may reveal some of the key physical features required for powerful computation and communication. In this paper, we investigate how simple physical principles bound the power of two different computational paradigms which combine computation and communication in a non-trivial fashion: computation with advice and interactive proof systems. We show that the existence of non-trivial dynamics in a theory implies a bound on the power of computation with advice. Moreover, we provide an explicit example of a theory with no non-trivial dynamics in which the power of computation with advice is unbounded. Finally, we show that the power of simple interactive proof systems in theories where local measurements suffice for tomography is non-trivially bounded. This result provides a proof that [Formula: see text] is contained in [Formula: see text], which does not make use of any uniquely quantum structure-such as the fact that observables correspond to self-adjoint operators-and thus may be of independent interest.

European Workshop on Planetary Sciences, Rome, Italy, April 23-27, 1979, Proceedings. Part 1

NASA Astrophysics Data System (ADS)

1980-02-01

Papers are presented on the dynamics and evolution of the solar system and its components. Specific topics include the dynamic stability of the solar system, the tidal friction theory of the earth moon system, the stability and irregularity of extrasolar planetary systems, angular momentum and magnetic braking during star formation, the collisional growth of planetesimals, the dynamics, interrelations and evolution of the asteroids and comets, the formation and stability of Saturn's rings, and the importance of nearly tangent orbits in planetary close encounters.

Extrapolation to Nonequilibrium from Coarse-Grained Response Theory

NASA Astrophysics Data System (ADS)

Basu, Urna; Helden, Laurent; Krüger, Matthias

2018-05-01

Nonlinear response theory, in contrast to linear cases, involves (dynamical) details, and this makes application to many-body systems challenging. From the microscopic starting point we obtain an exact response theory for a small number of coarse-grained degrees of freedom. With it, an extrapolation scheme uses near-equilibrium measurements to predict far-from-equilibrium properties (here, second order responses). Because it does not involve system details, this approach can be applied to many-body systems. It is illustrated in a four-state model and in the near critical Ising model.

Nursing Services Delivery Theory: an open system approach.

PubMed

Meyer, Raquel M; O'Brien-Pallas, Linda L

2010-12-01

This paper is a discussion of the derivation of the Nursing Services Delivery Theory from the application of open system theory to large-scale organizations. The underlying mechanisms by which staffing indicators influence outcomes remain under-theorized and unmeasured, resulting in a 'black box' that masks the nature and organization of nursing work. Theory linking nursing work, staffing, work environments, and outcomes in different settings is urgently needed to inform management decisions about the allocation of nurse staffing resources in organizations. A search of CINAHL and Business Source Premier for the years 1980-2008 was conducted using the following terms: theory, models, organization, organizational structure, management, administration, nursing units, and nursing. Seminal works were included. The healthcare organization is conceptualized as an open system characterized by energy transformation, a dynamic steady state, negative entropy, event cycles, negative feedback, differentiation, integration and coordination, and equifinality. The Nursing Services Delivery Theory proposes that input, throughput, and output factors interact dynamically to influence the global work demands placed on nursing work groups at the point of care in production subsystems. THE Nursing Services Delivery Theory can be applied to varied settings, cultures, and countries and supports the study of multi-level phenomena and cross-level effects. The Nursing Services Delivery Theory gives a relational structure for reconciling disparate streams of research related to nursing work, staffing, and work environments. The theory can guide future research and the management of nursing services in large-scale healthcare organizations. © 2010 Blackwell Publishing Ltd.

Nursing Services Delivery Theory: an open system approach

PubMed Central

Meyer, Raquel M; O’Brien-Pallas, Linda L

2010-01-01

meyer r.m. & o’brien-pallas l.l. (2010)Nursing services delivery theory: an open system approach. Journal of Advanced Nursing66(12), 2828–2838. Aim This paper is a discussion of the derivation of the Nursing Services Delivery Theory from the application of open system theory to large-scale organizations. Background The underlying mechanisms by which staffing indicators influence outcomes remain under-theorized and unmeasured, resulting in a ‘black box’ that masks the nature and organization of nursing work. Theory linking nursing work, staffing, work environments, and outcomes in different settings is urgently needed to inform management decisions about the allocation of nurse staffing resources in organizations. Data sources A search of CINAHL and Business Source Premier for the years 1980–2008 was conducted using the following terms: theory, models, organization, organizational structure, management, administration, nursing units, and nursing. Seminal works were included. Discussion The healthcare organization is conceptualized as an open system characterized by energy transformation, a dynamic steady state, negative entropy, event cycles, negative feedback, differentiation, integration and coordination, and equifinality. The Nursing Services Delivery Theory proposes that input, throughput, and output factors interact dynamically to influence the global work demands placed on nursing work groups at the point of care in production subsystems. Implications for nursing The Nursing Services Delivery Theory can be applied to varied settings, cultures, and countries and supports the study of multi-level phenomena and cross-level effects. Conclusion The Nursing Services Delivery Theory gives a relational structure for reconciling disparate streams of research related to nursing work, staffing, and work environments. The theory can guide future research and the management of nursing services in large-scale healthcare organizations. PMID:20831573

Characterization of Combustion Dynamics, Detection, and Prevention of an Unstable Combustion State Based on a Complex-Network Theory

NASA Astrophysics Data System (ADS)

Gotoda, Hiroshi; Kinugawa, Hikaru; Tsujimoto, Ryosuke; Domen, Shohei; Okuno, Yuta

2017-04-01

Complex-network theory has attracted considerable attention for nearly a decade, and it enables us to encompass our understanding of nonlinear dynamics in complex systems in a wide range of fields, including applied physics and mechanical, chemical, and electrical engineering. We conduct an experimental study using a pragmatic online detection methodology based on complex-network theory to prevent a limiting unstable state such as blowout in a confined turbulent combustion system. This study introduces a modified version of the natural visibility algorithm based on the idea of a visibility limit to serve as a pragmatic online detector. The average degree of the modified version of the natural visibility graph allows us to detect the onset of blowout, resulting in online prevention.

A cognitive-affective system theory of personality: reconceptualizing situations, dispositions, dynamics, and invariance in personality structure.

PubMed

Mischel, W; Shoda, Y

1995-04-01

A theory was proposed to reconcile paradoxical findings on the invariance of personality and the variability of behavior across situations. For this purpose, individuals were assumed to differ in (a) the accessibility of cognitive-affective mediating units (such as encodings, expectancies and beliefs, affects, and goals) and (b) the organization of relationships through which these units interact with each other and with psychological features of situations. The theory accounts for individual differences in predictable patterns of variability across situations (e.g., if A then she X, but if B then she Y), as well as for overall average levels of behavior, as essential expressions or behavioral signatures of the same underlying personality system. Situations, personality dispositions, dynamics, and structure were reconceptualized from this perspective.

Fundamental Design Principles for Transcription-Factor-Based Metabolite Biosensors.

PubMed

Mannan, Ahmad A; Liu, Di; Zhang, Fuzhong; Oyarzún, Diego A

2017-10-20

Metabolite biosensors are central to current efforts toward precision engineering of metabolism. Although most research has focused on building new biosensors, their tunability remains poorly understood and is fundamental for their broad applicability. Here we asked how genetic modifications shape the dose-response curve of biosensors based on metabolite-responsive transcription factors. Using the lac system in Escherichia coli as a model system, we built promoter libraries with variable operator sites that reveal interdependencies between biosensor dynamic range and response threshold. We developed a phenomenological theory to quantify such design constraints in biosensors with various architectures and tunable parameters. Our theory reveals a maximal achievable dynamic range and exposes tunable parameters for orthogonal control of dynamic range and response threshold. Our work sheds light on fundamental limits of synthetic biology designs and provides quantitative guidelines for biosensor design in applications such as dynamic pathway control, strain optimization, and real-time monitoring of metabolism.

Towards a Population Dynamics Theory for Evolutionary Computing: Learning from Biological Population Dynamics in Nature

NASA Astrophysics Data System (ADS)

Ma, Zhanshan (Sam)

In evolutionary computing (EC), population size is one of the critical parameters that a researcher has to deal with. Hence, it was no surprise that the pioneers of EC, such as De Jong (1975) and Holland (1975), had already studied the population sizing from the very beginning of EC. What is perhaps surprising is that more than three decades later, we still largely depend on the experience or ad-hoc trial-and-error approach to set the population size. For example, in a recent monograph, Eiben and Smith (2003) indicated: "In almost all EC applications, the population size is constant and does not change during the evolutionary search." Despite enormous research on this issue in recent years, we still lack a well accepted theory for population sizing. In this paper, I propose to develop a population dynamics theory forEC with the inspiration from the population dynamics theory of biological populations in nature. Essentially, the EC population is considered as a dynamic system over time (generations) and space (search space or fitness landscape), similar to the spatial and temporal dynamics of biological populations in nature. With this conceptual mapping, I propose to 'transplant' the biological population dynamics theory to EC via three steps: (i) experimentally test the feasibility—whether or not emulating natural population dynamics improves the EC performance; (ii) comparatively study the underlying mechanisms—why there are improvements, primarily via statistical modeling analysis; (iii) conduct theoretical analysis with theoretical models such as percolation theory and extended evolutionary game theory that are generally applicable to both EC and natural populations. This article is a summary of a series of studies we have performed to achieve the general goal [27][30]-[32]. In the following, I start with an extremely brief introduction on the theory and models of natural population dynamics (Sections 1 & 2). In Sections 4 to 6, I briefly discuss three categories of population dynamics models: deterministic modeling with Logistic chaos map as an example, stochastic modeling with spatial distribution patterns as an example, as well as survival analysis and extended evolutionary game theory (EEGT) modeling. Sample experiment results with Genetic algorithms (GA) are presented to demonstrate the applications of these models. The proposed EC population dynamics approach also makes survival selection largely unnecessary or much simplified since the individuals are naturally selected (controlled) by the mathematical models for EC population dynamics.

Theoretical foundations for finite-time transient stability and sensitivity analysis of power systems

NASA Astrophysics Data System (ADS)

Dasgupta, Sambarta

Transient stability and sensitivity analysis of power systems are problems of enormous academic and practical interest. These classical problems have received renewed interest, because of the advancement in sensor technology in the form of phasor measurement units (PMUs). The advancement in sensor technology has provided unique opportunity for the development of real-time stability monitoring and sensitivity analysis tools. Transient stability problem in power system is inherently a problem of stability analysis of the non-equilibrium dynamics, because for a short time period following a fault or disturbance the system trajectory moves away from the equilibrium point. The real-time stability decision has to be made over this short time period. However, the existing stability definitions and hence analysis tools for transient stability are asymptotic in nature. In this thesis, we discover theoretical foundations for the short-term transient stability analysis of power systems, based on the theory of normally hyperbolic invariant manifolds and finite time Lyapunov exponents, adopted from geometric theory of dynamical systems. The theory of normally hyperbolic surfaces allows us to characterize the rate of expansion and contraction of co-dimension one material surfaces in the phase space. The expansion and contraction rates of these material surfaces can be computed in finite time. We prove that the expansion and contraction rates can be used as finite time transient stability certificates. Furthermore, material surfaces with maximum expansion and contraction rate are identified with the stability boundaries. These stability boundaries are used for computation of stability margin. We have used the theoretical framework for the development of model-based and model-free real-time stability monitoring methods. Both the model-based and model-free approaches rely on the availability of high resolution time series data from the PMUs for stability prediction. The problem of sensitivity analysis of power system, subjected to changes or uncertainty in load parameters and network topology, is also studied using the theory of normally hyperbolic manifolds. The sensitivity analysis is used for the identification and rank ordering of the critical interactions and parameters in the power network. The sensitivity analysis is carried out both in finite time and in asymptotic. One of the distinguishing features of the asymptotic sensitivity analysis is that the asymptotic dynamics of the system is assumed to be a periodic orbit. For asymptotic sensitivity analysis we employ combination of tools from ergodic theory and geometric theory of dynamical systems.

Quantitative steps in the evolution of metabolic organisation as specified by the Dynamic Energy Budget theory.

PubMed

Kooijman, S A L M; Troost, T A

2007-02-01

The Dynamic Energy Budget (DEB) theory quantifies the metabolic organisation of organisms on the basis of mechanistically inspired assumptions. We here sketch a scenario for how its various modules, such as maintenance, storage dynamics, development, differentiation and life stages could have evolved since the beginning of life. We argue that the combination of homeostasis and maintenance induced the development of reserves and that subsequent increases in the maintenance costs came with increases of the reserve capacity. Life evolved from a multiple reserves - single structure system (prokaryotes, many protoctists) to systems with multiple reserves and two structures (plants) or single reserve and single structure (animals). This had profound consequences for the possible effects of temperature on rates. We present an alternative explanation for what became known as the down-regulation of maintenance at high growth rates in microorganisms; the density of the limiting reserve increases with the growth rate, and reserves do not require maintenance while structure-specific maintenance costs are independent of the growth rate. This is also the mechanism behind the variation of the respiration rate with body size among species. The DEB theory specifies reserve dynamics on the basis of the requirements of weak homeostasis and partitionability. We here present a new and simple mechanism for this dynamics which accounts for the rejection of mobilised reserve by busy maintenance/growth machinery. This module, like quite a few other modules of DEB theory, uses the theory of Synthesising Units; we review recent progress in this field. The plasticity of membranes that evolved in early eukaryotes is a major step forward in metabolic evolution; we discuss quantitative aspects of the efficiency of phagocytosis relative to the excretion of digestive enzymes to illustrate its importance. Some processes of adaptation and gene expression can be understood in terms of allocation linked to the relative workload of metabolic modules in (unicellular) prokaryotes and organs in (multicellular) eukaryotes. We argue that the evolution of demand systems can only be understood in the light of that of supply systems. We illustrate some important points with data from the literature.

Mathematic Model of Digital Control System with PID Regulator and Regular Step of Quantization with Information Transfer via the Channel of Plural Access

NASA Astrophysics Data System (ADS)

Abramov, G. V.; Emeljanov, A. E.; Ivashin, A. L.

Theoretical bases for modeling a digital control system with information transfer via the channel of plural access and a regular quantization cycle are submitted. The theory of dynamic systems with random changes of the structure including elements of the Markov random processes theory is used for a mathematical description of a network control system. The characteristics of similar control systems are received. Experimental research of the given control systems is carried out.

Noise-induced volatility of collective dynamics

NASA Astrophysics Data System (ADS)

Harras, Georges; Tessone, Claudio J.; Sornette, Didier

2012-01-01

Noise-induced volatility refers to a phenomenon of increased level of fluctuations in the collective dynamics of bistable units in the presence of a rapidly varying external signal, and intermediate noise levels. The archetypical signature of this phenomenon is that—beyond the increase in the level of fluctuations—the response of the system becomes uncorrelated with the external driving force, making it different from stochastic resonance. Numerical simulations and an analytical theory of a stochastic dynamical version of the Ising model on regular and random networks demonstrate the ubiquity and robustness of this phenomenon, which is argued to be a possible cause of excess volatility in financial markets, of enhanced effective temperatures in a variety of out-of-equilibrium systems, and of strong selective responses of immune systems of complex biological organisms. Extensive numerical simulations are compared with a mean-field theory for different network topologies.

Trajectory tracking control for underactuated stratospheric airship

NASA Astrophysics Data System (ADS)

Zheng, Zewei; Huo, Wei; Wu, Zhe

2012-10-01

Stratospheric airship is a new kind of aerospace system which has attracted worldwide developing interests for its broad application prospects. Based on the trajectory linearization control (TLC) theory, a novel trajectory tracking control method for an underactuated stratospheric airship is presented in this paper. Firstly, the TLC theory is described sketchily, and the dynamic model of the stratospheric airship is introduced with kinematics and dynamics equations. Then, the trajectory tracking control strategy is deduced in detail. The designed control system possesses a cascaded structure which consists of desired attitude calculation, position control loop and attitude control loop. Two sub-loops are designed for the position and attitude control loops, respectively, including the kinematics control loop and dynamics control loop. Stability analysis shows that the controlled closed-loop system is exponentially stable. Finally, simulation results for the stratospheric airship to track typical trajectories are illustrated to verify effectiveness of the proposed approach.

Integrating the social sciences to understand human-water dynamics

NASA Astrophysics Data System (ADS)

Carr, G.; Kuil, L., Jr.

2017-12-01

Many interesting and exciting socio-hydrological models have been developed in recent years. Such models often aim to capture the dynamic interplay between people and water for a variety of hydrological settings. As such, peoples' behaviours and decisions are brought into the models as drivers of and/or respondents to the hydrological system. To develop and run such models over a sufficiently long time duration to observe how the water-human system evolves the human component is often simplified according to one or two key behaviours, characteristics or decisions (e.g. a decision to move away from a drought or flood area; a decision to pump groundwater, or a decision to plant a less water demanding crop). To simplify the social component, socio-hydrological modellers often pull knowledge and understanding from existing social science theories. This requires them to negotiate complex territory, where social theories may be underdeveloped, contested, dynamically evolving, or case specific and difficult to generalise or upscale. A key question is therefore, how can this process be supported so that the resulting socio-hydrological models adequately describe the system and lead to meaningful understanding of how and why it behaves as it does? Collaborative interdisciplinary research teams that bring together social and natural scientists are likely to be critical. Joint development of the model framework requires specific attention to clarification to expose all underlying assumptions, constructive discussion and negotiation to reach agreement on the modelled system and its boundaries. Mutual benefits to social scientists can be highlighted, i.e. socio-hydrological work can provide insights for further exploring and testing social theories. Collaborative work will also help ensure underlying social theory is made explicit, and may identify ways to include and compare multiple theories. As socio-hydrology progresses towards supporting policy development, approaches that brings in stakeholders and non-scientist participants to develop the conceptual modelling framework will become essential. They are also critical for fully understanding human-water dynamics.

Time Factor in the Theory of Anthropogenic Risk Prediction in Complex Dynamic Systems

NASA Astrophysics Data System (ADS)

Ostreikovsky, V. A.; Shevchenko, Ye N.; Yurkov, N. K.; Kochegarov, I. I.; Grishko, A. K.

2018-01-01

The article overviews the anthropogenic risk models that take into consideration the development of different factors in time that influence the complex system. Three classes of mathematical models have been analyzed for the use in assessing the anthropogenic risk of complex dynamic systems. These models take into consideration time factor in determining the prospect of safety change of critical systems. The originality of the study is in the analysis of five time postulates in the theory of anthropogenic risk and the safety of highly important objects. It has to be stressed that the given postulates are still rarely used in practical assessment of equipment service life of critically important systems. That is why, the results of study presented in the article can be used in safety engineering and analysis of critically important complex technical systems.

How Stuttering Develops: The Multifactorial Dynamic Pathways Theory

PubMed Central

Weber, Christine

2017-01-01

Purpose We advanced a multifactorial, dynamic account of the complex, nonlinear interactions of motor, linguistic, and emotional factors contributing to the development of stuttering. Our purpose here is to update our account as the multifactorial dynamic pathways theory. Method We review evidence related to how stuttering develops, including genetic/epigenetic factors; motor, linguistic, and emotional features; and advances in neuroimaging studies. We update evidence for our earlier claim: Although stuttering ultimately reflects impairment in speech sensorimotor processes, its course over the life span is strongly conditioned by linguistic and emotional factors. Results Our current account places primary emphasis on the dynamic developmental context in which stuttering emerges and follows its course during the preschool years. Rapid changes in many neurobehavioral systems are ongoing, and critical interactions among these systems likely play a major role in determining persistence of or recovery from stuttering. Conclusion Stuttering, or childhood onset fluency disorder (Diagnostic and Statistical Manual of Mental Disorders, 5th edition; American Psychiatric Association [APA], 2013), is a neurodevelopmental disorder that begins when neural networks supporting speech, language, and emotional functions are rapidly developing. The multifactorial dynamic pathways theory motivates experimental and clinical work to determine the specific factors that contribute to each child's pathway to the diagnosis of stuttering and those most likely to promote recovery. PMID:28837728

How Stuttering Develops: The Multifactorial Dynamic Pathways Theory.

PubMed

Smith, Anne; Weber, Christine

2017-09-18

We advanced a multifactorial, dynamic account of the complex, nonlinear interactions of motor, linguistic, and emotional factors contributing to the development of stuttering. Our purpose here is to update our account as the multifactorial dynamic pathways theory. We review evidence related to how stuttering develops, including genetic/epigenetic factors; motor, linguistic, and emotional features; and advances in neuroimaging studies. We update evidence for our earlier claim: Although stuttering ultimately reflects impairment in speech sensorimotor processes, its course over the life span is strongly conditioned by linguistic and emotional factors. Our current account places primary emphasis on the dynamic developmental context in which stuttering emerges and follows its course during the preschool years. Rapid changes in many neurobehavioral systems are ongoing, and critical interactions among these systems likely play a major role in determining persistence of or recovery from stuttering. Stuttering, or childhood onset fluency disorder (Diagnostic and Statistical Manual of Mental Disorders, 5th edition; American Psychiatric Association [APA], 2013), is a neurodevelopmental disorder that begins when neural networks supporting speech, language, and emotional functions are rapidly developing. The multifactorial dynamic pathways theory motivates experimental and clinical work to determine the specific factors that contribute to each child's pathway to the diagnosis of stuttering and those most likely to promote recovery.

Polarization momentum transfer collision: Faxen-Holtzmark theory and quantum dynamic shielding.

PubMed

Ki, Dae-Han; Jung, Young-Dae

2013-04-21

The influence of the quantum dynamic shielding on the polarization momentum transport collision is investigated by using the Faxen-Holtzmark theory in strongly coupled Coulomb systems. The electron-atom polarization momentum transport cross section is derived as a function of the collision energy, de Broglie wavelength, Debye length, thermal energy, and atomic quantum states. It is found that the dynamic shielding enhances the scattering phase shift as well as the polarization momentum transport cross section. The variation of quantum effect on the momentum transport collision due to the change of thermal energy and de Broglie wavelength is also discussed.

Atomic motion from the mean square displacement in a monatomic liquid

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wallace, Duane C.; De Lorenzi-Venneri, Giulia; Chisolm, Eric D.

V-T theory is constructed in the many-body Hamiltonian formulation, and is being developed as a novel approach to liquid dynamics theory. In this theory the liquid atomic motion consists of two contributions, normal mode vibrations in a single representative potential energy valley, and transits, which carry the system across boundaries between valleys. The mean square displacement time correlation function (the MSD) is a direct measure of the atomic motion, and our goal is to determine if the V-T formalism can produce a physically sensible account of this motion. We employ molecular dynamics (MD) data for a system representing liquid Na,more » and find the motion evolves in three successive time intervals: on the first 'vibrational' interval, the vibrational motion alone gives a highly accurate account of the MD data; on the second 'crossover' interval, the vibrational MSD saturates to a constant while the transit motion builds up from zero; on the third 'random walk' interval, the transit motion produces a purely diffusive random walk of the vibrational equilibrium positions. Furthermore, this motional evolution agrees with, and adds refinement to, the MSD atomic motion as described by current liquid dynamics theories.« less

Atomic motion from the mean square displacement in a monatomic liquid

DOE PAGES

Wallace, Duane C.; De Lorenzi-Venneri, Giulia; Chisolm, Eric D.

2016-04-08

V-T theory is constructed in the many-body Hamiltonian formulation, and is being developed as a novel approach to liquid dynamics theory. In this theory the liquid atomic motion consists of two contributions, normal mode vibrations in a single representative potential energy valley, and transits, which carry the system across boundaries between valleys. The mean square displacement time correlation function (the MSD) is a direct measure of the atomic motion, and our goal is to determine if the V-T formalism can produce a physically sensible account of this motion. We employ molecular dynamics (MD) data for a system representing liquid Na,more » and find the motion evolves in three successive time intervals: on the first 'vibrational' interval, the vibrational motion alone gives a highly accurate account of the MD data; on the second 'crossover' interval, the vibrational MSD saturates to a constant while the transit motion builds up from zero; on the third 'random walk' interval, the transit motion produces a purely diffusive random walk of the vibrational equilibrium positions. Furthermore, this motional evolution agrees with, and adds refinement to, the MSD atomic motion as described by current liquid dynamics theories.« less

Domain-area distribution anomaly in segregating multicomponent superfluids

NASA Astrophysics Data System (ADS)

Takeuchi, Hiromitsu

2018-01-01

The domain-area distribution in the phase transition dynamics of Z2 symmetry breaking is studied theoretically and numerically for segregating binary Bose-Einstein condensates in quasi-two-dimensional systems. Due to the dynamic-scaling law of the phase ordering kinetics, the domain-area distribution is described by a universal function of the domain area, rescaled by the mean distance between domain walls. The scaling theory for general coarsening dynamics in two dimensions hypothesizes that the distribution during the coarsening dynamics has a hierarchy with the two scaling regimes, the microscopic and macroscopic regimes with distinct power-law exponents. The power law in the macroscopic regime, where the domain size is larger than the mean distance, is universally represented with the Fisher's exponent of the percolation theory in two dimensions. On the other hand, the power-law exponent in the microscopic regime is sensitive to the microscopic dynamics of the system. This conjecture is confirmed by large-scale numerical simulations of the coupled Gross-Pitaevskii equation for binary condensates. In the numerical experiments of the superfluid system, the exponent in the microscopic regime anomalously reaches to its theoretical upper limit of the general scaling theory. The anomaly comes from the quantum-fluid effect in the presence of circular vortex sheets, described by the hydrodynamic approximation neglecting the fluid compressibility. It is also found that the distribution of superfluid circulation along vortex sheets obeys a dynamic-scaling law with different power-law exponents in the two regimes. An analogy to quantum turbulence on the hierarchy of vorticity distribution and the applicability to chiral superfluid 3He in a slab are also discussed.

Environmental Monitoring for Situation Assessment using Mobile and Fixed Sensors

NASA Technical Reports Server (NTRS)

Fikes, Richard

2004-01-01

This project was co-led by Dr. Sheila McIlraith and Prof. Richard Fikes. Substantial research results and published papers describing those results were produced in multiple technology areas, including the following: 1) Monitoring a Complex Physical System using a Hybrid Dynamic Bayes Net; 2) A Formal Theory of Testing for Dynamical Systems; 3) Diagnosing Hybrid Systems Using a Bayesian Model Selection Approach.

Synthesis of Systemic Functional Theory & Dynamical Systems Theory for Socio-Cultural Modeling

DTIC Science & Technology

2011-01-26

is, language and other resources (e.g. images and sound resources) are conceptualised as inter-locking systems of meaning which realise four...hierarchical ranks and strata (e.g. sounds, word groups, clauses, and complex discourse structures in language, and elements, figures and episodes in images ...integrating platform for describing how language and other resources (e.g. images and sound) work together to fulfil particular objectives. While

Dynamic stability of maglev systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cai, Y.; Chen, S.S.; Mulcahy, T.M.

