scholarly journals On the fractal nature of complex syntax and the timescale problem

2020 ◽  
Vol 10 (4) ◽  
pp. 697-721
Author(s):  
D. Reid Evans
Keyword(s):  
Complex Systems ◽  
Dynamic Systems Theory ◽  
Self Similarity ◽  
Scale Invariant ◽  
Complex Dynamic Systems ◽  
Complex Syntax ◽  
Dynamic Relationship ◽  
Self Similar ◽  
Multiple Component ◽  
Dynamic Relationships

Fundamental to complex dynamic systems theory is the assumption that the recursive behavior of complex systems results in the generation of physical forms and dynamic processes that are self-similar and scale-invariant. Such fractal-like structures and the organismic benefit that they engender has been widely noted in physiology, biology, and medicine, yet discussions of the fractal-like nature of language have remained at the level of metaphor in applied linguistics. Motivated by the lack of empirical evidence supporting this assumption, the present study examines the extent to which the use and development of complex syntax in a learner of English as a second language demonstrate the characteristics of self-similarity and scale invariance at nested timescales. Findings suggest that the use and development of syntactic complexity are governed by fractal scaling as the dynamic relationship among the subconstructs of syntax maintain their complexity and variability across multiple temporal scales. Overall, fractal analysis appears to be a fruitful analytic tool when attempting to discern the dynamic relationships among the multiple component parts of complex systems as they interact over time.

scholarly journals Classroom-oriented research from a complex systems perspective

2016 ◽  
Vol 6 (3) ◽  
pp. 377-393 ◽  
Author(s):  
Diane Larsen-Freeman
Keyword(s):  
Complex Systems ◽  
Dynamic Systems ◽  
Dynamic Systems Theory ◽  
Complex Dynamic ◽  
Systems Perspective ◽  
Complex Dynamic Systems ◽  
Classroom Ecology ◽  
Theory Research ◽  
Different Levels ◽  
Oriented Research

Bringing a complex systems perspective to bear on classroom-oriented research challenges researchers to think differently, seeing the classroom ecology as one dynamic system nested in a hierarchy of such systems at different levels of scale, all of which are spatially and temporally situated. This article begins with an introduction to complex dynamic systems theory, in which challenges to traditional ways of conducting classroom research are interwoven. It concludes with suggestions for research methods that are more consistent with the theory. Research does not become easier when approached from a complex systems perspective, but it has the virtue of reflecting the way the world works.

scholarly journals Self-similarity principle: the reduced description of randomness

Open Physics ◽  
2013 ◽  
Vol 11 (6) ◽  
Author(s):  
Raoul Nigmatullin ◽  
José Machado ◽  
Rui Menezes
Keyword(s):  
Complex Systems ◽  
Complex Data ◽  
Self Similarity ◽  
Data Set ◽  
Surface Data ◽  
Fitting Method ◽  
Recorded Data ◽  
Self Similar ◽  
The Mathematical Model ◽  
To Receive

AbstractA new general fitting method based on the Self-Similar (SS) organization of random sequences is presented. The proposed analytical function helps to fit the response of many complex systems when their recorded data form a self-similar curve. The verified SS principle opens new possibilities for the fitting of economical, meteorological and other complex data when the mathematical model is absent but the reduced description in terms of some universal set of the fitting parameters is necessary. This fitting function is verified on economical (price of a commodity versus time) and weather (the Earth’s mean temperature surface data versus time) and for these nontrivial cases it becomes possible to receive a very good fit of initial data set. The general conditions of application of this fitting method describing the response of many complex systems and the forecast possibilities are discussed.

scholarly journals Variability as normal as apple pie

2021 ◽  
Vol 7 (s2) ◽  
Author(s):  
Marjolijn Verspoor ◽  
Wander Lowie ◽  
Kees de Bot
Keyword(s):  
Dynamic Systems ◽  
Dynamic Systems Theory ◽  
Complex Dynamic ◽  
Controlled Processes ◽  
Complex Dynamic Systems ◽  
L2 Development ◽  
Limited Degree ◽  
Development Phases ◽  
Longitudinal Case Studies ◽  
Over Time