1992-09-01

Since the occurrence of dynamic instabilities is not acceptable for any commercial maglev systems, it is important to consider the dynamic instability in the development of all maglev systems. This study is to consider the stability of maglev systems based on experimental data, scoping calculations and simple mathematical models. Divergence and flutter are obtained for coupled vibration of a three-degree-of-freedom maglev vehicle on the guideway which consists of double L-shaped aluminum segments attached to a rotating wheel. The theory and analysis developed in this study provides basic stability characteristics and identifies future research needs for maglev system.

Dynamics of one model of the fast kinematic dynamo

NASA Astrophysics Data System (ADS)

Medvedev, Timur; Medvedev, Vladislav; Zhuzhoma, Evgeny

2018-03-01

We suggest a new model of the fast nondissipative kinematic dynamo which describes the phenomenon of exponential growth of the magnetic field caused by the motion of the conducting medium. This phenomenon is known to occur in the evolution of magnetic fields of astrophysical bodies. In the 1970s A.D. Sakharov and Ya.B. Zeldovich proposed a “rope” scheme of this process which in terms of the modern theory of dynamical systems can be described as Smale solenoid. The main disadvantage of this scheme is that it is non-conservative. Our model is a modification of the Sakharov-Zeldovich’s model. We apply methods of the theory of dynamical systems to prove that it is free of this fault in the neighborhood of the nonwandering set.

Bringing Forth Mathematical Concepts: Signifying Sensorimotor Enactment in Fields of Promoted Action

ERIC Educational Resources Information Center

Abrahamson, Dor; Tminic, Dragan

2015-01-01

Inspired by Enactivist philosophy yet in dialog with it, we ask what theory of embodied cognition might best serve in articulating implications of Enactivism for mathematics education. We offer a blend of Dynamical Systems Theory and Sociocultural Theory as an analytic lens on micro-processes of action-to-concept evolution. We also illustrate the…

Theory of bi-molecular association dynamics in 2D for accurate model and experimental parameterization of binding rates

PubMed Central

Yogurtcu, Osman N.; Johnson, Margaret E.

2015-01-01

The dynamics of association between diffusing and reacting molecular species are routinely quantified using simple rate-equation kinetics that assume both well-mixed concentrations of species and a single rate constant for parameterizing the binding rate. In two-dimensions (2D), however, even when systems are well-mixed, the assumption of a single characteristic rate constant for describing association is not generally accurate, due to the properties of diffusional searching in dimensions d ≤ 2. Establishing rigorous bounds for discriminating between 2D reactive systems that will be accurately described by rate equations with a single rate constant, and those that will not, is critical for both modeling and experimentally parameterizing binding reactions restricted to surfaces such as cellular membranes. We show here that in regimes of intrinsic reaction rate (ka) and diffusion (D) parameters ka/D > 0.05, a single rate constant cannot be fit to the dynamics of concentrations of associating species independently of the initial conditions. Instead, a more sophisticated multi-parametric description than rate-equations is necessary to robustly characterize bimolecular reactions from experiment. Our quantitative bounds derive from our new analysis of 2D rate-behavior predicted from Smoluchowski theory. Using a recently developed single particle reaction-diffusion algorithm we extend here to 2D, we are able to test and validate the predictions of Smoluchowski theory and several other theories of reversible reaction dynamics in 2D for the first time. Finally, our results also mean that simulations of reactive systems in 2D using rate equations must be undertaken with caution when reactions have ka/D > 0.05, regardless of the simulation volume. We introduce here a simple formula for an adaptive concentration dependent rate constant for these chemical kinetics simulations which improves on existing formulas to better capture non-equilibrium reaction dynamics from dilute to dense systems. PMID:26328828

Generalized-active-space pair-density functional theory: an efficient method to study large, strongly correlated, conjugated systems

DOE PAGES

Ghosh, Soumen; Cramer, Christopher J.; Truhlar, Donald G.; ...

2017-01-19

Predicting ground- and excited-state properties of open-shell organic molecules by electronic structure theory can be challenging because an accurate treatment has to correctly describe both static and dynamic electron correlation. Strongly correlated systems, i.e., systems with near-degeneracy correlation effects, are particularly troublesome. Multiconfigurational wave function methods based on an active space are adequate in principle, but it is impractical to capture most of the dynamic correlation in these methods for systems characterized by many active electrons. Here, we recently developed a new method called multiconfiguration pair-density functional theory (MC-PDFT), that combines the advantages of wave function theory and density functionalmore » theory to provide a more practical treatment of strongly correlated systems. Here we present calculations of the singlet–triplet gaps in oligoacenes ranging from naphthalene to dodecacene. Calculations were performed for unprecedently large orbitally optimized active spaces of 50 electrons in 50 orbitals, and we test a range of active spaces and active space partitions, including four kinds of frontier orbital partitions. We show that MC-PDFT can predict the singlet–triplet splittings for oligoacenes consistent with the best available and much more expensive methods, and indeed MC-PDFT may constitute the benchmark against which those other models should be compared, given the absence of experimental data.« less

Generalized-active-space pair-density functional theory: an efficient method to study large, strongly correlated, conjugated systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghosh, Soumen; Cramer, Christopher J.; Truhlar, Donald G.

Predicting ground- and excited-state properties of open-shell organic molecules by electronic structure theory can be challenging because an accurate treatment has to correctly describe both static and dynamic electron correlation. Strongly correlated systems, i.e., systems with near-degeneracy correlation effects, are particularly troublesome. Multiconfigurational wave function methods based on an active space are adequate in principle, but it is impractical to capture most of the dynamic correlation in these methods for systems characterized by many active electrons. Here, we recently developed a new method called multiconfiguration pair-density functional theory (MC-PDFT), that combines the advantages of wave function theory and density functionalmore » theory to provide a more practical treatment of strongly correlated systems. Here we present calculations of the singlet–triplet gaps in oligoacenes ranging from naphthalene to dodecacene. Calculations were performed for unprecedently large orbitally optimized active spaces of 50 electrons in 50 orbitals, and we test a range of active spaces and active space partitions, including four kinds of frontier orbital partitions. We show that MC-PDFT can predict the singlet–triplet splittings for oligoacenes consistent with the best available and much more expensive methods, and indeed MC-PDFT may constitute the benchmark against which those other models should be compared, given the absence of experimental data.« less

Complete characterization of the stability of cluster synchronization in complex dynamical networks.

PubMed

Sorrentino, Francesco; Pecora, Louis M; Hagerstrom, Aaron M; Murphy, Thomas E; Roy, Rajarshi

2016-04-01

Synchronization is an important and prevalent phenomenon in natural and engineered systems. In many dynamical networks, the coupling is balanced or adjusted to admit global synchronization, a condition called Laplacian coupling. Many networks exhibit incomplete synchronization, where two or more clusters of synchronization persist, and computational group theory has recently proved to be valuable in discovering these cluster states based on the topology of the network. In the important case of Laplacian coupling, additional synchronization patterns can exist that would not be predicted from the group theory analysis alone. Understanding how and when clusters form, merge, and persist is essential for understanding collective dynamics, synchronization, and failure mechanisms of complex networks such as electric power grids, distributed control networks, and autonomous swarming vehicles. We describe a method to find and analyze all of the possible cluster synchronization patterns in a Laplacian-coupled network, by applying methods of computational group theory to dynamically equivalent networks. We present a general technique to evaluate the stability of each of the dynamically valid cluster synchronization patterns. Our results are validated in an optoelectronic experiment on a five-node network that confirms the synchronization patterns predicted by the theory.

Quantum State Diffusion

NASA Astrophysics Data System (ADS)

Percival, Ian

2005-10-01

1. Introduction; 2. Brownian motion and Itô calculus; 3. Open quantum systems; 4. Quantum state diffusion; 5. Localisation; 6. Numerical methods and examples; 7. Quantum foundations; 8. Primary state diffusion; 9. Classical dynamics of quantum localisation; 10. Semiclassical theory and linear dynamics.

Hamiltonian model and dynamic analyses for a hydro-turbine governing system with fractional item and time-lag

NASA Astrophysics Data System (ADS)

Xu, Beibei; Chen, Diyi; Zhang, Hao; Wang, Feifei; Zhang, Xinguang; Wu, Yonghong

2017-06-01

This paper focus on a Hamiltonian mathematical modeling for a hydro-turbine governing system including fractional item and time-lag. With regards to hydraulic pressure servo system, a universal dynamical model is proposed, taking into account the viscoelastic properties and low-temperature impact toughness of constitutive materials as well as the occurrence of time-lag in the signal transmissions. The Hamiltonian model of the hydro-turbine governing system is presented using the method of orthogonal decomposition. Furthermore, a novel Hamiltonian function that provides more detailed energy information is presented, since the choice of the Hamiltonian function is the key issue by putting the whole dynamical system to the theory framework of the generalized Hamiltonian system. From the numerical experiments based on a real large hydropower station, we prove that the Hamiltonian function can describe the energy variation of the hydro-turbine suitably during operation. Moreover, the effect of the fractional α and the time-lag τ on the dynamic variables of the hydro-turbine governing system are explored and their change laws identified, respectively. The physical meaning between fractional calculus and time-lag are also discussed in nature. All of the above theories and numerical results are expected to provide a robust background for the safe operation and control of large hydropower stations.

Dynamics of driven flow with exclusion in graphenelike structures

NASA Astrophysics Data System (ADS)

Stinchcombe, R. B.; de Queiroz, S. L. A.

2015-05-01

We present a mean-field theory for the dynamics of driven flow with exclusion in graphenelike structures, and numerically check its predictions. We treat first a specific combination of bond transmissivity rates, where mean field predicts, and numerics to a large extent confirms, that the sublattice structure characteristic of honeycomb networks becomes irrelevant. Dynamics, in the various regions of the phase diagram set by open boundary injection and ejection rates, is then in general identical to that of one-dimensional systems, although some discrepancies remain between mean-field theory and numerical results, in similar ways for both geometries. However, at the critical point for which the characteristic exponent is z =3 /2 in one dimension, the mean-field value z =2 is approached for very large systems with constant (finite) aspect ratio. We also treat a second combination of bond (and boundary) rates where, more typically, sublattice distinction persists. For the two rate combinations, in continuum or late-time limits, respectively, the coupled sets of mean-field dynamical equations become tractable with various techniques and give a two-band spectrum, gapless in the critical phase. While for the second rate combination quantitative discrepancies between mean-field theory and simulations increase for most properties and boundary rates investigated, theory still is qualitatively correct in general, and gives a fairly good quantitative account of features such as the late-time evolution of density profile differences from their steady-state values.

Parents' Goals for Children: The Dynamic Coexistence of Individualism and Collectivism in Cultures and Individuals

ERIC Educational Resources Information Center

Tamis-LeMonda, Catherine S.; Way, Niobe; Hughes, Diane; Yoshikawa, Hirokazu; Kalman, Ronit Kahana; Niwa, Erika Y.

2008-01-01

Current scholarship on the cultural value systems of individualism and collectivism, and the associated developmental goals of autonomy and relatedness, has moved beyond grand divide theories to emphasize variation within individuals and cultures. We present a theoretical model on the dynamic coexistence of cultural value systems (at the macro…

Reasons for Demotivation across Years of Study: Voices from Iranian English Major Students

ERIC Educational Resources Information Center

Hassaskhah, Jaleh; Mahdavi Zafarghandi, Amir; Fazeli, Maryam

2015-01-01

Language learning failure is often directly related to demotivation. The purpose of this study is to examine the process of demotivation and identify its sources within four years of an undergraduate degree programme. To this end, based on the complex dynamic systems perspective of the dynamic systems theories (DSTs), the demotivation test battery…

Understanding the Online Informal Learning of English as a Complex Dynamic System: An Emic Approach

ERIC Educational Resources Information Center

Sockett, Geoffrey

2013-01-01

Research into the online informal learning of English has already shown it to be a widespread phenomenon involving a range of comprehension and production activities such as viewing original version television series, listening to music on demand and social networking with other English users. Dynamic systems theory provides a suitable framework…

Understanding Learner Agency as a Complex Dynamic System

ERIC Educational Resources Information Center

Mercer, Sarah

2011-01-01

This paper attempts to contribute to a fuller understanding of the nature of language learner agency by considering it as a complex dynamic system. The purpose of the study was to explore detailed situated data to examine to what extent it is feasible to view learner agency through the lens of complexity theory. Data were generated through a…

Adiabatic markovian dynamics.

PubMed

Oreshkov, Ognyan; Calsamiglia, John

2010-07-30

We propose a theory of adiabaticity in quantum markovian dynamics based on a decomposition of the Hilbert space induced by the asymptotic behavior of the Lindblad semigroup. A central idea of our approach is that the natural generalization of the concept of eigenspace of the Hamiltonian in the case of markovian dynamics is a noiseless subsystem with a minimal noisy cofactor. Unlike previous attempts to define adiabaticity for open systems, our approach deals exclusively with physical entities and provides a simple, intuitive picture at the Hilbert-space level, linking the notion of adiabaticity to the theory of noiseless subsystems. As two applications of our theory, we propose a general framework for decoherence-assisted computation in noiseless codes and a dissipation-driven approach to holonomic computation based on adiabatic dragging of subsystems that is generally not achievable by nondissipative means.

Quantum Dynamics in Biological Systems

NASA Astrophysics Data System (ADS)

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.

The multi-layer multi-configuration time-dependent Hartree method for bosons: theory, implementation, and applications.

PubMed

Cao, Lushuai; Krönke, Sven; Vendrell, Oriol; Schmelcher, Peter

2013-10-07

We develop the multi-layer multi-configuration time-dependent Hartree method for bosons (ML-MCTDHB), a variational numerically exact ab initio method for studying the quantum dynamics and stationary properties of general bosonic systems. ML-MCTDHB takes advantage of the permutation symmetry of identical bosons, which allows for investigations of the quantum dynamics from few to many-body systems. Moreover, the multi-layer feature enables ML-MCTDHB to describe mixed bosonic systems consisting of arbitrary many species. Multi-dimensional as well as mixed-dimensional systems can be accurately and efficiently simulated via the multi-layer expansion scheme. We provide a detailed account of the underlying theory and the corresponding implementation. We also demonstrate the superior performance by applying the method to the tunneling dynamics of bosonic ensembles in a one-dimensional double well potential, where a single-species bosonic ensemble of various correlation strengths and a weakly interacting two-species bosonic ensemble are considered.

High frequency, multi-axis dynamic stiffness analysis of a fractionally damped elastomeric isolator using continuous system theory

NASA Astrophysics Data System (ADS)

Fredette, Luke; Singh, Rajendra

2017-02-01

A spectral element approach is proposed to determine the multi-axis dynamic stiffness terms of elastomeric isolators with fractional damping over a broad range of frequencies. The dynamic properties of a class of cylindrical isolators are modeled by using the continuous system theory in terms of homogeneous rods or Timoshenko beams. The transfer matrix type dynamic stiffness expressions are developed from exact harmonic solutions given translational or rotational displacement excitations. Broadband dynamic stiffness magnitudes (say up to 5 kHz) are computationally verified for axial, torsional, shear, flexural, and coupled stiffness terms using a finite element model. Some discrepancies are found between finite element and spectral element models for the axial and flexural motions, illustrating certain limitations of each method. Experimental validation is provided for an isolator with two cylindrical elements (that work primarily in the shear mode) using dynamic measurements, as reported in the prior literature, up to 600 Hz. Superiority of the fractional damping formulation over structural or viscous damping models is illustrated via experimental validation. Finally, the strengths and limitations of the spectral element approach are briefly discussed.

Data-driven discovery of Koopman eigenfunctions using deep learning

NASA Astrophysics Data System (ADS)

Lusch, Bethany; Brunton, Steven L.; Kutz, J. Nathan

2017-11-01

Koopman operator theory transforms any autonomous non-linear dynamical system into an infinite-dimensional linear system. Since linear systems are well-understood, a mapping of non-linear dynamics to linear dynamics provides a powerful approach to understanding and controlling fluid flows. However, finding the correct change of variables remains an open challenge. We present a strategy to discover an approximate mapping using deep learning. Our neural networks find this change of variables, its inverse, and a finite-dimensional linear dynamical system defined on the new variables. Our method is completely data-driven and only requires measurements of the system, i.e. it does not require derivatives or knowledge of the governing equations. We find a minimal set of approximate Koopman eigenfunctions that are sufficient to reconstruct and advance the system to future states. We demonstrate the method on several dynamical systems.

Nonadiabatic Molecular Dynamics and Orthogonality Constrained Density Functional Theory

NASA Astrophysics Data System (ADS)

Shushkov, Philip Georgiev

The exact quantum dynamics of realistic, multidimensional systems remains a formidable computational challenge. In many chemical processes, however, quantum effects such as tunneling, zero-point energy quantization, and nonadiabatic transitions play an important role. Therefore, approximate approaches that improve on the classical mechanical framework are of special practical interest. We propose a novel ring polymer surface hopping method for the calculation of chemical rate constants. The method blends two approaches, namely ring polymer molecular dynamics that accounts for tunneling and zero-point energy quantization, and surface hopping that incorporates nonadiabatic transitions. We test the method against exact quantum mechanical calculations for a one-dimensional, two-state model system. The method reproduces quite accurately the tunneling contribution to the rate and the distribution of reactants between the electronic states for this model system. Semiclassical instanton theory, an approach related to ring polymer molecular dynamics, accounts for tunneling by the use of periodic classical trajectories on the inverted potential energy surface. We study a model of electron transfer in solution, a chemical process where nonadiabatic events are prominent. By representing the tunneling electron with a ring polymer, we derive Marcus theory of electron transfer from semiclassical instanton theory after a careful analysis of the tunneling mode. We demonstrate that semiclassical instanton theory can recover the limit of Fermi's Golden Rule rate in a low-temperature, deep-tunneling regime. Mixed quantum-classical dynamics treats a few important degrees of freedom quantum mechanically, while classical mechanics describes affordably the rest of the system. But the interface of quantum and classical description is a challenging theoretical problem, especially for low-energy chemical processes. We therefore focus on the semiclassical limit of the coupled nuclear-electronic dynamics. We show that the time-dependent Schrodinger equation for the electrons employed in the widely used fewest switches surface hopping method is applicable only in the limit of nearly identical classical trajectories on the different potential energy surfaces. We propose a short-time decoupling algorithm that restricts the use of the Schrodinger equation only to the interaction regions. We test the short-time approximation on three model systems against exact quantum-mechanical calculations. The approximation improves the performance of the surface hopping approach. Nonadiabatic molecular dynamics simulations require the efficient and accurate computation of ground and excited state potential energy surfaces. Unlike the ground state calculations where standard methods exist, the computation of excited state properties is a challenging task. We employ time-independent density functional theory, in which the excited state energy is represented as a functional of the total density. We suggest an adiabatic-like approximation that simplifies the excited state exchange-correlation functional. We also derive a set of minimal conditions to impose exactly the orthogonality of the excited state Kohn-Sham determinant to the ground state determinant. This leads to an efficient, variational algorithm for the self-consistent optimization of the excited state energy. Finally, we assess the quality of the excitation energies obtained by the new method on a set of 28 organic molecules. The new approach provides results of similar accuracy to time-dependent density functional theory.

Towards generalizing co-evolutionary dynamics of socio-hydrology: Theoretical frameworks of cultural evolution and robustness-fragility tradeoff

NASA Astrophysics Data System (ADS)

Oh, W. S.; Yu, D. J.; Davis, T.; Hillis, V.; Waring, T. M.

2017-12-01

One ongoing challenge to socio-hydrology is the problem of generalization: to what extent do common human-water co-evolutions exist across distinct cases and what are underlying mechanisms of these co-evolutions. This problem stems in part from a lack of unifying theories in socio-hydrology, which hinders the explanation and generalization of results between cases in different regions. Theories help an analyst to make assumptions that are necessary to diagnose a specific phenomenon, to explain the general mechanisms of causation, and, thus, to predict future outcomes. To help address the issue, this study introduces two theories that are increasingly used in the fields of sustainability science and social-ecological systems research: robustness-fragility tradeoff (RFTO) and cultural multi-level selection (CMLS). We apply each of these theories to two distinct cases (water management issues in southwest Bangladesh and the Kissimmee River Basin, Florida) and interpret the phenomena of the levee and adaptation effects. CMLS and RFTO focus on complementary aspects of socio-hydrological phenomena. The theory of RFTO, which is mostly about inherent tradeoffs associated with infrastructure improvements, explains how efforts to increase system robustness can generate hidden endogenous risks. CMLS theory, rooted in the broader theory of cultural evolution, concerns how human cultural dynamics can act as an endogenous driver of system change across multiple levels of social organizations. Using the applied examples, we demonstrate that these two theories can provide an effective way to study social-hydrological systems and to overcome the generalization problem. Our work shows that multiple theories can be synthesized to give a richer understanding of diverse socio-hydrological patterns.

The Estimation Theory Framework of Data Assimilation

NASA Technical Reports Server (NTRS)

Cohn, S.; Atlas, Robert (Technical Monitor)

2002-01-01

Lecture 1. The Estimation Theory Framework of Data Assimilation: 1. The basic framework: dynamical and observation models; 2. Assumptions and approximations; 3. The filtering, smoothing, and prediction problems; 4. Discrete Kalman filter and smoother algorithms; and 5. Example: A retrospective data assimilation system

Quantum Information Biology: From Theory of Open Quantum Systems to Adaptive Dynamics

NASA Astrophysics Data System (ADS)

Asano, Masanari; Basieva, Irina; Khrennikov, Andrei; Ohya, Masanori; Tanaka, Yoshiharu; Yamato, Ichiro

This chapter reviews quantum(-like) information biology (QIB). Here biology is treated widely as even covering cognition and its derivatives: psychology and decision making, sociology, and behavioral economics and finances. QIB provides an integrative description of information processing by bio-systems at all scales of life: from proteins and cells to cognition, ecological and social systems. Mathematically QIB is based on the theory of adaptive quantum systems (which covers also open quantum systems). Ideologically QIB is based on the quantum-like (QL) paradigm: complex bio-systems process information in accordance with the laws of quantum information and probability. This paradigm is supported by plenty of statistical bio-data collected at all bio-scales. QIB re ects the two fundamental principles: a) adaptivity; and, b) openness (bio-systems are fundamentally open). In addition, quantum adaptive dynamics provides the most generally possible mathematical representation of these principles.

Network analysis applications in hydrology

NASA Astrophysics Data System (ADS)

Price, Katie

2017-04-01

Applied network theory has seen pronounced expansion in recent years, in fields such as epidemiology, computer science, and sociology. Concurrent development of analytical methods and frameworks has increased possibilities and tools available to researchers seeking to apply network theory to a variety of problems. While water and nutrient fluxes through stream systems clearly demonstrate a directional network structure, the hydrological applications of network theory remain under­explored. This presentation covers a review of network applications in hydrology, followed by an overview of promising network analytical tools that potentially offer new insights into conceptual modeling of hydrologic systems, identifying behavioral transition zones in stream networks and thresholds of dynamical system response. Network applications were tested along an urbanization gradient in Atlanta, Georgia, USA. Peachtree Creek and Proctor Creek. Peachtree Creek contains a nest of five long­term USGS streamflow and water quality gages, allowing network application of long­term flow statistics. The watershed spans a range of suburban and heavily urbanized conditions. Summary flow statistics and water quality metrics were analyzed using a suite of network analysis techniques, to test the conceptual modeling and predictive potential of the methodologies. Storm events and low flow dynamics during Summer 2016 were analyzed using multiple network approaches, with an emphasis on tomogravity methods. Results indicate that network theory approaches offer novel perspectives for understanding long­ term and event­based hydrological data. Key future directions for network applications include 1) optimizing data collection, 2) identifying "hotspots" of contaminant and overland flow influx to stream systems, 3) defining process domains, and 4) analyzing dynamic connectivity of various system components, including groundwater­surface water interactions.

Dynamics of essential collective motions in proteins: Theory

NASA Astrophysics Data System (ADS)

Stepanova, Maria

2007-11-01

A general theoretical background is introduced for characterization of conformational motions in protein molecules, and for building reduced coarse-grained models of proteins, based on the statistical analysis of their phase trajectories. Using the projection operator technique, a system of coupled generalized Langevin equations is derived for essential collective coordinates, which are generated by principal component analysis of molecular dynamic trajectories. The number of essential degrees of freedom is not limited in the theory. An explicit analytic relation is established between the generalized Langevin equation for essential collective coordinates and that for the all-atom phase trajectory projected onto the subspace of essential collective degrees of freedom. The theory introduced is applied to identify correlated dynamic domains in a macromolecule and to construct coarse-grained models representing the conformational motions in a protein through a few interacting domains embedded in a dissipative medium. A rigorous theoretical background is provided for identification of dynamic correlated domains in a macromolecule. Examples of domain identification in protein G are given and employed to interpret NMR experiments. Challenges and potential outcomes of the theory are discussed.

Quantum learning of classical stochastic processes: The completely positive realization problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Monràs, Alex; Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543; Winter, Andreas

2016-01-15

Among several tasks in Machine Learning, a specially important one is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of this is the task of inferring the hidden Markov model underlying a given stochastic process. This is known as the positive realization problem (PRP), [L. Benvenuti and L. Farina, IEEE Trans. Autom. Control 49(5), 651–664 (2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece inmore » the broad field of positive systems theory. We consider the scenario where the latent variables are quantum (i.e., quantum states of a finite-dimensional system) and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument — if any — yields the process at hand by iterative application. We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the hidden Markov model, or the iterated quantum instrument, is however devoid of any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The completely positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine learning, device-independent characterization and reverse-engineering of stochastic processes and quantum processors, and more generally, of dynamical processes with quantum memory [M. Guţă, Phys. Rev. A 83(6), 062324 (2011); M. Guţă and N. Yamamoto, e-print http://arxiv.org/abs/1303.3771 (2013)].« less

Variational principles for dissipative (sub)systems, with applications to the theory of linear dispersion and geometrical optics

DOE PAGES

Dodin, I. Y.; Zhmoginov, A. I.; Ruiz, D. E.

2017-02-24

Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables. We propose a different approach. Here, we show that for a broad class of dissipative systems of practical interest, variational principles can be formulated using constant Lagrange multipliers and Lagrangians nonlocal in time, which allow treating reversible and irreversible dynamics on the same footing. A general variational theory of linear dispersion is formulated as an example. Particularly, we present a variational formulation for linear geometrical optics inmore » a general dissipative medium, which is allowed to be nonstationary, inhomogeneous, anisotropic, and exhibit both temporal and spatial dispersion simultaneously.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, Junjun; Feng, Tongtong; Gu, Qiang, E-mail: qgu@ustb.edu.cn

Understanding the collective dynamics in a many-body system has been a central task in condensed matter physics. To achieve this task, we develop a Hartree–Fock theory to study the collective oscillations of spinor Fermi system, motivated by recent experiment on spin-9/2 fermions. We observe an oscillation period shoulder for small rotation angles. Different from previous studies, where the shoulder is found connected to the resonance from periodic to running phase, here the system is always in a running phase in the two-body phase space. This shoulder survives even in the many-body oscillations, which could be tested in the experiments. Wemore » also show how these collective oscillations evolve from two- to many-body. Our theory provides an alternative way to understand the collective dynamics in large-spin Fermi systems.« less

Dissipative dynamics in quasifission

NASA Astrophysics Data System (ADS)

Oberacker, V. E.; Umar, A. S.; Simenel, C.

2014-11-01

Quasifission is the primary reaction mechanism that prevents the formation of superheavy elements in heavy-ion fusion experiments. Employing the time-dependent density functional theory approach, we study quasifission in the systems Ca,4840+238U . Results show that for 48Ca projectiles the quasifission is substantially reduced in comparison to the 40Ca case. This partly explains the success of superheavy element formation with 48Ca beams. For the first time, we also calculate the repartition of excitation energies of the two fragments in a dynamic microscopic theory. The differences between both systems are interpreted in terms of initial neutron to proton asymmetry of the colliding partners.

Dynamics of elastic systems

NASA Astrophysics Data System (ADS)

Sankovich, Vladimir

1998-12-01

The goal of this paper is to build a consistent physical theory of the dynamics of the bat-ball interaction. This requires creating realistic models for both the softball bat and the softball. Some of the features of these models are known phenomenologically, from experiments conducted in our laboratory, others will be introduced and computed from first principles here for the first time. Both interacting objects are treated from the viewpoint of the theory of elasticity, and it is shown how a computer can be used to accurately calculate all the relevant characteristics of batball collisions. It is shown also how the major elastic parameters of the material constituting the interior of a softball can be determined using the existing experimental data. These parameters, such as the Young's modulus, the Poisson ratio and the damping coefficient are vital for the accurate description of the ball's dynamics. We are demonstrating how the existing theories of the elastic behavior of solid bars and hollow shells can be augmented to simplify the resulting equations and make the subsequent computer analysis feasible. The standard system of fourth-order PDE's is reduced to a system of the second order, because of the inclusion of the usually ignored effects of the shear forces in the bat.

Transition Manifolds of Complex Metastable Systems: Theory and Data-Driven Computation of Effective Dynamics.

PubMed

Bittracher, Andreas; Koltai, Péter; Klus, Stefan; Banisch, Ralf; Dellnitz, Michael; Schütte, Christof

2018-01-01

We consider complex dynamical systems showing metastable behavior, but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective dynamics. For answering this question, we aim at finding nonlinear coordinates, called reaction coordinates, such that the projection of the dynamics onto these coordinates preserves the dominant time scales of the dynamics. We show that, based on a specific reducibility property, the existence of good low-dimensional reaction coordinates preserving the dominant time scales is guaranteed. Based on this theoretical framework, we develop and test a novel numerical approach for computing good reaction coordinates. The proposed algorithmic approach is fully local and thus not prone to the curse of dimension with respect to the state space of the dynamics. Hence, it is a promising method for data-based model reduction of complex dynamical systems such as molecular dynamics.

Strong dynamics and lattice gauge theory

NASA Astrophysics Data System (ADS)

Schaich, David

In this dissertation I use lattice gauge theory to study models of electroweak symmetry breaking that involve new strong dynamics. Electroweak symmetry breaking (EWSB) is the process by which elementary particles acquire mass. First proposed in the 1960s, this process has been clearly established by experiments, and can now be considered a law of nature. However, the physics underlying EWSB is still unknown, and understanding it remains a central challenge in particle physics today. A natural possibility is that EWSB is driven by the dynamics of some new, strongly-interacting force. Strong interactions invalidate the standard analytical approach of perturbation theory, making these models difficult to study. Lattice gauge theory is the premier method for obtaining quantitatively-reliable, nonperturbative predictions from strongly-interacting theories. In this approach, we replace spacetime by a regular, finite grid of discrete sites connected by links. The fields and interactions described by the theory are likewise discretized, and defined on the lattice so that we recover the original theory in continuous spacetime on an infinitely large lattice with sites infinitesimally close together. The finite number of degrees of freedom in the discretized system lets us simulate the lattice theory using high-performance computing. Lattice gauge theory has long been applied to quantum chromodynamics, the theory of strong nuclear interactions. Using lattice gauge theory to study dynamical EWSB, as I do in this dissertation, is a new and exciting application of these methods. Of particular interest is non-perturbative lattice calculation of the electroweak S parameter. Experimentally S ≈ -0.15(10), which tightly constrains dynamical EWSB. On the lattice, I extract S from the momentum-dependence of vector and axial-vector current correlators. I created and applied computer programs to calculate these correlators and analyze them to determine S. I also calculated the masses and other properties of the new particles predicted by these theories. I find S ≳ 0.1 in the specific theories I study. Although this result still disagrees with experiment, it is much closer to the experimental value than is the conventional wisdom S ≳ 0.3. These results encourage further lattice studies to search for experimentally viable strongly-interacting theories of EWSB.

Thermal quantum time-correlation functions from classical-like dynamics

NASA Astrophysics Data System (ADS)

Hele, Timothy J. H.

2017-07-01

Thermal quantum time-correlation functions are of fundamental importance in quantum dynamics, allowing experimentally measurable properties such as reaction rates, diffusion constants and vibrational spectra to be computed from first principles. Since the exact quantum solution scales exponentially with system size, there has been considerable effort in formulating reliable linear-scaling methods involving exact quantum statistics and approximate quantum dynamics modelled with classical-like trajectories. Here, we review recent progress in the field with the development of methods including centroid molecular dynamics , ring polymer molecular dynamics (RPMD) and thermostatted RPMD (TRPMD). We show how these methods have recently been obtained from 'Matsubara dynamics', a form of semiclassical dynamics which conserves the quantum Boltzmann distribution. We also apply the Matsubara formalism to reaction rate theory, rederiving t → 0+ quantum transition-state theory (QTST) and showing that Matsubara-TST, like RPMD-TST, is equivalent to QTST. We end by surveying areas for future progress.

Guidance of Nonlinear Nonminimum-Phase Dynamic Systems

NASA Technical Reports Server (NTRS)

Devasia, Santosh

1996-01-01

The research work has advanced the inversion-based guidance theory for: systems with non-hyperbolic internal dynamics; systems with parameter jumps; and systems where a redesign of the output trajectory is desired. A technique to achieve output tracking for nonminimum phase linear systems with non-hyperbolic and near non-hyperbolic internal dynamics was developed. This approach integrated stable inversion techniques, that achieve exact-tracking, with approximation techniques, that modify the internal dynamics to achieve desirable performance. Such modification of the internal dynamics was used (a) to remove non-hyperbolicity which is an obstruction to applying stable inversion techniques and (b) to reduce large preactuation times needed to apply stable inversion for near non-hyperbolic cases. The method was applied to an example helicopter hover control problem with near non-hyperbolic internal dynamics for illustrating the trade-off between exact tracking and reduction of preactuation time. Future work will extend these results to guidance of nonlinear non-hyperbolic systems. The exact output tracking problem for systems with parameter jumps was considered. Necessary and sufficient conditions were derived for the elimination of switching-introduced output transient. While previous works had studied this problem by developing a regulator that maintains exact tracking through parameter jumps (switches), such techniques are, however, only applicable to minimum-phase systems. In contrast, our approach is also applicable to nonminimum-phase systems and leads to bounded but possibly non-causal solutions. In addition, for the case when the reference trajectories are generated by an exosystem, we developed an exact-tracking controller which could be written in a feedback form. As in standard regulator theory, we also obtained a linear map from the states of the exosystem to the desired system state, which was defined via a matrix differential equation.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

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

1994-07-01

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.more » 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 [ital ab] [ital 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.« less

Kinetic theory for strongly coupled Coulomb systems

NASA Astrophysics Data System (ADS)

Dufty, James; Wrighton, Jeffrey

2018-01-01

The calculation of dynamical properties for matter under extreme conditions is a challenging task. The popular Kubo-Greenwood model exploits elements from equilibrium density-functional theory (DFT) that allow a detailed treatment of electron correlations, but its origin is largely phenomenological; traditional kinetic theories have a more secure foundation but are limited to weak ion-electron interactions. The objective here is to show how a combination of the two evolves naturally from the short-time limit for the generator of the effective single-electron dynamics governing time correlation functions without such limitations. This provides a theoretical context for the current DFT-related approach, the Kubo-Greenwood model, while showing the nature of its corrections. The method is to calculate the short-time dynamics in the single-electron subspace for a given configuration of the ions. This differs from the usual kinetic theory approach in which an average over the ions is performed as well. In this way the effective ion-electron interaction includes strong Coulomb coupling and is shown to be determined from DFT. The correlation functions have the form of the random-phase approximation for an inhomogeneous system but with renormalized ion-electron and electron-electron potentials. The dynamic structure function, density response function, and electrical conductivity are calculated as examples. The static local field corrections in the dielectric function are identified in this way. The current analysis is limited to semiclassical electrons (quantum statistical potentials), so important quantum conditions are excluded. However, a quantization of the kinetic theory is identified for broader application while awaiting its detailed derivation.

Theory of networked minority games based on strategy pattern dynamics.

PubMed

Lo, T S; Chan, H Y; Hui, P M; Johnson, N F

2004-11-01

We formulate a theory of agent-based models in which agents compete to be in a winning group. The agents may be part of a network or not, and the winning group may be a minority group or not. An important feature of the present formalism is its focus on the dynamical pattern of strategy rankings, and its careful treatment of the strategy ties which arise during the system's temporal evolution. We apply it to the minority game with connected populations. Expressions for the mean success rate among the agents and for the mean success rate for agents with k neighbors are derived. We also use the theory to estimate the value of connectivity p above which the binary-agent-resource system with high resource levels makes the transition into the high-connectivity state.

MpTheory Java library: a multi-platform Java library for systems biology based on the Metabolic P theory.

PubMed

Marchetti, Luca; Manca, Vincenzo

2015-04-15

MpTheory Java library is an open-source project collecting a set of objects and algorithms for modeling observed dynamics by means of the Metabolic P (MP) theory, that is, a mathematical theory introduced in 2004 for modeling biological dynamics. By means of the library, it is possible to model biological systems both at continuous and at discrete time. Moreover, the library comprises a set of regression algorithms for inferring MP models starting from time series of observations. To enhance the modeling experience, beside a pure Java usage, the library can be directly used within the most popular computing environments, such as MATLAB, GNU Octave, Mathematica and R. The library is open-source and licensed under the GNU Lesser General Public License (LGPL) Version 3.0. Source code, binaries and complete documentation are available at http://mptheory.scienze.univr.it. luca.marchetti@univr.it, marchetti@cosbi.eu Supplementary data are available at Bioinformatics online. © The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Variational mixed quantum/semiclassical simulation of dihalogen guest and rare-gas solid host dynamics

NASA Astrophysics Data System (ADS)

Cheng, Xiaolu; Cina, Jeffrey A.

2014-07-01

A variational mixed quantum-semiclassical theory for the internal nuclear dynamics of a small molecule and the induced small-amplitude coherent motion of a low-temperature host medium is developed, tested, and used to simulate the temporal evolution of nonstationary states of the internal molecular and surrounding medium degrees of freedom. In this theory, termed the Fixed Vibrational Basis/Gaussian Bath (FVB/GB) method, the system is treated fully quantum mechanically while Gaussian wave packets are used for the bath degrees of freedom. An approximate time-dependent wave function of the entire model is obtained instead of just a reduced system density matrix, so the theory enables the analysis of the entangled system and bath dynamics that ensues following initial displacement of the internal-molecular (system) coordinate from its equilibrium position. The norm- and energy-conserving properties of the propagation of our trial wave function are natural consequences of the Dirac-Frenkel-McLachlan variational principle. The variational approach also stabilizes the time evolution in comparison to the same ansatz propagated under a previously employed locally quadratic approximation to the bath potential and system-bath interaction terms in the bath-parameter equations of motion. Dynamics calculations are carried out for molecular iodine in a 2D krypton lattice that reveal both the time-course of vibrational decoherence and the details of host-atom motion accompanying energy dissipation and dephasing. This work sets the stage for the comprehensive simulation of ultrafast time-resolved optical experiments on small molecules in low-temperature solids.

Dynamic evolution characteristics of a fractional order hydropower station system

NASA Astrophysics Data System (ADS)

Gao, Xiang; Chen, Diyi; Yan, Donglin; Xu, Beibei; Wang, Xiangyu

2018-01-01

This paper investigates the dynamic evolution characteristics of the hydropower station by introducing the fractional order damping forces. A careful analysis of the dynamic characteristics of the generator shaft system is carried out under different values of fractional order. It turns out the vibration state of the axis coordinates has a certain evolution law with the increase of the fractional order. Significantly, the obtained law exists in the horizontal evolution and vertical evolution of the dynamical behaviors. Meanwhile, some interesting dynamical phenomena were found in this process. The outcomes of this study enrich the nonlinear dynamic theory from the engineering practice of hydropower stations.

Adopting a Cultural Portfolio Project in Teaching German as a Foreign Language: Language Teacher Cognition as a Dynamic System

ERIC Educational Resources Information Center

Feryok, Anne; Oranje, Jo

2015-01-01

Intercultural language teaching and learning has increasingly been adopted in state school systems, yet studies have shown that language teachers struggle to include it in their practice. The aim of this study is to use dynamic systems theory to examine how a German as a foreign language teacher in a New Zealand secondary school adopted a project…

Toward experimental validation of a model for human sensorimotor learning and control in teleoperation

NASA Astrophysics Data System (ADS)

Roth, Eatai; Howell, Darrin; Beckwith, Cydney; Burden, Samuel A.

2017-05-01

Humans, interacting with cyber-physical systems (CPS), formulate beliefs about the system's dynamics. It is natural to expect that human operators, tasked with teleoperation, use these beliefs to control the remote robot. For tracking tasks in the resulting human-cyber-physical system (HCPS), theory suggests that human operators can achieve exponential tracking (in stable systems) without state estimation provided they possess an accurate model of the system's dynamics. This internalized inverse model, however, renders a portion of the system state unobservable to the human operator—the zero dynamics. Prior work shows humans can track through observable linear dynamics, thus we focus on nonlinear dynamics rendered unobservable through tracking control. We propose experiments to assess the human operator's ability to learn and invert such models, and distinguish this behavior from that achieved by pure feedback control.

Ab Initio and Monte Carlo Approaches For the MagnetocaloricEffect in Co- and In-Doped Ni-Mn-Ga Heusler Alloys

NASA Astrophysics Data System (ADS)

Sokolovskiy, Vladimir; Grünebohm, Anna; Buchelnikov, Vasiliy; Entel, Peter

2014-09-01

This special issue collects contributions from the participants of the "Information in Dynamical Systems and Complex Systems" workshop, which cover a wide range of important problems and new approaches that lie in the intersection of information theory and dynamical systems. The contributions include theoretical characterization and understanding of the different types of information flow and causality in general stochastic processes, inference and identification of coupling structure and parameters of system dynamics, rigorous coarse-grain modeling of network dynamical systems, and exact statistical testing of fundamental information-theoretic quantities such as the mutual information. The collective efforts reported herein reflect a modern perspective of the intimate connection between dynamical systems and information flow, leading to the promise of better understanding and modeling of natural complex systems and better/optimal design of engineering systems.

TRIZ theory in NEA photocathode preparation system

NASA Astrophysics Data System (ADS)

Qiao, Jianliang; Huang, Dayong; Li, Xiangjiang; Gao, Youtang

2016-09-01

The solutions to the engineering problems were provided according to the innovation principle based on the theory of TRIZ. The ultra high vacuum test and evaluation system for the preparation of negative electron affinity (NEA) photocathode has the characteristics of complex structure and powerful functions. Segmentation principle, advance function principle, curved surface principle, dynamic characteristics principle and nested principle adopted by the design of ultra high vacuum test and evaluation system for cathode preparation were analyzed. The applications of the physical contradiction and the substance-field analysis method of the theory of TRIZ in the cathode preparation ultra high vacuum test and evaluation system were discussed.

The Development of Subordinate Clauses in German and Swedish as L2s: A Theoretical and Methodological Camparison

ERIC Educational Resources Information Center

Baten, Kristof; Håkansson, Gisela

2015-01-01

In this article, we aim to contribute to the debate about the use of subordination as a measure of language proficiency. We compare two theories of SLA--specifically, processability theory (PT; Pienemann, 1998) and dynamic systems theory (DST; de Bot, Lowie, & Verspoor, 2007)--and, more particularly, how they address the development of…

Introduction

NASA Astrophysics Data System (ADS)

Cohen, E. G. D.

Lecture notes are organized around the key word dissipation, while focusing on a presentation of modern theoretical developments in the study of irreversible phenomena. A broad cross-disciplinary perspective towards non-equilibrium statistical mechanics is backed by the general theory of nonlinear and complex dynamical systems. The classical-quantum intertwine and semiclassical dissipative borderline issue (decoherence, "classical out of quantum") are here included . Special emphasis is put on links between the theory of classical and quantum dynamical systems (temporal disorder, dynamical chaos and transport processes) with central problems of non-equilibrium statistical mechanics like e.g. the connection between dynamics and thermodynamics, relaxation towards equilibrium states and mechanisms capable to drive and next maintain the physical system far from equilibrium, in a non-equilibrium steady (stationary) state. The notion of an equilibrium state - towards which a system naturally evolves if left undisturbed - is a fundamental concept of equilibrium statistical mechanics. Taken as a primitive point of reference that allows to give an unambiguous status to near equilibrium and far from equilibrium systems, together with the dynamical notion of a relaxation (decay) towards a prescribed asymptotic invariant measure or probability distribution (properties of ergodicity and mixing are implicit). A related issue is to keep under control the process of driving a physical system away from an initial state of equilibrium and either keeping it in another (non-equilibrium) steady state or allowing to restore the initial data (return back, relax). To this end various models of environment (heat bath, reservoir, thermostat, measuring instrument etc.), and the environment - system coupling are analyzed. The central theme of the book is the dynamics of dissipation and various mechanisms responsible for the irreversible behaviour (transport properties) of open systems on classical and quantum levels of description. A distinguishing feature of these lecture notes is that microscopic foundations of irreversibility are investigated basically in terms of "small" systems, when the "system" and/or "environment" may have a finite (and small) number of degrees of freedom and may be bounded. This is to be contrasted with the casual understanding of statistical mechanics which is regarded to refer to systems with a very large number of degrees of freedom. In fact, it is commonly accepted that the accumulation of effects due to many (range of the Avogadro number) particles is required for statistical mechanics reasoning. Albeit those large numbers are not at all sufficient for transport properties. A helpful hint towards this conceptual turnover comes from the observation that for chaotic dynamical systems the random time evolution proves to be compatible with the underlying purely deterministic laws of motion. Chaotic features of the classical dynamics already appear in systems with two degrees of freedom and such systems need to be described in statistical terms, if we wish to quantify the dynamics of relaxation towards an invariant ergodic measure. The relaxation towards equilibrium finds a statistical description through an analysis of statistical ensembles. This entails an extension of the range of validity of statistical mechanics to small classical systems. On the other hand, the dynamics of fluctuations in macroscopic dissipative systems (due to their molecular composition and thermal mobility) may render a characterization of such systems as being chaotic. That motivates attempts of understanding the role of microscopic chaos and various "chaotic hypotheses" - dynamical systems approach is being pushed down to the level of atoms, molecules and complex matter constituents, whose natural substitute are low-dimensional model subsystems (encompassing as well the mesoscopic "quantum chaos") - in non-equilibrium transport phenomena. On the way a number of questions is addressed like e.g.: is there, or what is the nature of a connection between chaos (modern theory of dynamical systems) and irreversible thermodynamics; can really quantum chaos explain some peculiar features of quantum transport? The answer in both cases is positive, modulo a careful discrimination between viewing the dynamical chaos as a necessary or sufficient basis for irreversibility. In those dynamical contexts, another key term dynamical semigroups refers to major technical tools appropriate for the "dissipative mathematics", modelling irreversible behaviour on the classical and quantum levels of description. Dynamical systems theory and "quantum chaos" research involve both a high level of mathematical sophistication and heavy computer "experimentation". One of the present volume specific flavors is a tutorial access to quite advanced mathematical tools. They gradually penetrate the classical and quantum dynamical semigroup description, while culminating in the noncommutative Brillouin zone construction as a prerequisite to understand transport in aperiodic solids. Lecture notes are structured into chapters to give a better insight into major conceptual streamlines. Chapter I is devoted to a discussion of non-equilibrium steady states and, through so-called chaotic hypothesis combined with suitable fluctuation theorems, elucidates the role of Sinai-Ruelle-Bowen distribution in both equilibrium and non-equilibrium statistical physics frameworks (E. G. D. Cohen). Links between dynamics and statistics (Boltzmann versus Tsallis) are also discussed. Fluctuation relations and a survey of deterministic thermostats are given in the context of non-equilibrium steady states of fluids (L. Rondoni). Response of systems driven far from equilibrium is analyzed on the basis of a central assertion about the existence of the statistical representation in terms of an ensemble of dynamical realizations of the driving process. Non-equilibrium work relation is deduced for irreversible processes (C. Jarzynski). The survey of non-equilibrium steady states in statistical mechanics of classical and quantum systems employs heat bath models and the random matrix theory input. The quantum heat bath analysis and derivation of fluctuation-dissipation theorems is performed by means of the influence functional technique adopted to solve quantum master equations (D. Kusnezov). Chapter II deals with an issue of relaxation and its dynamical theory in both classical and quantum contexts. Pollicott-Ruelle resonance background for the exponential decay scenario is discussed for irreversible processes of diffusion in the Lorentz gas and multibaker models (P. Gaspard). The Pollicott-Ruelle theory reappears as a major inspiration in the survey of the behaviour of ensembles of chaotic systems, with a focus on model systems for which no rigorous results concerning the exponential decay of correlations in time is available (S. Fishman). The observation, that non-equilibrium transport processes in simple classical chaotic systems can be described in terms of fractal structures developing in the system phase space, links their formation and properties with the entropy production in the course of diffusion processes displaying a low dimensional deterministic (chaotic) origin (J. R. Dorfman). Chapter III offers an introduction to the theory of dynamical semigroups. Asymptotic properties of Markov operators and Markov semigroups acting in the set of probability densities (statistical ensemble notion is implicit) are analyzed. Ergodicity, mixing, strong (complete) mixing and sweeping are discussed in the familiar setting of "noise, chaos and fractals" (R. Rudnicki). The next step comprises a passage to quantum dynamical semigroups and completely positive dynamical maps, with an ultimate goal to introduce a consistent framework for the analysis of irreversible phenomena in open quantum systems, where dissipation and decoherence are crucial concepts (R. Alicki). Friction and damping in classical and quantum mechanics of finite dissipative systems is analyzed by means of Markovian quantum semigroups with special emphasis on the issue of complete positivity (M. Fannes). Specific two-level model systems of elementary particle physics (kaons) and rudiments of neutron interferometry are employed to elucidate a distinction between positivity and complete positivity (F. Benatti). Quantization of dynamics of stochastic models related to equilibrium Gibbs states results in dynamical maps which form quantum stochastic dynamical semigroups (W. A. Majewski). Chapter IV addresses diverse but deeply interrelated features of driven chaotic (mesoscopic) classical and quantum systems, their dissipative properties, notions of quantum irreversibility, entanglement, dephasing and decoherence. A survey of non-perturbative quantum effects for open quantum systems is concluded by outlining the discrepancies between random matrix theory and non-perturbative semiclassical predictions (D. Cohen). As a useful supplement to the subject of bounded open systems, methods of quantum state control in a cavity (coherent versus incoherent dynamics and dissipation) are described for low dimensional quantum systems (A. Buchleitner). The dynamics of open quantum systems can be alternatively described by means of non-Markovian stochastic Schrödinger equation, jointly for an open system and its environment, which moves us beyond the Linblad evolution scenario of Markovian dynamical semigroups. The quantum Brownian motion is considered (W. Strunz) . Chapter V enforces a conceptual transition 'from "small" to "large" systems with emphasis on irreversible thermodynamics of quantum transport. Typical features of the statistical mechanics of infinitely extended systems and the dynamical (small) systems approach are described by means of representative examples of relaxation towards asymptotic steady states: quantum one-dimensional lattice conductor and an open multibaker map (S. Tasaki). Dissipative transport in aperiodic solids is reviewed by invoking methods on noncommutative geometry. The anomalous Drude formula is derived. The occurence of quantum chaos is discussed together with its main consequences (J. Bellissard). The chapter is concluded by a survey of scaling limits of the N-body Schrödinger quantum dynamics, where classical evolution equations of irreversible statistical mechanics (linear Boltzmann, Hartree, Vlasov) emerge "out of quantum". In particular, a scaling limit of one body quantum dynamics with impurities (static random potential) and that of quantum dynamics with weakly coupled phonons are shown to yield the linear Boltzmann equation (L. Erdös). Various interrelations between chapters and individual lectures, plus a detailed fine-tuned information about the subject matter coverage of the volume, can be recovered by examining an extensive index.

Using activity theory to study cultural complexity in medical education.

PubMed

Frambach, Janneke M; Driessen, Erik W; van der Vleuten, Cees P M

2014-06-01

There is a growing need for research on culture, cultural differences and cultural effects of globalization in medical education, but these are complex phenomena to investigate. Socio-cultural activity theory seems a useful framework to study cultural complexity, because it matches current views on culture as a dynamic process situated in a social context, and has been valued in diverse fields for yielding rich understandings of complex issues and key factors involved. This paper explains how activity theory can be used in (cross-)cultural medical education research. We discuss activity theory's theoretical background and principles, and we show how these can be applied to the cultural research practice by discussing the steps involved in a cross-cultural study that we conducted, from formulating research questions to drawing conclusions. We describe how the activity system, the unit of analysis in activity theory, can serve as an organizing principle to grasp cultural complexity. We end with reflections on the theoretical and practical use of activity theory for cultural research and note that it is not a shortcut to capture cultural complexity: it is a challenge for researchers to determine the boundaries of their study and to analyze and interpret the dynamics of the activity system.

Quantum criticality and black holes.

PubMed

Sachdev, Subir; Müller, Markus

2009-04-22

Many condensed matter experiments explore the finite temperature dynamics of systems near quantum critical points. Often, there are no well-defined quasiparticle excitations, and so quantum kinetic equations do not describe the transport properties completely. The theory shows that the transport coefficients are not proportional to a mean free scattering time (as is the case in the Boltzmann theory of quasiparticles), but are completely determined by the absolute temperature and by equilibrium thermodynamic observables. Recently, explicit solutions of this quantum critical dynamics have become possible via the anti-de Sitter/conformal field theory duality discovered in string theory. This shows that the quantum critical theory provides a holographic description of the quantum theory of black holes in a negatively curved anti-de Sitter space, and relates its transport coefficients to properties of the Hawking radiation from the black hole. We review how insights from this connection have led to new results for experimental systems: (i) the vicinity of the superfluid-insulator transition in the presence of an applied magnetic field, and its possible application to measurements of the Nernst effect in the cuprates, (ii) the magnetohydrodynamics of the plasma of Dirac electrons in graphene and the prediction of a hydrodynamic cyclotron resonance.

Beyond Kohn-Sham Approximation: Hybrid Multistate Wave Function and Density Functional Theory.

PubMed

Gao, Jiali; Grofe, Adam; Ren, Haisheng; Bao, Peng

2016-12-15

A multistate density functional theory (MSDFT) is presented in which the energies and densities for the ground and excited states are treated on the same footing using multiconfigurational approaches. The method can be applied to systems with strong correlation and to correctly describe the dimensionality of the conical intersections between strongly coupled dissociative potential energy surfaces. A dynamic-then-static framework for treating electron correlation is developed to first incorporate dynamic correlation into contracted state functions through block-localized Kohn-Sham density functional theory (KSDFT), followed by diagonalization of the effective Hamiltonian to include static correlation. MSDFT can be regarded as a hybrid of wave function and density functional theory. The method is built on and makes use of the current approximate density functional developed in KSDFT, yet it retains its computational efficiency to treat strongly correlated systems that are problematic for KSDFT but too large for accurate WFT. The results presented in this work show that MSDFT can be applied to photochemical processes involving conical intersections.

The uncertainty principle and quantum chaos

NASA Technical Reports Server (NTRS)

Chirikov, Boris V.

1993-01-01

The conception of quantum chaos is described in some detail. The most striking feature of this novel phenomenon is that all the properties of classical dynamical chaos persist here but, typically, on the finite and different time scales only. The ultimate origin of such a universal quantum stability is in the fundamental uncertainty principle which makes discrete the phase space and, hence, the spectrum of bounded quantum motion. Reformulation of the ergodic theory, as a part of the general theory of dynamical systems, is briefly discussed.

Dynamic analysis of horizontal axis wind turbine by thin-walled beam theory

NASA Astrophysics Data System (ADS)

Wang, Jianhong; Qin, Datong; Lim, Teik C.

2010-08-01

A mixed flexible-rigid multi-body mathematical model is applied to predict the dynamic performance of a wind turbine system. Since the tower and rotor are both flexible thin-walled structures, a consistent expression for their deformations is applied, which employs a successive series of transformations to locate any point on the blade and tower relative to an inertial coordinate system. The kinetic and potential energy terms of each flexible body and rigid body are derived for use in the Lagrange approach to formulate the wind turbine system's governing equation. The mode shapes are then obtained from the free vibration solution, while the distributions of dynamic stress and displacement of the tower and rotor are computed from the forced vibration response analysis. Using this dynamic model, the influence of the tower's stiffness on the blade tip deformation is studied. From the analysis, it is evident that the proposed model not only inherits the simplicity of the traditional 1-D beam element, but also able to provide detailed information about the tower and rotor response due to the incorporation of the flexible thin-walled beam theory.

Flatness-based embedded adaptive fuzzy control of turbocharged diesel engines

NASA Astrophysics Data System (ADS)

Rigatos, Gerasimos; Siano, Pierluigi; Arsie, Ivan

2014-10-01

In this paper nonlinear embedded control for turbocharged Diesel engines is developed with the use of Differential flatness theory and adaptive fuzzy control. It is shown that the dynamic model of the turbocharged Diesel engine is differentially flat and admits dynamic feedback linearization. It is also shown that the dynamic model can be written in the linear Brunovsky canonical form for which a state feedback controller can be easily designed. To compensate for modeling errors and external disturbances an adaptive fuzzy control scheme is implemanted making use of the transformed dynamical system of the diesel engine that is obtained through the application of differential flatness theory. Since only the system's output is measurable the complete state vector has to be reconstructed with the use of a state observer. It is shown that a suitable learning law can be defined for neuro-fuzzy approximators, which are part of the controller, so as to preserve the closed-loop system stability. With the use of Lyapunov stability analysis it is proven that the proposed observer-based adaptive fuzzy control scheme results in H∞ tracking performance.

Dynamic Structure Factor: An Introduction

NASA Astrophysics Data System (ADS)

Sturm, K.

1993-02-01

The doubly differential cross-section for weak inelastic scattering of waves or particles by manybody systems is derived in Born approximation and expressed in terms of the dynamic structure factor according to van Hove. The application of this very general scheme to scattering of neutrons, x-rays and high-energy electrons is discussed briefly. The dynamic structure factor, which is the space and time Fourier transform of the density-density correlation function, is a property of the many-body system independent of the external probe and carries information on the excitation spectrum of the system. The relation of the electronic structure factor to the density-density response function defined in linear-response theory is shown using the fluctuation-dissipation theorem. This is important for calculations, since the response function can be calculated approximately from the independent-particle response function in self-consistent field approximations, such as the random-phase approximation or the local-density approximation of the density functional theory. Since the density-density response function also determines the dielectric function, the dynamic structure can be expressed by the dielectric function.

Adaptive dynamical networks

NASA Astrophysics Data System (ADS)

Maslennikov, O. V.; Nekorkin, V. I.

2017-10-01

Dynamical networks are systems of active elements (nodes) interacting with each other through links. Examples are power grids, neural structures, coupled chemical oscillators, and communications networks, all of which are characterized by a networked structure and intrinsic dynamics of their interacting components. If the coupling structure of a dynamical network can change over time due to nodal dynamics, then such a system is called an adaptive dynamical network. The term ‘adaptive’ implies that the coupling topology can be rewired; the term ‘dynamical’ implies the presence of internal node and link dynamics. The main results of research on adaptive dynamical networks are reviewed. Key notions and definitions of the theory of complex networks are given, and major collective effects that emerge in adaptive dynamical networks are described.

Nonequilibrium fixed points in longitudinally expanding scalar theories: Infrared cascade, Bose condensation and a challenge for kinetic theory

DOE PAGES

Berges, J.; Schlichting, S.; Boguslavski, K.; ...

2015-11-05

In [Phys. Rev. Lett. 114, 061601 (2015)], we reported on a new universality class for longitudinally expanding systems, encompassing strongly correlated non-Abelian plasmas and N-component self-interacting scalar field theories. Using classical-statistical methods, we showed that these systems share the same self-similar scaling properties for a wide range of momenta in a limit where particles are weakly coupled but their occupancy is high. Here we significantly expand on our previous work and delineate two further self-similar regimes. One of these occurs in the deep infrared (IR) regime of very high occupancies, where the nonequilibrium dynamics leads to the formation of amore » Bose-Einstein condensate. The universal IR scaling exponents and the spectral index characterizing the isotropic IR distributions are described by an effective theory derived from a systematic large-N expansion at next-to-leading order. Remarkably, this effective theory can be cast as a vertex-resummed kinetic theory. The other novel self-similar regime occurs close to the hard physical scale of the theory, and sets in only at later times. In this study, we argue that the important role of the infrared dynamics ensures that key features of our results for scalar and gauge theories cannot be reproduced consistently in conventional kinetic theory frameworks.« less

Nonequilibrium fixed points in longitudinally expanding scalar theories: Infrared cascade, Bose condensation and a challenge for kinetic theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berges, J.; Schlichting, S.; Boguslavski, K.

In [Phys. Rev. Lett. 114, 061601 (2015)], we reported on a new universality class for longitudinally expanding systems, encompassing strongly correlated non-Abelian plasmas and N-component self-interacting scalar field theories. Using classical-statistical methods, we showed that these systems share the same self-similar scaling properties for a wide range of momenta in a limit where particles are weakly coupled but their occupancy is high. Here we significantly expand on our previous work and delineate two further self-similar regimes. One of these occurs in the deep infrared (IR) regime of very high occupancies, where the nonequilibrium dynamics leads to the formation of amore » Bose-Einstein condensate. The universal IR scaling exponents and the spectral index characterizing the isotropic IR distributions are described by an effective theory derived from a systematic large-N expansion at next-to-leading order. Remarkably, this effective theory can be cast as a vertex-resummed kinetic theory. The other novel self-similar regime occurs close to the hard physical scale of the theory, and sets in only at later times. In this study, we argue that the important role of the infrared dynamics ensures that key features of our results for scalar and gauge theories cannot be reproduced consistently in conventional kinetic theory frameworks.« less

Bioattractors: dynamical systems theory and the evolution of regulatory processes

PubMed Central

Jaeger, Johannes; Monk, Nick

2014-01-01

In this paper, we illustrate how dynamical systems theory can provide a unifying conceptual framework for evolution of biological regulatory systems. Our argument is that the genotype–phenotype map can be characterized by the phase portrait of the underlying regulatory process. The features of this portrait – such as attractors with associated basins and their bifurcations – define the regulatory and evolutionary potential of a system. We show how the geometric analysis of phase space connects Waddington's epigenetic landscape to recent computational approaches for the study of robustness and evolvability in network evolution. We discuss how the geometry of phase space determines the probability of possible phenotypic transitions. Finally, we demonstrate how the active, self-organizing role of the environment in phenotypic evolution can be understood in terms of dynamical systems concepts. This approach yields mechanistic explanations that go beyond insights based on the simulation of evolving regulatory networks alone. Its predictions can now be tested by studying specific, experimentally tractable regulatory systems using the tools of modern systems biology. A systematic exploration of such systems will enable us to understand better the nature and origin of the phenotypic variability, which provides the substrate for evolution by natural selection. PMID:24882812

Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow

NASA Astrophysics Data System (ADS)

Behtash, Alireza; Cruz-Camacho, C. N.; Martinez, M.

2018-02-01

The nonequilibrium attractors of systems undergoing Gubser flow within relativistic kinetic theory are studied. In doing so we employ well-established methods of nonlinear dynamical systems which rely on finding the fixed points, investigating the structure of the flow diagrams of the evolution equations, and characterizing the basin of attraction using a Lyapunov function near the stable fixed points. We obtain the attractors of anisotropic hydrodynamics, Israel-Stewart (IS) and transient fluid (DNMR) theories and show that they are indeed nonplanar and the basin of attraction is essentially three dimensional. The attractors of each hydrodynamical model are compared with the one obtained from the exact Gubser solution of the Boltzmann equation within the relaxation time approximation. We observe that the anisotropic hydrodynamics is able to match up to high numerical accuracy the attractor of the exact solution while the second-order hydrodynamical theories fail to describe it. We show that the IS and DNMR asymptotic series expansions diverge and use resurgence techniques to perform the resummation of these divergences. We also comment on a possible link between the manifold of steepest descent paths in path integrals and the basin of attraction for the attractors via Lyapunov functions that opens a new horizon toward an effective field theory description of hydrodynamics. Our findings indicate that the reorganization of the expansion series carried out by anisotropic hydrodynamics resums the Knudsen and inverse Reynolds numbers to all orders and thus, it can be understood as an effective theory for the far-from-equilibrium fluid dynamics.

Moving Word Learning to a Novel Space: A Dynamic Systems View of Referent Selection and Retention

ERIC Educational Resources Information Center

Samuelson, Larissa K.; Kucker, Sarah C.; Spencer, John P.

2017-01-01

Theories of cognitive development must address both the issue of how children bring their knowledge to bear on behavior in-the-moment, and how knowledge changes over time. We argue that seeking answers to these questions requires an appreciation of the dynamic nature of the developing system in its full, reciprocal complexity. We illustrate this…

On the Embedded Complementarity of Agent-Based and Aggregate Reasoning in Students' Developing Understanding of Dynamic Systems

ERIC Educational Resources Information Center

Stroup, Walter M.; Wilensky, Uri

2014-01-01

Placed in the larger context of broadening the engagement with systems dynamics and complexity theory in school-aged learning and teaching, this paper is intended to introduce, situate, and illustrate--with results from the use of network supported participatory simulations in classrooms--a stance we call "embedded complementarity" as an…

The dynamics of a harvested predator-prey system with Holling type IV functional response.

PubMed

Liu, Xinxin; Huang, Qingdao

2018-05-31

The paper aims to investigate the dynamical behavior of a predator-prey system with Holling type IV functional response in which both the species are subject to capturing. We mainly consider how the harvesting affects equilibria, stability, limit cycles and bifurcations in this system. We adopt the method of qualitative and quantitative analysis, which is based on the dynamical theory, bifurcation theory and numerical simulation. The boundedness of solutions, the existence and stability of equilibrium points of the system are further studied. Based on the Sotomayor's theorem, the existence of transcritical bifurcation and saddle-node bifurcation are derived. We use the normal form theorem to analyze the Hopf bifurcation. Simulation results show that the first Lyapunov coefficient is negative and a stable limit cycle may bifurcate. Numerical simulations are performed to make analytical studies more complete. This work illustrates that using the harvesting effort as control parameter can change the behaviors of the system, which may be useful for the biological management. Copyright © 2018 Elsevier B.V. All rights reserved.

Coupled forward-backward trajectory approach for nonequilibrium electron-ion dynamics

NASA Astrophysics Data System (ADS)

Sato, Shunsuke A.; Kelly, Aaron; Rubio, Angel

2018-04-01

We introduce a simple ansatz for the wave function of a many-body system based on coupled forward and backward propagating semiclassical trajectories. This method is primarily aimed at, but not limited to, treating nonequilibrium dynamics in electron-phonon systems. The time evolution of the system is obtained from the Euler-Lagrange variational principle, and we show that this ansatz yields Ehrenfest mean-field theory in the limit that the forward and backward trajectories are orthogonal, and in the limit that they coalesce. We investigate accuracy and performance of this method by simulating electronic relaxation in the spin-boson model and the Holstein model. Although this method involves only pairs of semiclassical trajectories, it shows a substantial improvement over mean-field theory, capturing quantum coherence of nuclear dynamics as well as electron-nuclear correlations. This improvement is particularly evident in nonadiabatic systems, where the accuracy of this coupled trajectory method extends well beyond the perturbative electron-phonon coupling regime. This approach thus provides an attractive route forward to the ab initio description of relaxation processes, such as thermalization, in condensed phase systems.

Dynamical Systems Analysis Of Transport In Flows Defined As Data Sets: Contaminant Control On The Coast Of Florida And Criteria For Warm Rings In The North Atlantic

NASA Astrophysics Data System (ADS)

Lekien, F.; Coulliette, C.

In this talk we will briefly describe the dynamical systems framework for Lagrangian transport. In particular, we will show how dynamical systems theory can now be uti- lized in the context of "real" problems, such as those derived from remote sensing observations or the input of a large scale numerical model. We will illustrate these ideas by two examples. Study of fluid transport near the Atlantic coast of Florida us- ing a velocity field observed experimentally from high frequency radar measurements reveals that dynamical systems theory can be used to reduce contaminant density in coastal areas. We also study intergyre transport in a quasigeostrophic model of the North Atlantic. We investigate the structure of eddies detaching from the Gulf Stream and prove that in a double gyre structure cyclonic rings cannot contain fluid from the other gyre. Only anticyclonic rings can contain "foreign" fluid coming from another gyre. This explains many phenomenons, such as why counter-clockwise rings South of the Gulf Stream contain colder fluid advected directly from the northern gyre, which has been illustrated in many observational studies.

Dynamic Grover search: applications in recommendation systems and optimization problems

NASA Astrophysics Data System (ADS)

Chakrabarty, Indranil; Khan, Shahzor; Singh, Vanshdeep

2017-06-01

In the recent years, we have seen that Grover search algorithm (Proceedings, 28th annual ACM symposium on the theory of computing, pp. 212-219, 1996) by using quantum parallelism has revolutionized the field of solving huge class of NP problems in comparisons to classical systems. In this work, we explore the idea of extending Grover search algorithm to approximate algorithms. Here we try to analyze the applicability of Grover search to process an unstructured database with a dynamic selection function in contrast to the static selection function used in the original work (Grover in Proceedings, 28th annual ACM symposium on the theory of computing, pp. 212-219, 1996). We show that this alteration facilitates us to extend the application of Grover search to the field of randomized search algorithms. Further, we use the dynamic Grover search algorithm to define the goals for a recommendation system based on which we propose a recommendation algorithm which uses binomial similarity distribution space giving us a quadratic speedup over traditional classical unstructured recommendation systems. Finally, we see how dynamic Grover search can be used to tackle a wide range of optimization problems where we improve complexity over existing optimization algorithms.

Correlated Fluctuations in Strongly Coupled Binary Networks Beyond Equilibrium

NASA Astrophysics Data System (ADS)

Dahmen, David; Bos, Hannah; Helias, Moritz

2016-07-01

Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering glassy magnetism and frustration, combinatorial optimization, protein folding, stock market dynamics, and social dynamics. The phase diagram of these systems is obtained in the thermodynamic limit by averaging over the quenched randomness of the couplings. However, many applications require the statistics of activity for a single realization of the possibly asymmetric couplings in finite-sized networks. Examples include reconstruction of couplings from the observed dynamics, representation of probability distributions for sampling-based inference, and learning in the central nervous system based on the dynamic and correlation-dependent modification of synaptic connections. The systematic cumulant expansion for kinetic binary (Ising) threshold units with strong, random, and asymmetric couplings presented here goes beyond mean-field theory and is applicable outside thermodynamic equilibrium; a system of approximate nonlinear equations predicts average activities and pairwise covariances in quantitative agreement with full simulations down to hundreds of units. The linearized theory yields an expansion of the correlation and response functions in collective eigenmodes, leads to an efficient algorithm solving the inverse problem, and shows that correlations are invariant under scaling of the interaction strengths.

SUSTAINABILITY, OPTION, THEORY, AND QUALITY CONTROL

EPA Science Inventory

Recently, Cabezas and Fath (2000) hypothesized that constant Fisher Information is a necessary condition for the persistence, i.e., sustainability of a dynamic regime of a system. A sustainable dynamic regime is one that persists and an unsustainable regime is one that does not ...

Dynamical Graph Theory Networks Methods for the Analysis of Sparse Functional Connectivity Networks and for Determining Pinning Observability in Brain Networks

PubMed Central

Meyer-Bäse, Anke; Roberts, Rodney G.; Illan, Ignacio A.; Meyer-Bäse, Uwe; Lobbes, Marc; Stadlbauer, Andreas; Pinker-Domenig, Katja

2017-01-01

Neuroimaging in combination with graph theory has been successful in analyzing the functional connectome. However almost all analysis are performed based on static graph theory. The derived quantitative graph measures can only describe a snap shot of the disease over time. Neurodegenerative disease evolution is poorly understood and treatment strategies are consequently only of limited efficiency. Fusing modern dynamic graph network theory techniques and modeling strategies at different time scales with pinning observability of complex brain networks will lay the foundation for a transformational paradigm in neurodegnerative diseases research regarding disease evolution at the patient level, treatment response evaluation and revealing some central mechanism in a network that drives alterations in these diseases. We model and analyze brain networks as two-time scale sparse dynamic graph networks with hubs (clusters) representing the fast sub-system and the interconnections between hubs the slow sub-system. Alterations in brain function as seen in dementia can be dynamically modeled by determining the clusters in which disturbance inputs have entered and the impact they have on the large-scale dementia dynamic system. Observing a small fraction of specific nodes in dementia networks such that the others can be recovered is accomplished by the novel concept of pinning observability. In addition, how to control this complex network seems to be crucial in understanding the progressive abnormal neural circuits in many neurodegenerative diseases. Detecting the controlling regions in the networks, which serve as key nodes to control the aberrant dynamics of the networks to a desired state and thus influence the progressive abnormal behavior, will have a huge impact in understanding and developing therapeutic solutions and also will provide useful information about the trajectory of the disease. In this paper, we present the theoretical framework and derive the necessary conditions for (1) area aggregation and time-scale modeling in brain networks and for (2) pinning observability of nodes in dynamic graph networks. Simulation examples are given to illustrate the theoretical concepts. PMID:29051730

Dynamical Graph Theory Networks Methods for the Analysis of Sparse Functional Connectivity Networks and for Determining Pinning Observability in Brain Networks.

PubMed

Meyer-Bäse, Anke; Roberts, Rodney G; Illan, Ignacio A; Meyer-Bäse, Uwe; Lobbes, Marc; Stadlbauer, Andreas; Pinker-Domenig, Katja

2017-01-01

Neuroimaging in combination with graph theory has been successful in analyzing the functional connectome. However almost all analysis are performed based on static graph theory. The derived quantitative graph measures can only describe a snap shot of the disease over time. Neurodegenerative disease evolution is poorly understood and treatment strategies are consequently only of limited efficiency. Fusing modern dynamic graph network theory techniques and modeling strategies at different time scales with pinning observability of complex brain networks will lay the foundation for a transformational paradigm in neurodegnerative diseases research regarding disease evolution at the patient level, treatment response evaluation and revealing some central mechanism in a network that drives alterations in these diseases. We model and analyze brain networks as two-time scale sparse dynamic graph networks with hubs (clusters) representing the fast sub-system and the interconnections between hubs the slow sub-system. Alterations in brain function as seen in dementia can be dynamically modeled by determining the clusters in which disturbance inputs have entered and the impact they have on the large-scale dementia dynamic system. Observing a small fraction of specific nodes in dementia networks such that the others can be recovered is accomplished by the novel concept of pinning observability. In addition, how to control this complex network seems to be crucial in understanding the progressive abnormal neural circuits in many neurodegenerative diseases. Detecting the controlling regions in the networks, which serve as key nodes to control the aberrant dynamics of the networks to a desired state and thus influence the progressive abnormal behavior, will have a huge impact in understanding and developing therapeutic solutions and also will provide useful information about the trajectory of the disease. In this paper, we present the theoretical framework and derive the necessary conditions for (1) area aggregation and time-scale modeling in brain networks and for (2) pinning observability of nodes in dynamic graph networks. Simulation examples are given to illustrate the theoretical concepts.

On Flexible Tubes Conveying Fluid: Geometric Nonlinear Theory, Stability and Dynamics

NASA Astrophysics Data System (ADS)

Gay-Balmaz, François; Putkaradze, Vakhtang

2015-08-01

We derive a fully three-dimensional, geometrically exact theory for flexible tubes conveying fluid. The theory also incorporates the change of the cross section available to the fluid motion during the dynamics. Our approach is based on the symmetry-reduced, exact geometric description for elastic rods, coupled with the fluid transport and subject to the volume conservation constraint for the fluid. We first derive the equations of motion directly, by using an Euler-Poincaré variational principle. We then justify this derivation with a more general theory elucidating the interesting mathematical concepts appearing in this problem, such as partial left (elastic) and right (fluid) invariance of the system, with the added holonomic constraint (volume). We analyze the fully nonlinear behavior of the model when the axis of the tube remains straight. We then proceed to the linear stability analysis and show that our theory introduces important corrections to previously derived results, both in the consistency at all wavelength and in the effects arising from the dynamical change of the cross section. Finally, we derive and analyze several analytical, fully nonlinear solutions of traveling wave type in two dimensions.

Trajectory design strategies that incorporate invariant manifolds and swingby

NASA Technical Reports Server (NTRS)

Guzman, J. J.; Cooley, D. S.; Howell, K. C.; Folta, D. C.

1998-01-01

Libration point orbits serve as excellent platforms for scientific investigations involving the Sun as well as planetary environments. Trajectory design in support of such missions is increasingly challenging as more complex missions are envisioned in the next few decades. Software tools for trajectory design in this regime must be further developed to incorporate better understanding of the solution space and, thus, improve the efficiency and expand the capabilities of current approaches. Only recently applied to trajectory design, dynamical systems theory now offers new insights into the natural dynamics associated with the multi-body problem. The goal of this effort is the blending of analysis from dynamical systems theory with the well established NASA Goddard software program SWINGBY to enhance and expand the capabilities for mission design. Basic knowledge concerning the solution space is improved as well.

A model for rotorcraft flying qualities studies

NASA Technical Reports Server (NTRS)

Mittal, Manoj; Costello, Mark F.

1993-01-01

This paper outlines the development of a mathematical model that is expected to be useful for rotorcraft flying qualities research. A computer model is presented that can be applied to a range of different rotorcraft configurations. The algorithm computes vehicle trim and a linear state-space model of the aircraft. The trim algorithm uses non linear optimization theory to solve the nonlinear algebraic trim equations. The linear aircraft equations consist of an airframe model and a flight control system dynamic model. The airframe model includes coupled rotor and fuselage rigid body dynamics and aerodynamics. The aerodynamic model for the rotors utilizes blade element theory and a three state dynamic inflow model. Aerodynamics of the fuselage and fuselage empennages are included. The linear state-space description for the flight control system is developed using standard block diagram data.

A Dynamic Differentiation Framework for Talent Enhancement: Findings from Syntheses and Teachers' Perspectives

ERIC Educational Resources Information Center

Smith, Susen

2015-01-01

Differentiating curriculum and pedagogy is a dynamic process that is dependent on the interrelationship between intrapersonal and environmental factors that can support the unique educational needs of gifted students. A Model of Dynamic Differentiation (MoDD) was developed from a larger study based on the ecological systems theory, an in-depth…

Theory of Gearing

DTIC Science & Technology

1989-12-01

motion of rigid bodies and their kinematical and dynamic characteristics, which are associated with different coordinate systems. In the theory of...rigidly connected surfaces EF and Ep with respect to gears I and 2 may be represented as the motion of a rigid body . However, we assume that in the... rigid body . Coordinate tran:;formation will be considered for systems with (1) common origin and noncoincident coordinate axes and (2) noncoincident

Dynamic trapping near a quantum critical point

NASA Astrophysics Data System (ADS)

Kolodrubetz, Michael; Katz, Emanuel; Polkovnikov, Anatoli

2015-02-01

The study of dynamics in closed quantum systems has been revitalized by the emergence of experimental systems that are well-isolated from their environment. In this paper, we consider the closed-system dynamics of an archetypal model: spins driven across a second-order quantum critical point, which are traditionally described by the Kibble-Zurek mechanism. Imbuing the driving field with Newtonian dynamics, we find that the full closed system exhibits a robust new phenomenon—dynamic critical trapping—in which the system is self-trapped near the critical point due to efficient absorption of field kinetic energy by heating the quantum spins. We quantify limits in which this phenomenon can be observed and generalize these results by developing a Kibble-Zurek scaling theory that incorporates the dynamic field. Our findings can potentially be interesting in the context of early universe physics, where the role of the driving field is played by the inflaton or a modulus field.

System Dynamics Approach for Critical Infrastructure and Decision Support. A Model for a Potable Water System.

NASA Astrophysics Data System (ADS)

Pasqualini, D.; Witkowski, M.

2005-12-01

The Critical Infrastructure Protection / Decision Support System (CIP/DSS) project, supported by the Science and Technology Office, has been developing a risk-informed Decision Support System that provides insights for making critical infrastructure protection decisions. The system considers seventeen different Department of Homeland Security defined Critical Infrastructures (potable water system, telecommunications, public health, economics, etc.) and their primary interdependencies. These infrastructures have been modeling in one model called CIP/DSS Metropolitan Model. The modeling approach used is a system dynamics modeling approach. System dynamics modeling combines control theory and the nonlinear dynamics theory, which is defined by a set of coupled differential equations, which seeks to explain how the structure of a given system determines its behavior. In this poster we present a system dynamics model for one of the seventeen critical infrastructures, a generic metropolitan potable water system (MPWS). Three are the goals: 1) to gain a better understanding of the MPWS infrastructure; 2) to identify improvements that would help protect MPWS; and 3) to understand the consequences, interdependencies, and impacts, when perturbations occur to the system. The model represents raw water sources, the metropolitan water treatment process, storage of treated water, damage and repair to the MPWS, distribution of water, and end user demand, but does not explicitly represent the detailed network topology of an actual MPWS. The MPWS model is dependent upon inputs from the metropolitan population, energy, telecommunication, public health, and transportation models as well as the national water and transportation models. We present modeling results and sensitivity analysis indicating critical choke points, negative and positive feedback loops in the system. A general scenario is also analyzed where the potable water system responds to a generic disruption.

Slow dynamics in translation-invariant quantum lattice models

NASA Astrophysics Data System (ADS)

Michailidis, Alexios A.; Žnidarič, Marko; Medvedyeva, Mariya; Abanin, Dmitry A.; Prosen, Tomaž; Papić, Z.

2018-03-01

Many-body quantum systems typically display fast dynamics and ballistic spreading of information. Here we address the open problem of how slow the dynamics can be after a generic breaking of integrability by local interactions. We develop a method based on degenerate perturbation theory that reveals slow dynamical regimes and delocalization processes in general translation invariant models, along with accurate estimates of their delocalization time scales. Our results shed light on the fundamental questions of the robustness of quantum integrable systems and the possibility of many-body localization without disorder. As an example, we construct a large class of one-dimensional lattice models where, despite the absence of asymptotic localization, the transient dynamics is exceptionally slow, i.e., the dynamics is indistinguishable from that of many-body localized systems for the system sizes and time scales accessible in experiments and numerical simulations.

Generalised teleparallel quintom dark energy non-minimally coupled with the scalar torsion and a boundary term

NASA Astrophysics Data System (ADS)

Bahamonde, Sebastian; Marciu, Mihai; Rudra, Prabir

2018-04-01

Within this work, we propose a new generalised quintom dark energy model in the teleparallel alternative of general relativity theory, by considering a non-minimal coupling between the scalar fields of a quintom model with the scalar torsion component T and the boundary term B. In the teleparallel alternative of general relativity theory, the boundary term represents the divergence of the torsion vector, B=2∇μTμ, and is related to the Ricci scalar R and the torsion scalar T, by the fundamental relation: R=‑T+B. We have investigated the dynamical properties of the present quintom scenario in the teleparallel alternative of general relativity theory by performing a dynamical system analysis in the case of decomposable exponential potentials. The study analysed the structure of the phase space, revealing the fundamental dynamical effects of the scalar torsion and boundary couplings in the case of a more general quintom scenario. Additionally, a numerical approach to the model is presented to analyse the cosmological evolution of the system.

The Mochi project: a field theory approach to plasma dynamics and self-organization

NASA Astrophysics Data System (ADS)

You, Setthivoine; von der Linden, Jens; Lavine, Eric Sander; Card, Alexander; Carroll, Evan

2016-10-01

The Mochi project is designed to study the interaction between plasma flows and magnetic fields from the point-of-view of canonical flux tubes. The Mochi Labjet experiment is being commissioned after achieving first plasma. Analytical and numerical tools are being developed to visualize canonical flux tubes. One analytical tool described here is a field theory approach to plasma dynamics and self-organization. A redefinition of the Lagrangian of a multi-particle system in fields reformulates the single-particle, kinetic, and fluid equations governing fluid and plasma dynamics as a single set of generalized Maxwell's equations and Ohm's law for canonical force-fields. The Lagrangian includes new terms representing the coupling between the motion of particle distributions, between distributions and electromagnetic fields, with relativistic contributions. The formulation shows that the concepts of self-organization and canonical helicity transport are applicable across single-particle, kinetic, and fluid regimes, at classical and relativistic scales. The theory gives the basis for comparing canonical helicity change to energy change in general systems. This work is supported by by US DOE Grant DE-SC0010340.

Quantum critical dynamics for a prototype class of insulating antiferromagnets

NASA Astrophysics Data System (ADS)

Wu, Jianda; Yang, Wang; Wu, Congjun; Si, Qimiao

2018-06-01

Quantum criticality is a fundamental organizing principle for studying strongly correlated systems. Nevertheless, understanding quantum critical dynamics at nonzero temperatures is a major challenge of condensed-matter physics due to the intricate interplay between quantum and thermal fluctuations. The recent experiments with the quantum spin dimer material TlCuCl3 provide an unprecedented opportunity to test the theories of quantum criticality. We investigate the nonzero-temperature quantum critical spin dynamics by employing an effective O (N ) field theory. The on-shell mass and the damping rate of quantum critical spin excitations as functions of temperature are calculated based on the renormalized coupling strength and are in excellent agreement with experiment observations. Their T lnT dependence is predicted to be dominant at very low temperatures, which will be tested in future experiments. Our work provides confidence that quantum criticality as a theoretical framework, which is being considered in so many different contexts of condensed-matter physics and beyond, is indeed grounded in materials and experiments accurately. It is also expected to motivate further experimental investigations on the applicability of the field theory to related quantum critical systems.

Phase-field modeling of isothermal quasi-incompressible multicomponent liquids

NASA Astrophysics Data System (ADS)

Tóth, Gyula I.

2016-09-01

In this paper general dynamic equations describing the time evolution of isothermal quasi-incompressible multicomponent liquids are derived in the framework of the classical Ginzburg-Landau theory of first order phase transformations. Based on the fundamental equations of continuum mechanics, a general convection-diffusion dynamics is set up first for compressible liquids. The constitutive relations for the diffusion fluxes and the capillary stress are determined in the framework of gradient theories. Next the general definition of incompressibility is given, which is taken into account in the derivation by using the Lagrange multiplier method. To validate the theory, the dynamic equations are solved numerically for the quaternary quasi-incompressible Cahn-Hilliard system. It is demonstrated that variable density (i) has no effect on equilibrium (in case of a suitably constructed free energy functional) and (ii) can influence nonequilibrium pattern formation significantly.

Active nematic gels as active relaxing solids

NASA Astrophysics Data System (ADS)

Turzi, Stefano S.

2017-11-01

I propose a continuum theory for active nematic gels, defined as fluids or suspensions of orientable rodlike objects endowed with active dynamics, that is based on symmetry arguments and compatibility with thermodynamics. The starting point is our recent theory that models (passive) nematic liquid crystals as relaxing nematic elastomers. The interplay between viscoelastic response and active dynamics of the microscopic constituents is naturally taken into account. By contrast with standard theories, activity is not introduced as an additional term of the stress tensor, but it is added as an external remodeling force that competes with the passive relaxation dynamics and drags the system out of equilibrium. In a simple one-dimensional channel geometry, we show that the interaction between nonuniform nematic order and activity results in either a spontaneous flow of particles or a self-organization into subchannels flowing in opposite directions.

Analytical Tools for Investigating and Modeling Agent-Based Systems

DTIC Science & Technology

2005-06-01

of Black Holes Cluster 10 : Juan M. Maldacena (1924), Journal of High Energy Physics Field theory models for tachyon and gauge field string dy...namics; Super-Poincare Invariant Superstring Field The- ory; Level Four Approximation to the Tachyon Potential in Superstring Field Theory; SO(32) Spinors

Teaching Model Building to High School Students: Theory and Reality.

ERIC Educational Resources Information Center

Roberts, Nancy; Barclay, Tim

1988-01-01

Builds on a National Science Foundation (NSF) microcomputer based laboratory project to introduce system dynamics into the precollege setting. Focuses on providing students with powerful and investigatory theory building tools. Discusses developed hardware, software, and curriculum materials used to introduce model building and simulations into…

Spectral functions of strongly correlated extended systems via an exact quantum embedding

NASA Astrophysics Data System (ADS)

Booth, George H.; Chan, Garnet Kin-Lic

2015-04-01

Density matrix embedding theory (DMET) [Phys. Rev. Lett. 109, 186404 (2012), 10.1103/PhysRevLett.109.186404], introduced an approach to quantum cluster embedding methods whereby the mapping of strongly correlated bulk problems to an impurity with finite set of bath states was rigorously formulated to exactly reproduce the entanglement of the ground state. The formalism provided similar physics to dynamical mean-field theory at a tiny fraction of the cost but was inherently limited by the construction of a bath designed to reproduce ground-state, static properties. Here, we generalize the concept of quantum embedding to dynamic properties and demonstrate accurate bulk spectral functions at similarly small computational cost. The proposed spectral DMET utilizes the Schmidt decomposition of a response vector, mapping the bulk dynamic correlation functions to that of a quantum impurity cluster coupled to a set of frequency-dependent bath states. The resultant spectral functions are obtained on the real-frequency axis, without bath discretization error, and allows for the construction of arbitrary dynamic correlation functions. We demonstrate the method on the one- (1D) and two-dimensional (2D) Hubbard model, where we obtain zero temperature and thermodynamic limit spectral functions, and show the trivial extension to two-particle Green's functions. This advance therefore extends the scope and applicability of DMET in condensed-matter problems as a computationally tractable route to correlated spectral functions of extended systems and provides a competitive alternative to dynamical mean-field theory for dynamic quantities.

Structural relaxation of polydisperse hard spheres: comparison of the mode-coupling theory to a Langevin dynamics simulation.

PubMed

Weysser, F; Puertas, A M; Fuchs, M; Voigtmann, Th

2010-07-01

We analyze the slow glassy structural relaxation as measured through collective and tagged-particle density correlation functions obtained from Brownian dynamics simulations for a polydisperse system of quasi-hard spheres in the framework of the mode-coupling theory (MCT) of the glass transition. Asymptotic analyses show good agreement for the collective dynamics when polydispersity effects are taken into account in a multicomponent calculation, but qualitative disagreement at small q when the system is treated as effectively monodisperse. The origin of the different small-q behavior is attributed to the interplay between interdiffusion processes and structural relaxation. Numerical solutions of the MCT equations are obtained taking properly binned partial static structure factors from the simulations as input. Accounting for a shift in the critical density, the collective density correlation functions are well described by the theory at all densities investigated in the simulations, with quantitative agreement best around the maxima of the static structure factor and worst around its minima. A parameter-free comparison of the tagged-particle dynamics however reveals large quantitative errors for small wave numbers that are connected to the well-known decoupling of self-diffusion from structural relaxation and to dynamical heterogeneities. While deviations from MCT behavior are clearly seen in the tagged-particle quantities for densities close to and on the liquid side of the MCT glass transition, no such deviations are seen in the collective dynamics.

Thermostatistically approaching living systems: Boltzmann Gibbs or nonextensive statistical mechanics?

NASA Astrophysics Data System (ADS)

Tsallis, Constantino

2006-03-01

Boltzmann-Gibbs ( BG) statistical mechanics is, since well over one century, successfully used for many nonlinear dynamical systems which, in one way or another, exhibit strong chaos. A typical case is a classical many-body short-range-interacting Hamiltonian system (e.g., the Lennard-Jones model for a real gas at moderately high temperature). Its Lyapunov spectrum (which characterizes the sensitivity to initial conditions) includes positive values. This leads to ergodicity, the stationary state being thermal equilibrium, hence standard applicability of the BG theory is verified. The situation appears to be of a different nature for various phenomena occurring in living organisms. Indeed, such systems exhibit a complexity which does not really accommodate with this standard dynamical behavior. Life appears to emerge and evolve in a kind of delicate situation, at the frontier between large order (low adaptability and long memory; typically characterized by regular dynamics, hence only nonpositive Lyapunov exponents) and large disorder (high adaptability and short memory; typically characterized by strong chaos, hence at least one positive Lyapunov exponent). Along this frontier, the maximal relevant Lyapunov exponents are either zero or close to that, characterizing what is currently referred to as weak chaos. This type of situation is shared by a great variety of similar complex phenomena in economics, linguistics, to cite but a few. BG statistical mechanics is built upon the entropy S=-k∑plnp. A generalization of this form, S=k(1-∑piq)/(q-1) (with S=S), has been proposed in 1988 as a basis for formulating what is nowadays currently called nonextensive statistical mechanics. This theory appears to be particularly adapted for nonlinear dynamical systems exhibiting, precisely, weak chaos. Here, we briefly review the theory, its dynamical foundation, its applications in a variety of disciplines (with special emphasis to living systems), and its connections with the ubiquitous scale-free networks.

An equation-free probabilistic steady-state approximation: dynamic application to the stochastic simulation of biochemical reaction networks.

PubMed

Salis, Howard; Kaznessis, Yiannis N

2005-12-01

Stochastic chemical kinetics more accurately describes the dynamics of "small" chemical systems, such as biological cells. Many real systems contain dynamical stiffness, which causes the exact stochastic simulation algorithm or other kinetic Monte Carlo methods to spend the majority of their time executing frequently occurring reaction events. Previous methods have successfully applied a type of probabilistic steady-state approximation by deriving an evolution equation, such as the chemical master equation, for the relaxed fast dynamics and using the solution of that equation to determine the slow dynamics. However, because the solution of the chemical master equation is limited to small, carefully selected, or linear reaction networks, an alternate equation-free method would be highly useful. We present a probabilistic steady-state approximation that separates the time scales of an arbitrary reaction network, detects the convergence of a marginal distribution to a quasi-steady-state, directly samples the underlying distribution, and uses those samples to accurately predict the state of the system, including the effects of the slow dynamics, at future times. The numerical method produces an accurate solution of both the fast and slow reaction dynamics while, for stiff systems, reducing the computational time by orders of magnitude. The developed theory makes no approximations on the shape or form of the underlying steady-state distribution and only assumes that it is ergodic. We demonstrate the accuracy and efficiency of the method using multiple interesting examples, including a highly nonlinear protein-protein interaction network. The developed theory may be applied to any type of kinetic Monte Carlo simulation to more efficiently simulate dynamically stiff systems, including existing exact, approximate, or hybrid stochastic simulation techniques.

Theory-Driven Models for Correcting Fight or Flight Imbalance in Gulf War Illness

DTIC Science & Technology

2011-09-01

testing on software • Performed static and dynamic analysis on safety code Research Interests To understand how the nervous system operates, how...dynamics of these systems to reset control of the HPA-immune axis to normal. We have completed the negotiation of sub-awards to the CFIDS Association...We propose that severe physical or psychological insult to the endocrine and immune systems can displace these from a normal regulatory equilibrium

Performance Characterization, Development, and Application of Artificial Potential Function Guidance Methods

DTIC Science & Technology

2014-03-01

to determine if a system is stabilizable with feedback. 12 that asymptotic stability is guaranteed by Lyapunov theory. The advantage of this method are...discretized dynamics are a sufficient representation of the continuous system . Given these assumptions, the optimal control problem for minimum transit time is...tion (APF) guidance performance when applied to systems with limited control au- thority in a dynamic environment and then to use the findings to

Theory of drives and emotions - from Sigmund Freud to Jaak Panksepp.

PubMed

Żechowski, Cezary

2017-12-30

The article discusses the development of psychoanalytic theory in the direction of broadening the reflection on their own based on data derived from empirical studies other than clinical case study. Particularly noteworthy is the convergence that followed between neuroscience and psychoanalysis and the rise of the so-called neuropsychoanalysis. Consequently, this led to eject empirical hypotheses and begin research on defense mechanisms, self, memory, dreams, empathy, dynamic unconscious and emotional-motivational processes (theory of drives). Currently neuropsychoanalysis constituted itself as a discipline contained in itself three separate areas: the psychodynamic neuroscience, clinical neuropsychoanalysis and theory building. The article introduces the theory of Jaak Panksepp emotional systems as an example of anintegrated neurobiology of affect, behavioral biology, evolutionary psychology and psychoanalysis. The theory of emotional systems includes the description of the SEEKING system representing basic motivational system of the organism. Apart from a new perspective on the theory of drives described by Sigmund Freud, it offers the possibility to take into account the emotional and motivational systems within the understanding of mental disorders such as depression, addiction and psychosis, which is the core of psychoanalytic thinking.

Dynamical gauge effects in an open quantum network

NASA Astrophysics Data System (ADS)

Zhao, Jianshi; Price, Craig; Liu, Qi; Gemelke, Nathan

2016-05-01

We describe new experimental techniques for simulation of high-energy field theories based on an analogy between open thermodynamic systems and effective dynamical gauge-fields following SU(2) × U(1) Yang-Mills models. By coupling near-resonant laser-modes to atoms moving in a disordered optical environment, we create an open system which exhibits a non-equilibrium phase transition between two steady-state behaviors, exhibiting scale-invariant behavior near the transition. By measuring transport of atoms through the disordered network, we observe two distinct scaling behaviors, corresponding to the classical and quantum limits for the dynamical gauge field. This behavior is loosely analogous to dynamical gauge effects in quantum chromodynamics, and can mapped onto generalized open problems in theoretical understanding of quantized non-Abelian gauge theories. Additional, the scaling behavior can be understood from the geometric structure of the gauge potential and linked to the measure of information in the local disordered potential, reflecting an underlying holographic principle. We acknowledge support from NSF Award No.1068570, and the Charles E. Kaufman Foundation.

Asteroids - the modern challenge of celestial dynamics

NASA Astrophysics Data System (ADS)

Dikova, Smiliana

2002-11-01

Among the most powerful statements in Science are those that mark absolute limits to knowledge. For example, Relativity and Quantum Theory touched the limits of speed and accuracy. Deterministic Chaos - the new scientific paradigma of our days, also falls in this class theories. Chaos means complexity in space and unpredictability in time. It shows the limit of our basic counting system and leads to a limited predictability of the long time dynamical evolution. Perhaps for that reason, in 1986 Sir James Lighthill remarked for all physicists: "We collectively wish to apologize for having misled the general educated public by spreading ideas about the determinism of systems satisfying Newton's laws of motion that, after 1960, were proved incorrect." Our main thesis is that Asteroid Dynamics is the arena where the drama Chaos versus predictability is initiated and developed. The aim of the present research is to show the way in which Deterministic Chaos restricts the long term dynamical predictability of asteroid motions.

In-flight alignment using H ∞ filter for strapdown INS on aircraft.

PubMed

Pei, Fu-Jun; Liu, Xuan; Zhu, Li

2014-01-01

In-flight alignment is an effective way to improve the accuracy and speed of initial alignment for strapdown inertial navigation system (INS). During the aircraft flight, strapdown INS alignment was disturbed by lineal and angular movements of the aircraft. To deal with the disturbances in dynamic initial alignment, a novel alignment method for SINS is investigated in this paper. In this method, an initial alignment error model of SINS in the inertial frame is established. The observability of the system is discussed by piece-wise constant system (PWCS) theory and observable degree is computed by the singular value decomposition (SVD) theory. It is demonstrated that the system is completely observable, and all the system state parameters can be estimated by optimal filter. Then a H ∞ filter was designed to resolve the uncertainty of measurement noise. The simulation results demonstrate that the proposed algorithm can reach a better accuracy under the dynamic disturbance condition.

[Current aspects of the physiopathology of the infectious process. II. Cybernetic elements in the pathogenetic structure of infectious diseases].

PubMed

Dragomirescu, M; Buzinschi, S

1980-01-01

The authors discuss the applicability of general cybernetic principles (the theory of systems and self-regulated mechanisms based on inversed connections) to the pathophysiologic structure of infections. With reference to concrete examples they outline the following elements: the appartenance of the infectious process to the notion of system (as conceived in the theory of systems), the previsible character of the functional potential of the structured system in the components of infection, and the sequental correspondence between system dynamics and the dynamics of the infectious process. Starting from the mechanism of action of the main microbial toxins, the aptitude of the latter to act upon the functional code of the macroorganism, altering the cellular and supracellular self-regulated biosystems, is demonstrated. Finally, the practical implications of assimilating cybernetic processes in the pathophysiology of infectious diseases are analyzed.

Wave kinetics of random fibre lasers

PubMed Central

Churkin, D V.; Kolokolov, I V.; Podivilov, E V.; Vatnik, I D.; Nikulin, M A.; Vergeles, S S.; Terekhov, I S.; Lebedev, V V.; Falkovich, G.; Babin, S A.; Turitsyn, S K.

2015-01-01

Traditional wave kinetics describes the slow evolution of systems with many degrees of freedom to equilibrium via numerous weak non-linear interactions and fails for very important class of dissipative (active) optical systems with cyclic gain and losses, such as lasers with non-linear intracavity dynamics. Here we introduce a conceptually new class of cyclic wave systems, characterized by non-uniform double-scale dynamics with strong periodic changes of the energy spectrum and slow evolution from cycle to cycle to a statistically steady state. Taking a practically important example—random fibre laser—we show that a model describing such a system is close to integrable non-linear Schrödinger equation and needs a new formalism of wave kinetics, developed here. We derive a non-linear kinetic theory of the laser spectrum, generalizing the seminal linear model of Schawlow and Townes. Experimental results agree with our theory. The work has implications for describing kinetics of cyclical systems beyond photonics. PMID:25645177

Internal kinematics and dynamics of galaxies; Proceedings of the Symposium, Universitede Franche-Comte, Besancon, France, August 9-13, 1982

NASA Astrophysics Data System (ADS)

Athanassoula, E.

Various aspects of the internal kinematics and dynamics of galaxies are considered. The kinematics of the gas and the underlying mass distribution are discussed, including the systematics of H II rotation curves, H I velocity fields and rotation curves, the distribution of molecular clouds in spiral galaxies, gas at large radii, the implications for galactic mass models of vertical motion and the thickness of H I disks, and mass distribution and dark halos. The theory of spiral structure is addressed, along with conflicts and directions in spiral structure studies. Theories of warps are covered. Barred galaxies are treated, including their morphology, stellar kinematics, and dynamics, the stability of their disks, theoretical studies of their gas flows, and the formation of rings and lenses. Spheroidal systems are considered, including dynamics of early type galaxies, models of ellipticals and bulges, and interstellar matter in elliptical galaxies. Simulations and observational evidence for mergers are addressed, and the formation of galaxies and dynamics of globular cluster systems are examined. For individual items see A83-49202 to A83-49267

Dynamics of two-phase interfaces and surface tensions: A density-functional theory perspective

NASA Astrophysics Data System (ADS)

Yatsyshin, Petr; Sibley, David N.; Duran-Olivencia, Miguel A.; Kalliadasis, Serafim

2016-11-01

Classical density functional theory (DFT) is a statistical mechanical framework for the description of fluids at the nanoscale, where the inhomogeneity of the fluid structure needs to be carefully accounted for. By expressing the grand free-energy of the fluid as a functional of the one-body density, DFT offers a theoretically consistent and computationally accessible way to obtain two-phase interfaces and respective interfacial tensions in a ternary solid-liquid-gas system. The dynamic version of DFT (DDFT) can be rigorously derived from the Smoluchowsky picture of the dynamics of colloidal particles in a solvent. It is generally agreed that DDFT can capture the diffusion-driven evolution of many soft-matter systems. In this context, we use DDFT to investigate the dynamic behaviour of two-phase interfaces in both equilibrium and dynamic wetting and discuss the possibility of defining a time-dependent surface tension, which still remains in debate. We acknowledge financial support from the European Research Council via Advanced Grant No. 247031 and from the Engineering and Physical Sciences Research Council of the UK via Grants No. EP/L027186 and EP/L020564.

Driving the brain towards creativity and intelligence: A network control theory analysis.

PubMed

Kenett, Yoed N; Medaglia, John D; Beaty, Roger E; Chen, Qunlin; Betzel, Richard F; Thompson-Schill, Sharon L; Qiu, Jiang

2018-01-04

High-level cognitive constructs, such as creativity and intelligence, entail complex and multiple processes, including cognitive control processes. Recent neurocognitive research on these constructs highlight the importance of dynamic interaction across neural network systems and the role of cognitive control processes in guiding such a dynamic interaction. How can we quantitatively examine the extent and ways in which cognitive control contributes to creativity and intelligence? To address this question, we apply a computational network control theory (NCT) approach to structural brain imaging data acquired via diffusion tensor imaging in a large sample of participants, to examine how NCT relates to individual differences in distinct measures of creative ability and intelligence. Recent application of this theory at the neural level is built on a model of brain dynamics, which mathematically models patterns of inter-region activity propagated along the structure of an underlying network. The strength of this approach is its ability to characterize the potential role of each brain region in regulating whole-brain network function based on its anatomical fingerprint and a simplified model of node dynamics. We find that intelligence is related to the ability to "drive" the brain system into easy to reach neural states by the right inferior parietal lobe and lower integration abilities in the left retrosplenial cortex. We also find that creativity is related to the ability to "drive" the brain system into difficult to reach states by the right dorsolateral prefrontal cortex (inferior frontal junction) and higher integration abilities in sensorimotor areas. Furthermore, we found that different facets of creativity-fluency, flexibility, and originality-relate to generally similar but not identical network controllability processes. We relate our findings to general theories on intelligence and creativity. Copyright © 2018 Elsevier Ltd. All rights reserved.

Consistent multiphase-field theory for interface driven multidomain dynamics

NASA Astrophysics Data System (ADS)

Tóth, Gyula I.; Pusztai, Tamás; Gránásy, László

2015-11-01

We present a multiphase-field theory for describing pattern formation in multidomain and/or multicomponent systems. The construction of the free energy functional and the dynamic equations is based on criteria that ensure mathematical and physical consistency. We first analyze previous multiphase-field theories and identify their advantageous and disadvantageous features. On the basis of this analysis, we introduce a way of constructing the free energy surface and derive a generalized multiphase description for arbitrary number of phases (or domains). The presented approach retains the variational formalism, reduces (or extends) naturally to lower (or higher) number of fields on the level of both the free energy functional and the dynamic equations, enables the use of arbitrary pairwise equilibrium interfacial properties, penalizes multiple junctions increasingly with the number of phases, ensures non-negative entropy production and the convergence of the dynamic solutions to the equilibrium solutions, and avoids the appearance of spurious phases on binary interfaces. The approach is tested for multicomponent phase separation and grain coarsening.

Aristotle and Information Theory: A Comparison of the Influence of Causal Assumptions on Two Theories of Communication. (Janua Linguarum Series Maior 35.)

ERIC Educational Resources Information Center

Rosenfield, Lawrence William

This study sought to discover what critical apparatus would be most appropriate for observers of verbal discourse who choose to accept Aristotelian or "information theory" causal accounts of dynamic process. The major conclusions were: (1) Both causal systems employ a static grid to express relationships; but while the Aristotelian relations are…

System learning approach to assess sustainability and ...

EPA Pesticide Factsheets

This paper presents a methodology that combines the power of an Artificial Neural Network and Information Theory to forecast variables describing the condition of a regional system. The novelty and strength of this approach is in the application of Fisher information, a key method in Information Theory, to preserve trends in the historical data and prevent over fitting projections. The methodology was applied to demographic, environmental, food and energy consumption, and agricultural production in the San Luis Basin regional system in Colorado, U.S.A. These variables are important for tracking conditions in human and natural systems. However, available data are often so far out of date that they limit the ability to manage these systems. Results indicate that the approaches developed provide viable tools for forecasting outcomes with the aim of assisting management toward sustainable trends. This methodology is also applicable for modeling different scenarios in other dynamic systems. Indicators are indispensable for tracking conditions in human and natural systems, however, available data is sometimes far out of date and limit the ability to gauge system status. Techniques like regression and simulation are not sufficient because system characteristics have to be modeled ensuring over simplification of complex dynamics. This work presents a methodology combining the power of an Artificial Neural Network and Information Theory to capture patterns in a real dyna

Quantum Impurity Models as Reference Systems for Strongly Correlated Materials: The Road from the Kondo Impurity Model to First Principles Electronic Structure Calculations with Dynamical Mean-Field Theory

NASA Astrophysics Data System (ADS)

Kotliar, Gabriel

2005-01-01

Dynamical mean field theory (DMFT) relates extended systems (bulk solids, surfaces and interfaces) to quantum impurity models (QIM) satisfying a self-consistency condition. This mapping provides an economic description of correlated electron materials. It is currently used in practical computations of physical properties of real materials. It has also great conceptual value, providing a simple picture of correlated electron phenomena on the lattice, using concepts derived from quantum impurity models such as the Kondo effect. DMFT can also be formulated as a first principles electronic structure method and is applicable to correlated materials.

Correspondence between nonrelativistic anti-de Sitter space and conformal field theory, and aging-gravity duality.

PubMed

Minic, Djordje; Pleimling, Michel

2008-12-01

We point out that the recent discussion of nonrelativistic anti-de Sitter space and conformal field theory correspondence has a direct application in nonequilibrium statistical physics, a fact which has not been emphasized in the recent literature on the subject. In particular, we propose a duality between aging in systems far from equilibrium characterized by the dynamical exponent z=2 and gravity in a specific background. The key ingredient in our proposal is the recent geometric realization of the Schrödinger group. We also discuss the relevance of the proposed correspondence for the more general aging phenomena in systems where the value of the dynamical exponent is different from 2.

Dynamics of Ranking Processes in Complex Systems

NASA Astrophysics Data System (ADS)

Blumm, Nicholas; Ghoshal, Gourab; Forró, Zalán; Schich, Maximilian; Bianconi, Ginestra; Bouchaud, Jean-Philippe; Barabási, Albert-László

2012-09-01

The world is addicted to ranking: everything, from the reputation of scientists, journals, and universities to purchasing decisions is driven by measured or perceived differences between them. Here, we analyze empirical data capturing real time ranking in a number of systems, helping to identify the universal characteristics of ranking dynamics. We develop a continuum theory that not only predicts the stability of the ranking process, but shows that a noise-induced phase transition is at the heart of the observed differences in ranking regimes. The key parameters of the continuum theory can be explicitly measured from data, allowing us to predict and experimentally document the existence of three phases that govern ranking stability.

Stratified rotating Boussinesq equations in geophysical fluid dynamics: Dynamic bifurcation and periodic solutions

NASA Astrophysics Data System (ADS)

Hsia, Chun-Hsiung; Ma, Tian; Wang, Shouhong

2007-06-01

The main objective of this article is to study the dynamics of the stratified rotating Boussinesq equations, which are a basic model in geophysical fluid dynamics. First, for the case where the Prandtl number is greater than 1, a complete stability and bifurcation analysis near the first critical Rayleigh number is carried out. Second, for the case where the Prandtl number is smaller than 1, the onset of the Hopf bifurcation near the first critical Rayleigh number is established, leading to the existence of nontrivial periodic solutions. The analysis is based on a newly developed bifurcation and stability theory for nonlinear dynamical systems (both finite and infinite dimensional) by two of the authors [T. Ma and S. Wang, Bifurcation Theory and Applications, World Scientific Series on Nonlinear Sciences Vol. 53 (World Scientific, Singapore, 2005)].

From the Law of Large Numbers to Large Deviation Theory in Statistical Physics: An Introduction

NASA Astrophysics Data System (ADS)

Cecconi, Fabio; Cencini, Massimo; Puglisi, Andrea; Vergni, Davide; Vulpiani, Angelo

This contribution aims at introducing the topics of this book. We start with a brief historical excursion on the developments from the law of large numbers to the central limit theorem and large deviations theory. The same topics are then presented using the language of probability theory. Finally, some applications of large deviations theory in physics are briefly discussed through examples taken from statistical mechanics, dynamical and disordered systems.

Onsets of hierarchy truncation and self–consistent Born approximation with quantum mechanics prescriptions invariance

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Hou-Dao; Yan, YiJing, E-mail: yyan@ust.hk; iChEM and Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026

2015-12-07

The issue of efficient hierarchy truncation is related to many approximate theories. In this paper, we revisit this issue from both the numerical efficiency and quantum mechanics prescription invariance aspects. The latter requires that the truncation approximation made in Schrödinger picture, such as the quantum master equations and their self–consistent–Born–approximation improvements, should be transferable to their Heisenberg–picture correspondences, without further approximations. We address this issue with the dissipaton equation of motion (DEOM), which is a unique theory for the dynamics of not only reduced systems but also hybrid bath environments. We also highlight the DEOM theory is not only aboutmore » how its dynamical variables evolve in time, but also the underlying dissipaton algebra. We demonstrate this unique feature of DEOM with model systems and report some intriguing nonlinear Fano interferences characteristics that are experimentally measurable.« less

FASTSIM2: a second-order accurate frictional rolling contact algorithm

NASA Astrophysics Data System (ADS)

Vollebregt, E. A. H.; Wilders, P.

2011-01-01

In this paper we consider the frictional (tangential) steady rolling contact problem. We confine ourselves to the simplified theory, instead of using full elastostatic theory, in order to be able to compute results fast, as needed for on-line application in vehicle system dynamics simulation packages. The FASTSIM algorithm is the leading technology in this field and is employed in all dominant railway vehicle system dynamics packages (VSD) in the world. The main contribution of this paper is a new version "FASTSIM2" of the FASTSIM algorithm, which is second-order accurate. This is relevant for VSD, because with the new algorithm 16 times less grid points are required for sufficiently accurate computations of the contact forces. The approach is based on new insights in the characteristics of the rolling contact problem when using the simplified theory, and on taking precise care of the contact conditions in the numerical integration scheme employed.

Pilot-Wave Hydrodynamics

NASA Astrophysics Data System (ADS)

Bush, John W. M.

2015-01-01

Yves Couder, Emmanuel Fort, and coworkers recently discovered that a millimetric droplet sustained on the surface of a vibrating fluid bath may self-propel through a resonant interaction with its own wave field. This article reviews experimental evidence indicating that the walking droplets exhibit certain features previously thought to be exclusive to the microscopic, quantum realm. It then reviews theoretical descriptions of this hydrodynamic pilot-wave system that yield insight into the origins of its quantum-like behavior. Quantization arises from the dynamic constraint imposed on the droplet by its pilot-wave field, and multimodal statistics appear to be a feature of chaotic pilot-wave dynamics. I attempt to assess the potential and limitations of this hydrodynamic system as a quantum analog. This fluid system is compared to quantum pilot-wave theories, shown to be markedly different from Bohmian mechanics and more closely related to de Broglie's original conception of quantum dynamics, his double-solution theory, and its relatively recent extensions through researchers in stochastic electrodynamics.

Thermodynamics of a periodically driven qubit

NASA Astrophysics Data System (ADS)

Donvil, Brecht

2018-04-01

We present a new approach to the open system dynamics of a periodically driven qubit in contact with a temperature bath. We are specifically interested in the thermodynamics of the qubit. It is well known that by combining the Markovian approximation with Floquet theory it is possible to derive a stochastic Schrödinger equation in for the state of the qubit. We follow here a different approach. We use Floquet theory to embed the time-non autonomous qubit dynamics into time-autonomous yet infinite dimensional dynamics. We refer to the resulting infinite dimensional system as the dressed-qubit. Using the Markovian approximation we derive the stochastic Schrödinger equation for the dressed-qubit. The advantage of our approach is that the jump operators are ladder operators of the Hamiltonian. This simplifies the formulation of the thermodynamics. We use the thermodynamics of the infinite dimensional system to recover the thermodynamical description for the driven qubit. We compare our results with the existing literature and recover the known results.

What happens to the motor theory of perception when the motor system is damaged?

PubMed

Stasenko, Alena; Garcea, Frank E; Mahon, Bradford Z

2013-09-01

Motor theories of perception posit that motor information is necessary for successful recognition of actions. Perhaps the most well known of this class of proposals is the motor theory of speech perception, which argues that speech recognition is fundamentally a process of identifying the articulatory gestures (i.e. motor representations) that were used to produce the speech signal. Here we review neuropsychological evidence from patients with damage to the motor system, in the context of motor theories of perception applied to both manual actions and speech. Motor theories of perception predict that patients with motor impairments will have impairments for action recognition. Contrary to that prediction, the available neuropsychological evidence indicates that recognition can be spared despite profound impairments to production. These data falsify strong forms of the motor theory of perception, and frame new questions about the dynamical interactions that govern how information is exchanged between input and output systems.

What happens to the motor theory of perception when the motor system is damaged?

PubMed Central

Stasenko, Alena; Garcea, Frank E.; Mahon, Bradford Z.

2016-01-01

Motor theories of perception posit that motor information is necessary for successful recognition of actions. Perhaps the most well known of this class of proposals is the motor theory of speech perception, which argues that speech recognition is fundamentally a process of identifying the articulatory gestures (i.e. motor representations) that were used to produce the speech signal. Here we review neuropsychological evidence from patients with damage to the motor system, in the context of motor theories of perception applied to both manual actions and speech. Motor theories of perception predict that patients with motor impairments will have impairments for action recognition. Contrary to that prediction, the available neuropsychological evidence indicates that recognition can be spared despite profound impairments to production. These data falsify strong forms of the motor theory of perception, and frame new questions about the dynamical interactions that govern how information is exchanged between input and output systems. PMID:26823687

Nonlinear dynamics as an engine of computation.

PubMed

Kia, Behnam; Lindner, John F; Ditto, William L

2017-03-06

Control of chaos teaches that control theory can tame the complex, random-like behaviour of chaotic systems. This alliance between control methods and physics-cybernetical physics-opens the door to many applications, including dynamics-based computing. In this article, we introduce nonlinear dynamics and its rich, sometimes chaotic behaviour as an engine of computation. We review our work that has demonstrated how to compute using nonlinear dynamics. Furthermore, we investigate the interrelationship between invariant measures of a dynamical system and its computing power to strengthen the bridge between physics and computation.This article is part of the themed issue 'Horizons of cybernetical physics'. © 2017 The Author(s).

Nonlinear dynamics as an engine of computation

PubMed Central

Lindner, John F.; Ditto, William L.

2017-01-01

Control of chaos teaches that control theory can tame the complex, random-like behaviour of chaotic systems. This alliance between control methods and physics—cybernetical physics—opens the door to many applications, including dynamics-based computing. In this article, we introduce nonlinear dynamics and its rich, sometimes chaotic behaviour as an engine of computation. We review our work that has demonstrated how to compute using nonlinear dynamics. Furthermore, we investigate the interrelationship between invariant measures of a dynamical system and its computing power to strengthen the bridge between physics and computation. This article is part of the themed issue ‘Horizons of cybernetical physics’. PMID:28115619

Positioning (Mis)Aligned: The (Un)Making of Intercultural Asynchronous Computer-Mediated Communication

ERIC Educational Resources Information Center

Wu, Zhiwei

2018-01-01

Framed from positioning theory and dynamic systems theory, the paper reports on a naturalistic study involving four Chinese participants and their American peers in an intercultural asynchronous computer-mediated communication (ACMC) activity. Based on the moment-by-moment analysis and triangulation of forum posts, reflective essays, and…

The "Chaos" Pattern in Piaget's Theory of Cognitive Development.

ERIC Educational Resources Information Center

Lindsay, Jean S.

Piaget's theory of the cognitive development of the child is related to the recently developed non-linear "chaos" model. The term "chaos" refers to the tendency of dynamical, non-linear systems toward irregular, sometimes unpredictable, deterministic behavior. Piaget identified this same pattern in his model of cognitive…

Organisational Leadership and Chaos Theory: Let's Be Careful

ERIC Educational Resources Information Center

Galbraith, Peter

2004-01-01

This article addresses issues associated with applications of ideas from "chaos theory" to educational administration and leadership as found in the literature. Implications are considered in relation to claims concerning the behaviour of non-linear dynamic systems, and to the nature of the interpretations and recommendations that are made. To aid…

Theory and Simulations of Solar System Plasmas

NASA Technical Reports Server (NTRS)

Goldstein, Melvyn L.

2011-01-01

"Theory and simulations of solar system plasmas" aims to highlight results from microscopic to global scales, achieved by theoretical investigations and numerical simulations of the plasma dynamics in the solar system. The theoretical approach must allow evidencing the universality of the phenomena being considered, whatever the region is where their role is studied; at the Sun, in the solar corona, in the interplanetary space or in planetary magnetospheres. All possible theoretical issues concerning plasma dynamics are welcome, especially those using numerical models and simulations, since these tools are mandatory whenever analytical treatments fail, in particular when complex nonlinear phenomena are at work. Comparative studies for ongoing missions like Cassini, Cluster, Demeter, Stereo, Wind, SDO, Hinode, as well as those preparing future missions and proposals, like, e.g., MMS and Solar Orbiter, are especially encouraged.

Ultrafast dynamics induced by the interaction of molecules with electromagnetic fields: Several quantum, semiclassical, and classical approaches.

PubMed

Antipov, Sergey V; Bhattacharyya, Swarnendu; El Hage, Krystel; Xu, Zhen-Hao; Meuwly, Markus; Rothlisberger, Ursula; Vaníček, Jiří

2017-11-01

Several strategies for simulating the ultrafast dynamics of molecules induced by interactions with electromagnetic fields are presented. After a brief overview of the theory of molecule-field interaction, we present several representative examples of quantum, semiclassical, and classical approaches to describe the ultrafast molecular dynamics, including the multiconfiguration time-dependent Hartree method, Bohmian dynamics, local control theory, semiclassical thawed Gaussian approximation, phase averaging, dephasing representation, molecular mechanics with proton transfer, and multipolar force fields. In addition to the general overview, some focus is given to the description of nuclear quantum effects and to the direct dynamics, in which the ab initio energies and forces acting on the nuclei are evaluated on the fly. Several practical applications, performed within the framework of the Swiss National Center of Competence in Research "Molecular Ultrafast Science and Technology," are presented: These include Bohmian dynamics description of the collision of H with H 2 , local control theory applied to the photoinduced ultrafast intramolecular proton transfer, semiclassical evaluation of vibrationally resolved electronic absorption, emission, photoelectron, and time-resolved stimulated emission spectra, infrared spectroscopy of H-bonding systems, and multipolar force fields applications in the condensed phase.

Ultrafast dynamics induced by the interaction of molecules with electromagnetic fields: Several quantum, semiclassical, and classical approaches

PubMed Central

Antipov, Sergey V.; Bhattacharyya, Swarnendu; El Hage, Krystel; Xu, Zhen-Hao; Meuwly, Markus; Rothlisberger, Ursula; Vaníček, Jiří

2018-01-01

Several strategies for simulating the ultrafast dynamics of molecules induced by interactions with electromagnetic fields are presented. After a brief overview of the theory of molecule-field interaction, we present several representative examples of quantum, semiclassical, and classical approaches to describe the ultrafast molecular dynamics, including the multiconfiguration time-dependent Hartree method, Bohmian dynamics, local control theory, semiclassical thawed Gaussian approximation, phase averaging, dephasing representation, molecular mechanics with proton transfer, and multipolar force fields. In addition to the general overview, some focus is given to the description of nuclear quantum effects and to the direct dynamics, in which the ab initio energies and forces acting on the nuclei are evaluated on the fly. Several practical applications, performed within the framework of the Swiss National Center of Competence in Research “Molecular Ultrafast Science and Technology,” are presented: These include Bohmian dynamics description of the collision of H with H2, local control theory applied to the photoinduced ultrafast intramolecular proton transfer, semiclassical evaluation of vibrationally resolved electronic absorption, emission, photoelectron, and time-resolved stimulated emission spectra, infrared spectroscopy of H-bonding systems, and multipolar force fields applications in the condensed phase. PMID:29376107

Hybrid particle-continuum simulations coupling Brownian dynamics and local dynamic density functional theory.

PubMed

Qi, Shuanhu; Schmid, Friederike

2017-11-08

We present a multiscale hybrid particle-field scheme for the simulation of relaxation and diffusion behavior of soft condensed matter systems. It combines particle-based Brownian dynamics and field-based local dynamics in an adaptive sense such that particles can switch their level of resolution on the fly. The switching of resolution is controlled by a tuning function which can be chosen at will according to the geometry of the system. As an application, the hybrid scheme is used to study the kinetics of interfacial broadening of a polymer blend, and is validated by comparing the results to the predictions from pure Brownian dynamics and pure local dynamics calculations.

Frequency-dependent dynamic magnetic properties of the Ising bilayer system consisting of spin-3/2 and spin-5/2 spins

NASA Astrophysics Data System (ADS)

Keskin, Mustafa; Ertaş, Mehmet

2018-04-01

Dynamic magnetic properties of the Ising bilayer system consisting of the mixed (3/2, 5/2) Ising spins with a crystal-field interaction in an oscillating field on a two-layer square lattice is studied by the use of dynamic mean-field theory based on the Glauber-type stochastic. Dynamic phase transition temperatures are obtained and dynamic phase diagrams are presented in three different planes. The frequency dependence of dynamic hysteresis loops is also investigated in detail. We compare the results with some available theoretical and experimental works and observe a quantitatively good agreement with some theoretical and experimental results.

Psychology and social networks: a dynamic network theory perspective.

PubMed

Westaby, James D; Pfaff, Danielle L; Redding, Nicholas

2014-04-01

Research on social networks has grown exponentially in recent years. However, despite its relevance, the field of psychology has been relatively slow to explain the underlying goal pursuit and resistance processes influencing social networks in the first place. In this vein, this article aims to demonstrate how a dynamic network theory perspective explains the way in which social networks influence these processes and related outcomes, such as goal achievement, performance, learning, and emotional contagion at the interpersonal level of analysis. The theory integrates goal pursuit, motivation, and conflict conceptualizations from psychology with social network concepts from sociology and organizational science to provide a taxonomy of social network role behaviors, such as goal striving, system supporting, goal preventing, system negating, and observing. This theoretical perspective provides psychologists with new tools to map social networks (e.g., dynamic network charts), which can help inform the development of change interventions. Implications for social, industrial-organizational, and counseling psychology as well as conflict resolution are discussed, and new opportunities for research are highlighted, such as those related to dynamic network intelligence (also known as cognitive accuracy), levels of analysis, methodological/ethical issues, and the need to theoretically broaden the study of social networking and social media behavior. (PsycINFO Database Record (c) 2014 APA, all rights reserved).

Global Stability and Dynamics of Strongly Nonlinear Systems Using Koopman Operator Theory

DTIC Science & Technology

2017-03-01

calculus, applied mathematics, Director’s Research Initiative 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU 18... research of Svenkeson et al.4 Section 2 is Accomplishments and Section 3 is the Conclusion. 2. Accomplishments 2.1 Prescribed External Forcing To study ...ARL-TR-7959 MAR 2017 US Army Research Laboratory Global Stability and Dynamics of Strongly Nonlinear Systems Using Koopman

Dynamic kinetic energy potential for orbital-free density functional theory.

PubMed

Neuhauser, Daniel; Pistinner, Shlomo; Coomar, Arunima; Zhang, Xu; Lu, Gang

2011-04-14

A dynamic kinetic energy potential (DKEP) is developed for time-dependent orbital-free (TDOF) density function theory applications. This potential is constructed to affect only the dynamical (ω ≠ 0) response of an orbital-free electronic system. It aims at making the orbital-free simulation respond in the same way as that of a noninteracting homogenous electron gas (HEG), as required by a correct kinetic energy, therefore enabling extension of the success of orbital-free density functional theory in the static case (e.g., for embedding and description of processes in bulk materials) to dynamic processes. The potential is constructed by expansions of terms, each of which necessitates only simple time evolution (concurrent with the TDOF evolution) and a spatial convolution at each time-step. With 14 such terms a good fit is obtained to the response of the HEG at a large range of frequencies, wavevectors, and densities. The method is demonstrated for simple jellium spheres, approximating Na(9)(+) and Na(65)(+) clusters. It is applicable both to small and large (even ultralarge) excitations and the results converge (i.e., do not blow up) as a function of time. An extension to iterative frequency-resolved extraction is briefly outlined, as well as possibly numerically simpler expansions. The approach could also be extended to fit, instead of the HEG susceptibility, either an experimental susceptibility or a theoretically derived one for a non-HEG system. The DKEP potential should be a powerful tool for embedding a dynamical system described by a more accurate method (such as time-dependent density functional theory, TDDFT) in a large background described by TDOF with a DKEP potential. The type of expansions used and envisioned should be useful for other approaches, such as memory functionals in TDDFT. Finally, an appendix details the formal connection between TDOF and TDDFT.

Periodic Peakons, Pseudo-Peakons and Compactons of Ion-Acoustic Wave Model in Electronegative Plasmas with Electrons Featuring Tsallis Distribution

NASA Astrophysics Data System (ADS)

Li, Jibin

The dynamical model of the nonlinear ion-acoustic oscillations is governed by a partial differential equation system. Its traveling system is just a singular traveling wave system of first class depending on four parameters. By using the method of dynamical systems and the theory of singular traveling wave systems, in this paper, we show that there exist parameter groups such that this singular system has pseudo-peakons, periodic peakons and compactons as well as kink and anti-kink wave solutions.

General framework for fluctuating dynamic density functional theory

NASA Astrophysics Data System (ADS)

Durán-Olivencia, Miguel A.; Yatsyshin, Peter; Goddard, Benjamin D.; Kalliadasis, Serafim

2017-12-01

We introduce a versatile bottom-up derivation of a formal theoretical framework to describe (passive) soft-matter systems out of equilibrium subject to fluctuations. We provide a unique connection between the constituent-particle dynamics of real systems and the time evolution equation of their measurable (coarse-grained) quantities, such as local density and velocity. The starting point is the full Hamiltonian description of a system of colloidal particles immersed in a fluid of identical bath particles. Then, we average out the bath via Zwanzig’s projection-operator techniques and obtain the stochastic Langevin equations governing the colloidal-particle dynamics. Introducing the appropriate definition of the local number and momentum density fields yields a generalisation of the Dean-Kawasaki (DK) model, which resembles the stochastic Navier-Stokes description of a fluid. Nevertheless, the DK equation still contains all the microscopic information and, for that reason, does not represent the dynamical law of observable quantities. We address this controversial feature of the DK description by carrying out a nonequilibrium ensemble average. Adopting a natural decomposition into local-equilibrium and nonequilibrium contribution, where the former is related to a generalised version of the canonical distribution, we finally obtain the fluctuating-hydrodynamic equation governing the time-evolution of the mesoscopic density and momentum fields. Along the way, we outline the connection between the ad hoc energy functional introduced in previous DK derivations and the free-energy functional from classical density-functional theory. The resultant equation has the structure of a dynamical density-functional theory (DDFT) with an additional fluctuating force coming from the random interactions with the bath. We show that our fluctuating DDFT formalism corresponds to a particular version of the fluctuating Navier-Stokes equations, originally derived by Landau and Lifshitz. Our framework thus provides the formal apparatus for ab initio derivations of fluctuating DDFT equations capable of describing the dynamics of soft-matter systems in and out of equilibrium.

Adaptive evolution of body size subject to indirect effect in trophic cascade system.

PubMed

Wang, Xin; Fan, Meng; Hao, Lina

2017-09-01

Trophic cascades represent a classic example of indirect effect and are wide-spread in nature. Their ecological impact are well established, but the evolutionary consequences have received even less theoretical attention. We theoretically and numerically investigate the trait (i.e., body size of consumer) evolution in response to indirect effect in a trophic cascade system. By applying the quantitative trait evolutionary theory and the adaptive dynamic theory, we formulate and explore two different types of eco-evolutionary resource-consumer-predator trophic cascade model. First, an eco-evolutionary model incorporating the rapid evolution is formulated to investigate the effect of rapid evolution of the consumer's body size, and to explore the impact of density-mediate indirect effect on the population dynamics and trait dynamics. Next, by employing the adaptive dynamic theory, a long-term evolutionary model of consumer body size is formulated to evaluate the effect of long-term evolution on the population dynamics and the effect of trait-mediate indirect effect. Those models admit rich dynamics that has not been observed yet in empirical studies. It is found that, both in the trait-mediated and density-mediated system, the body size of consumer in predator-consumer-resource interaction (indirect effect) evolves smaller than that in consumer-resource and predator-consumer interaction (direct effect). Moreover, in the density-mediated system, we found that the evolution of consumer body size contributes to avoiding consumer extinction (i.e., evolutionary rescue). The trait-mediate and density-mediate effects may produce opposite evolutionary response. This study suggests that the trophic cascade indirect effect affects consumer evolution, highlights a more comprehensive mechanistic understanding of the intricate interplay between ecological and evolutionary force. The modeling approaches provide avenue for study on indirect effects from an evolutionary perspective. Copyright © 2017 Elsevier B.V. All rights reserved.

Shear-transformation-zone theory of linear glassy dynamics.

PubMed

Bouchbinder, Eran; Langer, J S

2011-06-01

We present a linearized shear-transformation-zone (STZ) theory of glassy dynamics in which the internal STZ transition rates are characterized by a broad distribution of activation barriers. For slowly aging or fully aged systems, the main features of the barrier-height distribution are determined by the effective temperature and other near-equilibrium properties of the configurational degrees of freedom. Our theory accounts for the wide range of relaxation rates observed in both metallic glasses and soft glassy materials such as colloidal suspensions. We find that the frequency-dependent loss modulus is not just a superposition of Maxwell modes. Rather, it exhibits an α peak that rises near the viscous relaxation rate and, for nearly jammed, glassy systems, extends to much higher frequencies in accord with experimental observations. We also use this theory to compute strain recovery following a period of large, persistent deformation and then abrupt unloading. We find that strain recovery is determined in part by the initial barrier-height distribution, but that true structural aging also occurs during this process and determines the system's response to subsequent perturbations. In particular, we find by comparison with experimental data that the initial deformation produces a highly disordered state with a large population of low activation barriers, and that this state relaxes quickly toward one in which the distribution is dominated by the high barriers predicted by the near-equilibrium analysis. The nonequilibrium dynamics of the barrier-height distribution is the most important of the issues raised and left unresolved in this paper.

Grigori Kuzmin and Stellar Dynamics

NASA Astrophysics Data System (ADS)

de Zeeuw, P. Tim; van de Ven, Glenn

Grigori Kuzmin was a very gifted dynamicist and one of the towering figures in the distinguished history of the Tartu Observatory. He obtained a number of important results in relative isolation which were later rediscovered in the West. This work laid the foundation for further advances in the theory of stellar systems in dynamical equilibrium, thereby substantially increasing our understanding of galaxy dynamics.

Application of the Real-Time Time-Dependent Density Functional Theory to Excited-State Dynamics of Molecules and 2D Materials

NASA Astrophysics Data System (ADS)

Miyamoto, Yoshiyuki; Rubio, Angel

2018-04-01

We review our recent developments in the ab initio simulation of excited-state dynamics within the framework of time-dependent density functional theory (TDDFT). Our targets range from molecules to 2D materials, although the methods are general and can be applied to any other finite and periodic systems. We discuss examples of excited-state dynamics obtained by real-time TDDFT coupled with molecular dynamics (MD) and the Ehrenfest approximation, including photoisomerization in molecules, photoenhancement of the weak interatomic attraction of noble gas atoms, photoenhancement of the weak interlayer interaction of 2D materials, pulse-laser-induced local bond breaking of adsorbed atoms on 2D sheets, modulation of UV light intensity by graphene nanoribbons at terahertz frequencies, and collision of high-speed ions with the 2D material to simulate the images taken by He ion microscopy. We illustrate how the real-time TDDFT approach is useful for predicting and understanding non-equilibrium dynamics in condensed matter. We also discuss recent developments that address the excited-state dynamics of systems out of equilibrium and future challenges in this fascinating field of research.

Communication: Towards first principles theory of relaxation in supercooled liquids formulated in terms of cooperative motion.

PubMed

Freed, Karl F

2014-10-14

A general theory of the long time, low temperature dynamics of glass-forming fluids remains elusive despite the almost 20 years since the famous pronouncement by the Nobel Laureate P. W. Anderson, "The deepest and most interesting unsolved problem in solid state theory is probably the theory of the nature of glass and the glass transition" [Science 267, 1615 (1995)]. While recent work indicates that Adam-Gibbs theory (AGT) provides a framework for computing the structural relaxation time of supercooled fluids and for analyzing the properties of the cooperatively rearranging dynamical strings observed in low temperature molecular dynamics simulations, the heuristic nature of AGT has impeded general acceptance due to the lack of a first principles derivation [G. Adam and J. H. Gibbs, J. Chem. Phys. 43, 139 (1965)]. This deficiency is rectified here by a statistical mechanical derivation of AGT that uses transition state theory and the assumption that the transition state is composed of elementary excitations of a string-like form. The strings are assumed to form in equilibrium with the mobile particles in the fluid. Hence, transition state theory requires the strings to be in mutual equilibrium and thus to have the size distribution of a self-assembling system, in accord with the simulations and analyses of Douglas and co-workers. The average relaxation rate is computed as a grand canonical ensemble average over all string sizes, and use of the previously determined relation between configurational entropy and the average cluster size in several model equilibrium self-associating systems produces the AGT expression in a manner enabling further extensions and more fundamental tests of the assumptions.

Communication: Towards first principles theory of relaxation in supercooled liquids formulated in terms of cooperative motion

NASA Astrophysics Data System (ADS)

Freed, Karl F.

2014-10-01

A general theory of the long time, low temperature dynamics of glass-forming fluids remains elusive despite the almost 20 years since the famous pronouncement by the Nobel Laureate P. W. Anderson, "The deepest and most interesting unsolved problem in solid state theory is probably the theory of the nature of glass and the glass transition" [Science 267, 1615 (1995)]. While recent work indicates that Adam-Gibbs theory (AGT) provides a framework for computing the structural relaxation time of supercooled fluids and for analyzing the properties of the cooperatively rearranging dynamical strings observed in low temperature molecular dynamics simulations, the heuristic nature of AGT has impeded general acceptance due to the lack of a first principles derivation [G. Adam and J. H. Gibbs, J. Chem. Phys. 43, 139 (1965)]. This deficiency is rectified here by a statistical mechanical derivation of AGT that uses transition state theory and the assumption that the transition state is composed of elementary excitations of a string-like form. The strings are assumed to form in equilibrium with the mobile particles in the fluid. Hence, transition state theory requires the strings to be in mutual equilibrium and thus to have the size distribution of a self-assembling system, in accord with the simulations and analyses of Douglas and co-workers. The average relaxation rate is computed as a grand canonical ensemble average over all string sizes, and use of the previously determined relation between configurational entropy and the average cluster size in several model equilibrium self-associating systems produces the AGT expression in a manner enabling further extensions and more fundamental tests of the assumptions.

Communication: Towards first principles theory of relaxation in supercooled liquids formulated in terms of cooperative motion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Freed, Karl F., E-mail: freed@uchicago.edu

A general theory of the long time, low temperature dynamics of glass-forming fluids remains elusive despite the almost 20 years since the famous pronouncement by the Nobel Laureate P. W. Anderson, “The deepest and most interesting unsolved problem in solid state theory is probably the theory of the nature of glass and the glass transition” [Science 267, 1615 (1995)]. While recent work indicates that Adam-Gibbs theory (AGT) provides a framework for computing the structural relaxation time of supercooled fluids and for analyzing the properties of the cooperatively rearranging dynamical strings observed in low temperature molecular dynamics simulations, the heuristic naturemore » of AGT has impeded general acceptance due to the lack of a first principles derivation [G. Adam and J. H. Gibbs, J. Chem. Phys. 43, 139 (1965)]. This deficiency is rectified here by a statistical mechanical derivation of AGT that uses transition state theory and the assumption that the transition state is composed of elementary excitations of a string-like form. The strings are assumed to form in equilibrium with the mobile particles in the fluid. Hence, transition state theory requires the strings to be in mutual equilibrium and thus to have the size distribution of a self-assembling system, in accord with the simulations and analyses of Douglas and co-workers. The average relaxation rate is computed as a grand canonical ensemble average over all string sizes, and use of the previously determined relation between configurational entropy and the average cluster size in several model equilibrium self-associating systems produces the AGT expression in a manner enabling further extensions and more fundamental tests of the assumptions.« less

Grounded and embodied mathematical cognition: Promoting mathematical insight and proof using action and language.

PubMed

Nathan, Mitchell J; Walkington, Candace

2017-01-01

We develop a theory of grounded and embodied mathematical cognition (GEMC) that draws on action-cognition transduction for advancing understanding of how the body can support mathematical reasoning. GEMC proposes that participants' actions serve as inputs capable of driving the cognition-action system toward associated cognitive states. This occurs through a process of transduction that promotes valuable mathematical insights by eliciting dynamic depictive gestures that enact spatio-temporal properties of mathematical entities. Our focus here is on pre-college geometry proof production. GEMC suggests that action alone can foster insight but is insufficient for valid proof production if action is not coordinated with language systems for propositionalizing general properties of objects and space. GEMC guides the design of a video game-based learning environment intended to promote students' mathematical insights and informal proofs by eliciting dynamic gestures through in-game directed actions. GEMC generates several hypotheses that contribute to theories of embodied cognition and to the design of science, technology, engineering, and mathematics (STEM) education interventions. Pilot study results with a prototype video game tentatively support theory-based predictions regarding the role of dynamic gestures for fostering insight and proof-with-insight, and for the role of action coupled with language to promote proof-with-insight. But the pilot yields mixed results for deriving in-game interventions intended to elicit dynamic gesture production. Although our central purpose is an explication of GEMC theory and the role of action-cognition transduction, the theory-based video game design reveals the potential of GEMC to improve STEM education, and highlights the complex challenges of connecting embodiment research to education practices and learning environment design.

Electron wavepacket dynamics in highly quasi-degenerate coupled electronic states: a theory for chemistry where the notion of adiabatic potential energy surface loses the sense.

PubMed

Yonehara, Takehiro; Takatsuka, Kazuo

2012-12-14

We develop a theory and the method of its application for chemical dynamics in systems, in which the adiabatic potential energy hyper-surfaces (PES) are densely quasi-degenerate to each other in a wide range of molecular geometry. Such adiabatic electronic states tend to couple each other through strong nonadiabatic interactions. Technically, therefore, it is often extremely hard to accurately single out the individual PES in those systems. Moreover, due to the mutual nonadiabatic couplings that may spread wide in space and due to the energy-time uncertainty relation, the notion of the isolated and well-defined potential energy surface should lose the sense. On the other hand, such dense electronic states should offer a very interesting molecular field in which chemical reactions to proceed in characteristic manners. However, to treat these systems, the standard theoretical framework of chemical reaction dynamics, which starts from the Born-Oppenheimer approximation and ends up with quantum nuclear wavepacket dynamics, is not very useful. We here explore this problem with our developed nonadiabatic electron wavepacket theory, which we call the phase-space averaging and natural branching (PSANB) method [T. Yonehara and K. Takatsuka, J. Chem. Phys. 129, 134109 (2008)], or branching-path representation, in which the packets are propagated in time along the non-Born-Oppenheimer branching paths. In this paper, after outlining the basic theory, we examine using a one-dimensional model how well the PSANB method works with such densely quasi-degenerate nonadiabatic systems. To do so, we compare the performance of PSANB with the full quantum mechanical results and those given by the fewest switches surface hopping (FSSH) method, which is known to be one of the most reliable and flexible methods to date. It turns out that the PSANB electron wavepacket approach actually yields very good results with far fewer initial sampling paths. Then we apply the electron wavepacket dynamics in path-branching representation and the so-called semiclassical Ehrenfest theory to a hydrogen molecule embedded in twelve membered boron cluster (B(12)) in excited states, which are densely quasi-degenerate due to the vacancy in 2p orbitals of boron atom [1s(2)2s(2)2p(1)]. Bond dissociation of the hydrogen molecule quickly takes place in the cluster and the resultant hydrogen atoms are squeezed out to the surface of the cluster. We further study collision dynamics between H(2) and B(12), which also gives interesting phenomena. The present study suggests an interesting functionality of the boron clusters.

In Situ Probe Science at Saturn

NASA Astrophysics Data System (ADS)

Atkinson, David H.; Lunine, Jonathan I.; Simon-Miller, Amy A.; Atreya, Sushil K.; Brinckerhoff, William B.; Colaprete, Anthony; Coustenis, Athena; Fletcher, Leigh N.; Guillot, Tristan; Lebreton, Jean-Pierre; Mahaffy, Paul; Mousis, Olivier; Orton, Glenn S.; Reh, Kim; Spilker, Linda J.; Spilker, Thomas R.; Webster, Chris R.

2014-05-01

A fundamental goal of solar system exploration is to understand the origin of the solar system, the initial stages, conditions, and processes by which the solar system formed, how the formation process was initiated, and the nature of the interstellar seed material from which the solar system was born. Key to understanding solar system formation and subsequent dynamical and chemical evolution is the origin and evolution of the giant planets and their atmospheres. Several theories have been put forward to explain the process of solar system formation, and the origin and evolution of the giant planets and their atmospheres. Each theory offers quantifiable predictions of the abundances of noble gases He, Ne, Ar, Kr, and Xe, and abundances of key isotopic ratios 4He/3He, D/H, 15N/14N, 18O/16O, and 13C/12C. Detection of certain disequilibrium species, diagnostic of deeper internal processes and dynamics of the atmosphere, would also help discriminate between competing theories. Many of the key atmospheric constituents needed to discriminate between alternative theories of giant planet formation and chemical evolution are either spectrally inactive or primarily located in the deeper atmosphere inaccessible to remote sensing from Earth, flyby, or orbiting spacecraft. Abundance measurements of these key constituents, including the two major molecular carriers of carbon, methane and carbon monoxide (neither of which condense in Saturn's atmosphere), sulfur which is expected to be well-mixed below the 4 to 5-bar ammonium hydrosulfide (NH4SH) cloud, and gradients of nitrogen below the NH4SH cloud and oxygen in the upper layers of the H2O and H2O-NH4 solution cloud, must be made in situ and can only be achieved by an entry probe descending through 10 bars. Measurements of the critical abundance profiles of these key constituents into the deeper well-mixed atmosphere must be complemented by measurements of the profiles of atmospheric structure and dynamics at high vertical resolution that also require in situ exploration. The atmospheres of the giant planets can also serve as laboratories to better understand the atmospheric chemistries, dynamics, processes, and climates on all planets in the solar system including Earth, and offer a context and provide a ground truth for exoplanets and exoplanetary systems. Additionally, Giant planets have long been thought to play a critical role in the development of potentially habitable planetary systems. In the context of giant planet science provided by the Galileo, Juno, and Cassini missions to Jupiter and Saturn, a small, relatively shallow Saturn probe capable of measuring abundances and isotopic ratios of key atmospheric constituents, and atmospheric structure including pressures, temperatures, dynamics, and cloud locations and properties not accessible by remote sensing can serve to test competing theories of solar system and giant planet origin, chemical, and dynamical evolution. Acknowledgements This research was carried out in part at the Jet Propulsion Laboratory, California Institute of Technology, under contract with NASA. Copyright 2013 California Institute of Technology. U.S. Government sponsorship acknowledged. O. Mousis acknowledges support from CNES.

Complex dynamics of a new 3D Lorenz-type autonomous chaotic system

NASA Astrophysics Data System (ADS)

Zhang, Fuchen; Liao, Xiaofeng; Zhang, Guangyun; Mu, Chunlai

2017-12-01

This paper investigates a new three-dimensional continuous quadratic autonomous chaotic system which is not topologically equivalent to the Lorenz system. The dynamical behaviours of this system are further investigated in detail, including the ultimate boundedness, the invariant sets and the global attraction domain according to Lyapunov stability theory of dynamical systems. The innovation of the paper lies in the fact that this paper not only proves this chaotic system is globally bounded for the parameters of this system but also gives a family of mathematical expressions of global exponential attractive sets with respect to the parameters of this system. To validate the ultimate bound estimation, numerical simulations are also investigated. Numerical simulations verify the effectiveness and feasibility of the theoretical scheme.

Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory

NASA Astrophysics Data System (ADS)

Rohringer, G.; Hafermann, H.; Toschi, A.; Katanin, A. A.; Antipov, A. E.; Katsnelson, M. I.; Lichtenstein, A. I.; Rubtsov, A. N.; Held, K.

2018-04-01

Strong electronic correlations pose one of the biggest challenges to solid state theory. Recently developed methods that address this problem by starting with the local, eminently important correlations of dynamical mean field theory (DMFT) are reviewed. In addition, nonlocal correlations on all length scales are generated through Feynman diagrams, with a local two-particle vertex instead of the bare Coulomb interaction as a building block. With these diagrammatic extensions of DMFT long-range charge, magnetic, and superconducting fluctuations as well as (quantum) criticality can be addressed in strongly correlated electron systems. An overview is provided of the successes and results achieved, mainly for model Hamiltonians, and an outline is given of future prospects for realistic material calculations.

Nonlinear Dynamics of Complex Coevolutionary Systems in Historical Times

NASA Astrophysics Data System (ADS)

Perdigão, Rui A. P.

2016-04-01

A new theoretical paradigm for statistical-dynamical modeling of complex coevolutionary systems is introduced, with the aim to provide historical geoscientists with a practical tool to analyse historical data and its underlying phenomenology. Historical data is assumed to represent the history of dynamical processes of physical and socio-economic nature. If processes and their governing laws are well understood, they are often treated with traditional dynamical equations: deterministic approach. If the governing laws are unknown or impracticable, the process is often treated as if being random (even if it is not): statistical approach. Although single eventful details - such as the exact spatiotemporal structure of a particular hydro-meteorological incident - may often be elusive to a detailed analysis, the overall dynamics exhibit group properties summarized by a simple set of categories or dynamical regimes at multiple scales - from local short-lived convection patterns to large-scale hydro-climatic regimes. The overwhelming microscale complexity is thus conveniently wrapped into a manageable group entity, such as a statistical distribution. In a stationary setting whereby the distribution is assumed to be invariant, alternating regimes are approachable as dynamical intermittence. For instance, in the context of bimodal climatic oscillations such as NAO and ENSO, each mode corresponds to a dynamical regime or phase. However, given external forcings or longer-term internal variability and multiscale coevolution, the structural properties of the system may change. These changes in the dynamical structure bring about a new distribution and associated regimes. The modes of yesteryear may no longer exist as such in the new structural order of the system. In this context, aside from regime intermittence, the system exhibits structural regime change. New oscillations may emerge whilst others fade into the annals of history, e.g. particular climate fluctuations during the Little Ice Age. Traditional theories of stochastic processes and dynamical systems are grounded on the existence of so-called dynamical invariants; properties that remain unchanged as the dynamics unfold, assuming structural invariance and ergodicity of the underlying system. However, such theories are no longer optimal when trying to understand and model long-term historical records of coevolutionary systems. A new paradigm is thus needed. Therefore, we introduce a new class of dynamical systems that reinvent themselves as the dynamics unfold. Rather than only changing variables and parameters under a rigid framework, the governing laws are malleable themselves. The novel formulation captures and explains the coevolutionary dynamics of multiscale hydroclimatic systems, bringing along a physically sound understanding of their regimes, transitions and extremes over a long-term history.

Birth of an abstraction: a dynamical systems account of the discovery of an elsewhere principle in a category learning task.

PubMed

Tabor, Whitney; Cho, Pyeong W; Dankowicz, Harry

2013-01-01

Human participants and recurrent ("connectionist") neural networks were both trained on a categorization system abstractly similar to natural language systems involving irregular ("strong") classes and a default class. Both the humans and the networks exhibited staged learning and a generalization pattern reminiscent of the Elsewhere Condition (Kiparsky, 1973). Previous connectionist accounts of related phenomena have often been vague about the nature of the networks' encoding systems. We analyzed our network using dynamical systems theory, revealing topological and geometric properties that can be directly compared with the mechanisms of non-connectionist, rule-based accounts. The results reveal that the networks "contain" structures related to mechanisms posited by rule-based models, partly vindicating the insights of these models. On the other hand, they support the one mechanism (OM), as opposed to the more than one mechanism (MOM), view of symbolic abstraction by showing how the appearance of MOM behavior can arise emergently from one underlying set of principles. The key new contribution of this study is to show that dynamical systems theory can allow us to explicitly characterize the relationship between the two perspectives in implemented models. © 2013 Cognitive Science Society, Inc.

Nonequilibrium thermodynamics and information theory: basic concepts and relaxing dynamics

NASA Astrophysics Data System (ADS)

Altaner, Bernhard

2017-11-01

Thermodynamics is based on the notions of energy and entropy. While energy is the elementary quantity governing physical dynamics, entropy is the fundamental concept in information theory. In this work, starting from first principles, we give a detailed didactic account on the relations between energy and entropy and thus physics and information theory. We show that thermodynamic process inequalities, like the second law, are equivalent to the requirement that an effective description for physical dynamics is strongly relaxing. From the perspective of information theory, strongly relaxing dynamics govern the irreversible convergence of a statistical ensemble towards the maximally non-commital probability distribution that is compatible with thermodynamic equilibrium parameters. In particular, Markov processes that converge to a thermodynamic equilibrium state are strongly relaxing. Our framework generalizes previous results to arbitrary open and driven systems, yielding novel thermodynamic bounds for idealized and real processes. , which features invited work from the best early-career researchers working within the scope of J. Phys. A. This project is part of the Journal of Physics series’ 50th anniversary celebrations in 2017. Bernhard Altaner was selected by the Editorial Board of J. Phys. A as an Emerging Talent.

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

NASA Astrophysics Data System (ADS)

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

2016-04-01

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

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schmidt, Patrick; Lucquiaud, Mathieu; Valluri, Prashant, E-mail: prashant.valluri@ed.ac.uk

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

Facilitating Understanding of Movements in Dynamic Visualizations: An Embodied Perspective

ERIC Educational Resources Information Center

de Koning, Bjorn B.; Tabbers, Huib K.

2011-01-01

Learners studying mechanical or technical processes via dynamic visualizations often fail to build an accurate mental representation of the system's movements. Based on embodied theories of cognition assuming that action, perception, and cognition are closely intertwined, this paper proposes that the learning effectiveness of dynamic…

Hamiltonian flows with random-walk behaviour originating from zero-sum games and fictitious play

NASA Astrophysics Data System (ADS)

van Strien, Sebastian

2011-06-01

In this paper we introduce Hamiltonian dynamics, inspired by zero-sum games (best response and fictitious play dynamics). The Hamiltonian functions we consider are continuous and piecewise affine (and of a very simple form). It follows that the corresponding Hamiltonian vector fields are discontinuous and multi-valued. Differential equations with discontinuities along a hyperplane are often called 'Filippov systems', and there is a large literature on such systems, see for example (di Bernardo et al 2008 Theory and applications Piecewise-Smooth Dynamical Systems (Applied Mathematical Sciences vol 163) (London: Springer); Kunze 2000 Non-Smooth Dynamical Systems (Lecture Notes in Mathematics vol 1744) (Berlin: Springer); Leine and Nijmeijer 2004 Dynamics and Bifurcations of Non-smooth Mechanical Systems (Lecture Notes in Applied and Computational Mechanics vol 18) (Berlin: Springer)). The special feature of the systems we consider here is that they have discontinuities along a large number of intersecting hyperplanes. Nevertheless, somewhat surprisingly, the flow corresponding to such a vector field exists, is unique and continuous. We believe that these vector fields deserve attention, because it turns out that the resulting dynamics are rather different from those found in more classically defined Hamiltonian dynamics. The vector field is extremely simple: outside codimension-one hyperplanes it is piecewise constant and so the flow phit piecewise a translation (without stationary points). Even so, the dynamics can be rather rich and complicated as a detailed study of specific examples show (see for example theorems 7.1 and 7.2 and also (Ostrovski and van Strien 2011 Regular Chaotic Dynf. 16 129-54)). In the last two sections of the paper we give some applications to game theory, and finish with posing a version of the Palis conjecture in the context of the class of non-smooth systems studied in this paper. To Jacob Palis on his 70th birthday.

Robust control synthesis for uncertain dynamical systems

NASA Technical Reports Server (NTRS)

Byun, Kuk-Whan; Wie, Bong; Sunkel, John

1989-01-01

This paper presents robust control synthesis techniques for uncertain dynamical systems subject to structured parameter perturbation. Both QFT (quantitative feedback theory) and H-infinity control synthesis techniques are investigated. Although most H-infinity-related control techniques are not concerned with the structured parameter perturbation, a new way of incorporating the parameter uncertainty in the robust H-infinity control design is presented. A generic model of uncertain dynamical systems is used to illustrate the design methodologies investigated in this paper. It is shown that, for a certain noncolocated structural control problem, use of both techniques results in nonminimum phase compensation.

Living in the branches: population dynamics and ecological processes in dendritic networks

USGS Publications Warehouse

Grant, E.H.C.; Lowe, W.H.; Fagan, W.F.

2007-01-01

Spatial structure regulates and modifies processes at several levels of ecological organization (e.g. individual/genetic, population and community) and is thus a key component of complex systems, where knowledge at a small scale can be insufficient for understanding system behaviour at a larger scale. Recent syntheses outline potential applications of network theory to ecological systems, but do not address the implications of physical structure for network dynamics. There is a specific need to examine how dendritic habitat structure, such as that found in stream, hedgerow and cave networks, influences ecological processes. Although dendritic networks are one type of ecological network, they are distinguished by two fundamental characteristics: (1) both the branches and the nodes serve as habitat, and (2) the specific spatial arrangement and hierarchical organization of these elements interacts with a species' movement behaviour to alter patterns of population distribution and abundance, and community interactions. Here, we summarize existing theory relating to ecological dynamics in dendritic networks, review empirical studies examining the population- and community-level consequences of these networks, and suggest future research integrating spatial pattern and processes in dendritic systems.

Quantum dissipation theory and applications to quantum transport and quantum measurement in mesoscopic systems

NASA Astrophysics Data System (ADS)

Cui, Ping

The thesis comprises two major themes of quantum statistical dynamics. One is the development of quantum dissipation theory (QDT). It covers the establishment of some basic relations of quantum statistical dynamics, the construction of several nonequivalent complete second-order formulations, and the development of exact QDT. Another is related to the applications of quantum statistical dynamics to a variety of research fields. In particular, unconventional but novel theories of the electron transfer in Debye solvents, quantum transport, and quantum measurement are developed on the basis of QDT formulations. The thesis is organized as follows. In Chapter 1, we present some background knowledge in relation to the aforementioned two themes of this thesis. The key quantity in QDT is the reduced density operator rho(t) ≡ trBrho T(t); i.e., the partial trace of the total system and bath composite rhoT(t) over the bath degrees of freedom. QDT governs the evolution of reduced density operator, where the effects of bath are treated in a quantum statistical manner. In principle, the reduced density operator contains all dynamics information of interest. However, the conventional quantum transport theory is formulated in terms of nonequilibrium Green's function. The newly emerging field of quantum measurement in relation to quantum information and quantum computing does exploit a sort of QDT formalism. Besides the background of the relevant theoretical development, some representative experiments on molecular nanojunctions are also briefly discussed. In chapter 2, we outline some basic (including new) relations that highlight several important issues on QDT. The content includes the background of nonequilibrium quantum statistical mechanics, the general description of the total composite Hamiltonian with stochastic system-bath interaction, a novel parameterization scheme for bath correlation functions, a newly developed exact theory of driven Brownian oscillator (DBO) systems, and its closely related solvation mode transformation of system-bath coupling Hamiltonian in general. The exact QDT of DBO systems is also used to clarify the validity of conventional QDT formulations that involve Markovian approximation. In Chapter 3, we develop three nonequivalent but all complete second-order QDT (CS-QDT) formulations. Two of them are of the conventional prescriptions in terms of time-local dissipation and memory kernel, respectively. The third one is called the correlated driving-dissipation equations of motion (CODDE). This novel CS-QDT combines the merits of the former two for its advantages in both the application and numerical implementation aspects. Also highlighted is the importance of correlated driving-dissipation effects on the dynamics of the reduced system. In Chapter 4, we construct an exact QDT formalism via the calculus on path integrals. The new theory aims at the efficient evaluation of non-Markovian dissipation beyond the weak system-bath interaction regime in the presence of time-dependent external field. By adopting exponential-like expansions for bath correlation function, hierarchical equations of motion formalism and continued fraction Liouville-space Green's function formalism are established. The latter will soon be used together with the Dyson equation technique for an efficient evaluation of non-perturbative reduced density matrix dynamics. The interplay between system-bath interaction strength, non-Markovian property, and the required level of hierarchy is also studied with the aid of simple spin-boson systems, together with the three proposed schemes to truncate the infinite hierarchy. In Chapter 5, we develop a nonperturbative theory of electron transfer (ET) in Debye solvents. The resulting exact and analytical rate expression is constructed on the basis of the aforementioned continued fraction Liouville-space Green's function formalism, together with the Dyson equation technique. Not only does it recover the celebrated Marcus' inversion and Kramers' turnover behaviors, the new theory also shows some distinct quantum solvation effects that can alter the ET mechanism. Moreover, the present theory predicts further for the ET reaction thermodynamics, such as equilibrium Gibbs free-energy and entropy, some interesting solvent-dependent features that are calling for experimental verification. In Chapter 6, we discuss the constructed QDTs, in terms of their unified mathematical structure that supports a linear dynamics space, and thus facilitates their applications to various physical problems. The involving details are exemplified with the CODDE form of QDT. As the linear space is concerned, we identify the Schrodinger versus Heisenberg picture and the forward versus backward propagation of the reduced, dissipative Liouville dynamics. For applications we discuss the reduced linear response theory and the optimal control problems, in which the correlated effects of non-Markovian dissipation and field driving are shown to be important. In Chapter 7, we turn to quantum transport, i.e., electric current through molecular or mesoscopic systems under finite applied voltage. By viewing the nonequilibrium transport setup as a quantum open system, we develop a reduced-density-matrix approach to quantum transport. The resulting current is explicitly expressed in terms of the molecular reduced density matrix by tracing out the degrees of freedom of the electrodes at finite bias and temperature. We propose a conditional quantum master equation theory, which is an extension of the conventional (or unconditional) QDT by tracing out the well-defined bath subsets individually, instead of the entire bath degrees of freedom. Both the current and the noise spectrum can be conveniently analyzed in terms of the conditional reduced density matrix dynamics. By far, the QDT (including the conditional one) has only been exploited in second-order form. A self-consistent Born approximation for the system-electrode coupling is further proposed to recover all existing nonlinear current-voltage behaviors including the nonequilibrium Kondo effect. Transport theory based on the exact QDT formalism will be developed in future. In Chapter 8, we study the quantum measurement of a qubit with a quantum-point-contact detector. On the basis of a unified quantum master equation (a form of QDT), we study the measurement-induced relaxation and dephasing of the qubit. Our treatment pays particular attention on the detailed-balance relation, which is a consequence of properly accounting for the energy exchange between the qubit and detector during the measurement process. We also derive a conditional quantum master equation for quantum measurement in general, and study the readout characteristics of the qubit measurement. Our theory is applicable to the quantum measurement at arbitrary voltage and temperature. A number of remarkable new features are found and highlighted in concern with their possible relevance to future experiments. In Chapter 9, we discuss the further development of QDT, aiming at an efficient evaluation of many-electron systems. This will be carried out by reducing the many-particle (Fermion or Boson) QDT to a single-particle one by exploring, e.g. the Wick's contraction theorem. It also results in a time-dependent density functional theory (TDDFT) for transport through complex large-scale (e.g. molecules) systems. Primary results of the TDDFT-QDT are reported. In Chapter 10, we summary the thesis, and comment and remark on the future work on both the theoretical and application aspects of QDT.

Are galaxy distributions scale invariant? A perspective from dynamical systems theory

NASA Astrophysics Data System (ADS)

McCauley, J. L.

2002-06-01

Unless there is an evidence for fractal scaling with a single exponent over distances 0.1<=r<=100h-1Mpc, then the widely accepted notion of scale invariance of the correlation integral for 0.1<=r<=10h-1Mpc must be questioned. The attempt to extract a scaling exponent /ν from the correlation integral /n(r) by plotting /log(n(r)) vs. /log(r) is unreliable unless the underlying point set is approximately monofractal. The extraction of a spectrum of generalized dimensions νq from a plot of the correlation integral generating function Gn(q) by a similar procedure is probably an indication that Gn(q) does not scale at all. We explain these assertions after defining the term multifractal, mutually inconsistent definitions having been confused together in the cosmology literature. Part of this confusion is traced to the confusion in interpreting a measure-theoretic formula written down by Hentschel and Procaccia in the dynamical systems theory literature, while other errors follow from confusing together entirely different definitions of multifractal from two different schools of thought. Most important are serious errors in data analysis that follow from taking for granted a largest term approximation that is inevitably advertised in the literature on both fractals and dynamical systems theory.

Hopping and the Stokes-Einstein relation breakdown in simple glass formers.

PubMed

Charbonneau, Patrick; Jin, Yuliang; Parisi, Giorgio; Zamponi, Francesco

2014-10-21

One of the most actively debated issues in the study of the glass transition is whether a mean-field description is a reasonable starting point for understanding experimental glass formers. Although the mean-field theory of the glass transition--like that of other statistical systems--is exact when the spatial dimension d → ∞, the evolution of systems properties with d may not be smooth. Finite-dimensional effects could dramatically change what happens in physical dimensions,d = 2, 3. For standard phase transitions finite-dimensional effects are typically captured by renormalization group methods, but for glasses the corrections are much more subtle and only partially understood. Here, we investigate hopping between localized cages formed by neighboring particles in a model that allows to cleanly isolate that effect. By bringing together results from replica theory, cavity reconstruction, void percolation, and molecular dynamics, we obtain insights into how hopping induces a breakdown of the Stokes-Einstein relation and modifies the mean-field scenario in experimental systems. Although hopping is found to supersede the dynamical glass transition, it nonetheless leaves a sizable part of the critical regime untouched. By providing a constructive framework for identifying and quantifying the role of hopping, we thus take an important step toward describing dynamic facilitation in the framework of the mean-field theory of glasses.

Coupled Cluster Method with Single and Double Excitations Tailored by Matrix Product State Wave Functions.

PubMed

Veis, Libor; Antalík, Andrej; Brabec, Jiří; Neese, Frank; Legeza, Örs; Pittner, Jiří

2016-10-03

In the past decade, the quantum chemical version of the density matrix renormalization group (DMRG) method has established itself as the method of choice for calculations of strongly correlated molecular systems. Despite its favorable scaling, it is in practice not suitable for computations of dynamic correlation. We present a novel method for accurate "post-DMRG" treatment of dynamic correlation based on the tailored coupled cluster (CC) theory in which the DMRG method is responsible for the proper description of nondynamic correlation, whereas dynamic correlation is incorporated through the framework of the CC theory. We illustrate the potential of this method on prominent multireference systems, in particular, N 2 and Cr 2 molecules and also oxo-Mn(Salen), for which we have performed the first post-DMRG computations in order to shed light on the energy ordering of the lowest spin states.

Hidden dynamics in models of discontinuity and switching

NASA Astrophysics Data System (ADS)

Jeffrey, Mike R.

2014-04-01

Sharp switches in behaviour, like impacts, stick-slip motion, or electrical relays, can be modelled by differential equations with discontinuities. A discontinuity approximates fine details of a switching process that lie beyond a bulk empirical model. The theory of piecewise-smooth dynamics describes what happens assuming we can solve the system of equations across its discontinuity. What this typically neglects is that effects which are vanishingly small outside the discontinuity can have an arbitrarily large effect at the discontinuity itself. Here we show that such behaviour can be incorporated within the standard theory through nonlinear terms, and these introduce multiple sliding modes. We show that the nonlinear terms persist in more precise models, for example when the discontinuity is smoothed out. The nonlinear sliding can be eliminated, however, if the model contains an irremovable level of unknown error, which provides a criterion for systems to obey the standard Filippov laws for sliding dynamics at a discontinuity.

Image-plane processing of visual information

NASA Technical Reports Server (NTRS)

Huck, F. O.; Fales, C. L.; Park, S. K.; Samms, R. W.

1984-01-01

Shannon's theory of information is used to optimize the optical design of sensor-array imaging systems which use neighborhood image-plane signal processing for enhancing edges and compressing dynamic range during image formation. The resultant edge-enhancement, or band-pass-filter, response is found to be very similar to that of human vision. Comparisons of traits in human vision with results from information theory suggest that: (1) Image-plane processing, like preprocessing in human vision, can improve visual information acquisition for pattern recognition when resolving power, sensitivity, and dynamic range are constrained. Improvements include reduced sensitivity to changes in lighter levels, reduced signal dynamic range, reduced data transmission and processing, and reduced aliasing and photosensor noise degradation. (2) Information content can be an appropriate figure of merit for optimizing the optical design of imaging systems when visual information is acquired for pattern recognition. The design trade-offs involve spatial response, sensitivity, and sampling interval.

Diffusion and interactions of interstitials in hard-sphere interstitial solid solutions

NASA Astrophysics Data System (ADS)

van der Meer, Berend; Lathouwers, Emma; Smallenburg, Frank; Filion, Laura

2017-12-01

Using computer simulations, we study the dynamics and interactions of interstitial particles in hard-sphere interstitial solid solutions. We calculate the free-energy barriers associated with their diffusion for a range of size ratios and densities. By applying classical transition state theory to these free-energy barriers, we predict the diffusion coefficients, which we find to be in good agreement with diffusion coefficients as measured using event-driven molecular dynamics simulations. These results highlight that transition state theory can capture the interstitial dynamics in the hard-sphere model system. Additionally, we quantify the interactions between the interstitials. We find that, apart from excluded volume interactions, the interstitial-interstitial interactions are almost ideal in our system. Lastly, we show that the interstitial diffusivity can be inferred from the large-particle fluctuations alone, thus providing an empirical relationship between the large-particle fluctuations and the interstitial diffusivity.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sanz, Alejandro; Ezquerra, Tiberio A.; Nogales, Aurora, E-mail: aurora.nogales@csic.es

The dynamics of lower disorder-order temperature diblock copolymer leading to phase separation has been observed by X ray photon correlation spectroscopy. Two different modes have been characterized. A non-diffusive mode appears at temperatures below the disorder to order transition, which can be associated to compositional fluctuations, that becomes slower as the interaction parameter increases, in a similar way to the one observed for diblock copolymers exhibiting phase separation upon cooling. At temperatures above the disorder to order transition T{sub ODT}, the dynamics becomes diffusive, indicating that after phase separation in Lower Disorder-Order Transition (LDOT) diblock copolymers, the diffusion of chainmore » segments across the interface is the governing dynamics. As the segregation is stronger, the diffusive process becomes slower. Both observed modes have been predicted by the theory describing upper order-disorder transition systems, assuming incompressibility. However, the present results indicate that the existence of these two modes is more universal as they are present also in compressible diblock copolymers exhibiting a lower disorder-order transition. No such a theory describing the dynamics in LDOT block copolymers is available, and these experimental results may offer some hints to understanding the dynamics in these systems. The dynamics has also been studied in the ordered state, and for the present system, the non-diffusive mode disappears and only a diffusive mode is observed. This mode is related to the transport of segment in the interphase, due to the weak segregation on this system.« less

A Novel Type of Chaotic Attractor for Quadratic Systems Without Equilibriums

NASA Astrophysics Data System (ADS)

Dantsev, Danylo

In this paper, a new chaotic dynamic system without equilibriums is presented. A conducted research of the qualitative properties of the discovered system reveals a noncompliance between the bifurcation behavior of the system and the Feigenbaum-Sharkovskii-Magnitsky theory. Additional research of known systems confirms the discrepancy.

On the Pontryagin maximum principle for systems with delays. Economic applications

NASA Astrophysics Data System (ADS)

Kim, A. V.; Kormyshev, V. M.; Kwon, O. B.; Mukhametshin, E. R.

2017-11-01

The Pontryagin maximum principle [6] is the key stone of finite-dimensional optimal control theory [1, 2, 5]. So beginning with opening the maximum principle it was important to extend the maximum principle on various classes of dynamical systems. In t he paper we consider some aspects of application of i-smooth analysis [3, 4] in the theory of the Pontryagin maximum principle [6] for systems with delays, obtained results can be applied by elaborating optimal program controls in economic models with delays.

Analysis on the dynamic error for optoelectronic scanning coordinate measurement network

NASA Astrophysics Data System (ADS)

Shi, Shendong; Yang, Linghui; Lin, Jiarui; Guo, Siyang; Ren, Yongjie

2018-01-01

Large-scale dynamic three-dimension coordinate measurement technique is eagerly demanded in equipment manufacturing. Noted for advantages of high accuracy, scale expandability and multitask parallel measurement, optoelectronic scanning measurement network has got close attention. It is widely used in large components jointing, spacecraft rendezvous and docking simulation, digital shipbuilding and automated guided vehicle navigation. At present, most research about optoelectronic scanning measurement network is focused on static measurement capacity and research about dynamic accuracy is insufficient. Limited by the measurement principle, the dynamic error is non-negligible and restricts the application. The workshop measurement and positioning system is a representative which can realize dynamic measurement function in theory. In this paper we conduct deep research on dynamic error resources and divide them two parts: phase error and synchronization error. Dynamic error model is constructed. Based on the theory above, simulation about dynamic error is carried out. Dynamic error is quantized and the rule of volatility and periodicity has been found. Dynamic error characteristics are shown in detail. The research result lays foundation for further accuracy improvement.

The Design of Power System Stability Controller Based on the PCH Theory and Improved Genetic Algorithm

NASA Astrophysics Data System (ADS)

Liu, Zhijian; Yin, Donghui; Yan, Jun

2017-05-01

Low frequency oscillation is still frequently happened in the power system and it affects the safety and stability of power system directly. With the continuously expending of the interconnection scale of power grid, the risk of low frequency oscillation becomes more and more noticeable. Firstly, the basic theory of port-controlled Hamilton (PCH) and its application is analyzed. Secondly, based on the PCH theory and the dynamic model of system, from the viewpoint of energy, the nonlinear stability controller of power system is designed. By the improved genetic algorithm, the parameters of the PCH model are optimized. Finally, a simulation model with PCH is built to vary the effectiveness of the method proposed in this paper.

New phenomena in non-equilibrium quantum physics

NASA Astrophysics Data System (ADS)

Kitagawa, Takuya

From its beginning in the early 20th century, quantum theory has become progressively more important especially due to its contributions to the development of technologies. Quantum mechanics is crucial for current technology such as semiconductors, and also holds promise for future technologies such as superconductors and quantum computing. Despite of the success of quantum theory, its applications have been mostly limited to equilibrium or static systems due to 1. lack of experimental controllability of non-equilibrium quantum systems 2. lack of theoretical frameworks to understand non-equilibrium dynamics. Consequently, physicists have not yet discovered too many interesting phenomena in non-equilibrium quantum systems from both theoretical and experimental point of view and thus, non-equilibrium quantum physics did not attract too much attentions. The situation has recently changed due to the rapid development of experimental techniques in condensed matter as well as cold atom systems, which now enables a better control of non-equilibrium quantum systems. Motivated by this experimental progress, we constructed theoretical frameworks to study three different non-equilibrium regimes of transient dynamics, steady states and periodically drives. These frameworks provide new perspectives for dynamical quantum process, and help to discover new phenomena in these systems. In this thesis, we describe these frameworks through explicit examples and demonstrate their versatility. Some of these theoretical proposals have been realized in experiments, confirming the applicability of the theories to realistic experimental situations. These studies have led to not only the improved fundamental understanding of non-equilibrium processes in quantum systems, but also suggested entirely different venues for developing quantum technologies.

Dynamical analysis of an orbiting three-rigid-body system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pagnozzi, Daniele, E-mail: daniele.pagnozzi@strath.ac.uk, E-mail: james.biggs@strath.ac.uk; Biggs, James D., E-mail: daniele.pagnozzi@strath.ac.uk, E-mail: james.biggs@strath.ac.uk

2014-12-10

The development of multi-joint-spacecraft mission concepts calls for a deeper understanding of their nonlinear dynamics to inform and enhance system design. This paper presents a study of a three-finite-shape rigid-body system under the action of an ideal central gravitational field. The aim of this paper is to gain an insight into the natural dynamics of this system. The Hamiltonian dynamics is derived and used to identify relative attitude equilibria of the system with respect to the orbital reference frame. Then a numerical investigation of the behaviour far from the equilibria is provided using tools from modern dynamical systems theory suchmore » as energy methods, phase portraits and Poincarè maps. Results reveal a complex structure of the dynamics as well as the existence of connections between some of the equilibria. Stable equilibrium configurations appear to be surrounded by very narrow regions of regular and quasi-regular motions. Trajectories evolve on chaotic motions in the rest of the domain.« less

Threshold virus dynamics with impulsive antiretroviral drug effects

PubMed Central

Lou, Jie; Lou, Yijun; Wu, Jianhong

2013-01-01

The purposes of this paper are twofold: to develop a rigorous approach to analyze the threshold behaviors of nonlinear virus dynamics models with impulsive drug effects and to examine the feasibility of virus clearance following the Manuals of National AIDS Free Antiviral Treatment in China. An impulsive system of differential equations is developed to describe the within-host virus dynamics of both wild-type and drug-resistant strains when a combination of antiretroviral drugs is used to induce instantaneous drug effects at a sequence of dosing times equally spaced while drug concentrations decay exponentially after the dosing time. Threshold parameters are derived using the basic reproduction number of periodic epidemic models, and are used to depict virus clearance/persistence scenarios using the theory of asymptotic periodic systems and the persistence theory of discrete dynamical systems. Numerical simulations using model systems parametrized in terms of the antiretroviral therapy recommended in the aforementioned Manuals illustrate the theoretical threshold virus dynamics, and examine conditions under which the impulsive antiretroviral therapy leads to treatment success. In particular, our results show that only the drug-resistant strain can dominate (the first-line treatment program guided by the Manuals) or both strains may be rapidly eliminated (the second-line treatment program), thus the work indicates the importance of implementing the second-line treatment program as soon as possible. PMID:21987085

Spin-orbit coupling and tidal dissipation in hot Jupiter systems

NASA Astrophysics Data System (ADS)

Shabaltas, Natalia Igorevna

Hot Jupiters are giant planets located extremely close to their host stars, with orbital periods less than 5 days. Many aspects of hot Jupiter (HJ) formation remain unclear, but several clues, such as the observed misalignment between their orbital axes and their hosts' spin axes, point to a dynamical origin. In the first portion of this work we explore the stellar spin-orbit dynamics of one such dynamical formation channel, the Lidov-Kozai mechanism. We show that the coupling between the stellar spin and the planet orbit can lead to complex, and sometimes chaotic, behavior of the stellar spin vector. Many features of this behavior arise due to a set of resonances between the stellar spin axis precession timescale and the Lidov-Kozai timescale. Under the assumption that the stellar quadrupole does not induce precession in the planet's orbit, given a system with a set of initial parameters, we show that it is possible to predict whether the system can attain high spin-orbit misalignments. In the second portion of this work, we discuss tidal dissipation in giant planets, another aspect that is crucial to dynamical HJ formation theories. We show that tidal dissipation in the cores of giant planets can be significant, and can help reconcile inconsistencies in the tidal dissipation efficiencies inferred from observations of Jupiter's moons and from high-eccentricity HJ migration theories. Finally, we improve upon existing core tidal dissipation theories by presenting semi-analytical formulae for dissipation in a core surrounded by a polytropic n = 1 envelope.

Evaluation of protein-protein docking model structures using all-atom molecular dynamics simulations combined with the solution theory in the energy representation

NASA Astrophysics Data System (ADS)

Takemura, Kazuhiro; Guo, Hao; Sakuraba, Shun; Matubayasi, Nobuyuki; Kitao, Akio

2012-12-01

We propose a method to evaluate binding free energy differences among distinct protein-protein complex model structures through all-atom molecular dynamics simulations in explicit water using the solution theory in the energy representation. Complex model structures are generated from a pair of monomeric structures using the rigid-body docking program ZDOCK. After structure refinement by side chain optimization and all-atom molecular dynamics simulations in explicit water, complex models are evaluated based on the sum of their conformational and solvation free energies, the latter calculated from the energy distribution functions obtained from relatively short molecular dynamics simulations of the complex in water and of pure water based on the solution theory in the energy representation. We examined protein-protein complex model structures of two protein-protein complex systems, bovine trypsin/CMTI-1 squash inhibitor (PDB ID: 1PPE) and RNase SA/barstar (PDB ID: 1AY7), for which both complex and monomer structures were determined experimentally. For each system, we calculated the energies for the crystal complex structure and twelve generated model structures including the model most similar to the crystal structure and very different from it. In both systems, the sum of the conformational and solvation free energies tended to be lower for the structure similar to the crystal. We concluded that our energy calculation method is useful for selecting low energy complex models similar to the crystal structure from among a set of generated models.

Evaluation of protein-protein docking model structures using all-atom molecular dynamics simulations combined with the solution theory in the energy representation.

PubMed

Takemura, Kazuhiro; Guo, Hao; Sakuraba, Shun; Matubayasi, Nobuyuki; Kitao, Akio

2012-12-07

We propose a method to evaluate binding free energy differences among distinct protein-protein complex model structures through all-atom molecular dynamics simulations in explicit water using the solution theory in the energy representation. Complex model structures are generated from a pair of monomeric structures using the rigid-body docking program ZDOCK. After structure refinement by side chain optimization and all-atom molecular dynamics simulations in explicit water, complex models are evaluated based on the sum of their conformational and solvation free energies, the latter calculated from the energy distribution functions obtained from relatively short molecular dynamics simulations of the complex in water and of pure water based on the solution theory in the energy representation. We examined protein-protein complex model structures of two protein-protein complex systems, bovine trypsin/CMTI-1 squash inhibitor (PDB ID: 1PPE) and RNase SA/barstar (PDB ID: 1AY7), for which both complex and monomer structures were determined experimentally. For each system, we calculated the energies for the crystal complex structure and twelve generated model structures including the model most similar to the crystal structure and very different from it. In both systems, the sum of the conformational and solvation free energies tended to be lower for the structure similar to the crystal. We concluded that our energy calculation method is useful for selecting low energy complex models similar to the crystal structure from among a set of generated models.

General Theory and Algorithms for the Non-Casual Inversion, Slewing and Control of Space-Based Articulated Structures

DTIC Science & Technology

1993-10-01

Structures: Simultaneous Trajectory Tracking and Vibration Reduction ... 10 3 . Buckling Control of a Flexible Beam Using Piezoelectric Actuators...bounded solution for the inverse dynamic torque has to be non-causal. Bayo, et. al. [ 3 ], extended the inverse dynamics to planar, multiple-link systems...presented by &ayo and Moulin [4] for the single link system, with provisions for 3 extension to multiple link systems. An equivalent time domain approach for

Asynchronous Data-Driven Classification of Weapon Systems

DTIC Science & Technology

2009-10-01

Classification of Weapon SystemsF Xin Jin† Kushal Mukherjee† Shalabh Gupta† Asok Ray † Shashi Phoha† Thyagaraju Damarla‡ xuj103@psu.edu kum162@psu.edu szg107...Orlando, FL. [8] A. Ray , “Symbolic dynamic analysis of complex systems for anomaly detection,” Signal Processing, vol. 84, no. 7, pp. 1115–1130, July...2004. [9] S. Gupta and A. Ray , “Symbolic dynamic filtering for data-driven pat- tern recognition,” PATTERN RECOGNITION: Theory and Application

Deterministic representation of chaos with application to turbulence

NASA Technical Reports Server (NTRS)

Zak, M.

1987-01-01

Chaotic motions of nonlinear dynamical systems are decomposed into mean components and fluctuations. The approach is based upon the concept that the fluctuations driven by the instability of the original (unperturbed) motion grow until a new stable state is approached. The Reynolds-type equations written for continuous as well as for finite-degrees-of-freedom dynamical systems are closed by using this stabilization principle. The theory is applied to conservative systems, to strange attractors and to turbulent motions.

Market mechanism based on the endogenous changing of game types such as Minority-Majority games

NASA Astrophysics Data System (ADS)

Ahn, Sanghyun; Lim, Gyuchang; Kim, Sooyong; Kim, Kyungsik

2010-03-01

In many social and biological systems agents simultaneously and adaptively compete for limited resources, thereby altering their environment. We propose a evolution function extending Minority-Majority Games that captures the competition between agents to make money. The dynamics changes the ratio of two types of boundedly rational traders, fundamentalists and chartists with the payoff function endogenously. In the previous game theories, the best strategies are not always targeting the minority but are shifting opportunistically between the minority and the majority. And using a mixture of local bifurcation theory and numerical methods, there are possible bifurcation routes to complicated asset price dynamics, chaotic attractors. Hereby we improve the thinking logic of the atoms for attaching the dynamics to the market. This working shows that removing unrealistic features of the game theories leads to models which reproduce a behavior close to what is observed in real markets.

Mott-Hubbard transition and Anderson localization: A generalized dynamical mean-field theory approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kuchinskii, E. Z.; Nekrasov, I. A.; Sadovskii, M. V.

The DOS, the dynamic (optical) conductivity, and the phase diagram of a strongly correlated and strongly disordered paramagnetic Anderson-Hubbard model are analyzed within the generalized dynamical mean field theory (DMFT + {sigma} approximation). Strong correlations are taken into account by the DMFT, and disorder is taken into account via an appropriate generalization of the self-consistent theory of localization. The DMFT effective single-impurity problem is solved by a numerical renormalization group (NRG); we consider the three-dimensional system with a semielliptic DOS. The correlated metal, Mott insulator, and correlated Anderson insulator phases are identified via the evolution of the DOS and dynamicmore » conductivity, demonstrating both the Mott-Hubbard and Anderson metal-insulator transition and allowing the construction of the complete zero-temperature phase diagram of the Anderson-Hubbard model. Rather unusual is the possibility of a disorder-induced Mott insulator-to-metal transition.« less

Free energy landscape theory of glass transition

NASA Astrophysics Data System (ADS)

Odagaki, Takashi

2010-03-01

I first present a free energy landscape (FEL) description of statistical mechanics, which is an exact reformulation of statistical mechanics and can be applied to non-equilibrium systems. Then, I discuss thermodynamic and dynamic properties of the vitrification process on the basis of the FEL formalism. I show that thermodynamic and dynamic anomalies at the glass transition, including the cooling rate dependence, can be understood in a unified manner which has not been achieved by any other theories of the glass transition. Namely, I show that the vitrification is a transition from annealed to quenched averages in the FEL and that the fast beta, the JG and the slow alpha relaxations are attributed to stochastic dynamics within a basin of FEL, jumping motion among locally connected basins and diffusive dynamics over barriers of the FEL.

Fully dynamical simulation of central nuclear collisions.

PubMed

van der Schee, Wilke; Romatschke, Paul; Pratt, Scott

2013-11-27

We present a fully dynamical simulation of central nuclear collisions around midrapidity at LHC energies. Unlike previous treatments, we simulate all phases of the collision, including the equilibration of the system. For the simulation, we use numerical relativity solutions to anti-de Sitter space/conformal field theory for the preequilibrium stage, viscous hydrodynamics for the plasma equilibrium stage, and kinetic theory for the low-density hadronic stage. Our preequilibrium stage provides initial conditions for hydrodynamics, resulting in sizable radial flow. The resulting light particle spectra reproduce the measurements from the ALICE experiment at all transverse momenta.