Abstract In recent studies in second language (L2) development, notably within the focus of Complex Dynamic Systems Theory (CDST), non-systematic variation has been extensively studied as intra-individual variation, which we will refer to as variability. This paper argues that variability is functional and is needed for development. With examples of four longitudinal case studies we hope to show that variability over time provides valuable information about the process of development. Phases of increased variability in linguistic constructions are often a sign that the learner is trying out different constructions, and as such variability can be evidence for change, and change can be learning. Also, a limited degree of variability is inherent in automatic or controlled processes. Conversely, the absence of variability is likely to show that no learning is going on or the system is frozen.

scholarly journals Onset of the Mach Reflection of Zel’dovich–von Neumann–Döring Detonations

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 314
Author(s):  
Tianyu Jing ◽  
Huilan Ren ◽  
Jian Li
Keyword(s):  
Hot Spot ◽  
Mach Reflection ◽  
Near Field ◽  
The Self ◽  
Small Scale ◽  
Mach Stem ◽  
Self Similarity ◽  
Von Neumann ◽  
Similarity Problem ◽  
Self Similar

The present study investigates the similarity problem associated with the onset of the Mach reflection of Zel’dovich–von Neumann–Döring (ZND) detonations in the near field. The results reveal that the self-similarity in the frozen-limit regime is strictly valid only within a small scale, i.e., of the order of the induction length. The Mach reflection becomes non-self-similar during the transition of the Mach stem from “frozen” to “reactive” by coupling with the reaction zone. The triple-point trajectory first rises from the self-similar result due to compressive waves generated by the “hot spot”, and then decays after establishment of the reactive Mach stem. It is also found, by removing the restriction, that the frozen limit can be extended to a much larger distance than expected. The obtained results elucidate the physical origin of the onset of Mach reflection with chemical reactions, which has previously been observed in both experiments and numerical simulations.

scholarly journals Depressurization-Induced Nucleation in the “Polylactide-Carbon Dioxide” System: Self-Similarity of the Bubble Embryos Expansion

Polymers ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1115
Author(s):  
Dmitry Zimnyakov ◽  
Marina Alonova ◽  
Ekaterina Ushakova
Keyword(s):  
Initial Rate ◽  
Initial Pressure ◽  
External Pressure ◽  
Self Similarity ◽  
Embryo Formation ◽  
Linear Behavior ◽  
Joint Influence ◽  
External Pressures ◽  
Adiabatic Cooling ◽  
Self Similar

Self-similar expansion of bubble embryos in a plasticized polymer under quasi-isothermal depressurization is examined using the experimental data on expansion rates of embryos in the CO2-plasticized d,l-polylactide and modeling the results. The CO2 initial pressure varied from 5 to 14 MPa, and the depressurization rate was 5 × 10−3 MPa/s. The constant temperature in experiments was in a range from 310 to 338 K. The initial rate of embryos expansion varied from ≈0.1 to ≈10 µm/s, with a decrease in the current external pressure. While modeling, a non-linear behavior of CO2 isotherms near the critical point was taken into account. The modeled data agree satisfactorily with the experimental results. The effect of a remarkable increase in the expansion rate at a decreasing external pressure is interpreted in terms of competing effects, including a decrease in the internal pressure, an increase in the polymer viscosity, and an increase in the embryo radius at the time of embryo formation. The vanishing probability of finding the steadily expanding embryos for external pressures around the CO2 critical pressure is interpreted in terms of a joint influence of the quasi-adiabatic cooling and high compressibility of CO2 in the embryos.

Toward a transdisciplinary integration of research purposes and methods for complex dynamic systems theory: beyond the quantitative–qualitative divide

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Phil Hiver ◽  
Ali H. Al-Hoorie ◽  
Diane Larsen-Freeman
Keyword(s):  
Systems Theory ◽  
Dynamic Systems ◽  
Applied Linguistics ◽  
Integrated Approach ◽  
Dynamic Systems Theory ◽  
Complex Dynamic ◽  
Transdisciplinary Approach ◽  
Complex Dynamic Systems ◽  
Human And Social Sciences ◽  
Starting Point

Abstract Complexity theory/dynamic systems theory has challenged conventional approaches to applied linguistics research by encouraging researchers to adopt a pragmatic transdisciplinary approach that is less paradigmatic and more problem-oriented in nature. Its proponents have argued that the starting point in research design should not be the quantitative–qualitative distinction, or even mixed methods, but the distinction between individual versus group-based designs (i.e., idiographic versus nomothetic). Taking insights from transdisciplinary complexity research in other human and social sciences, we propose an integrative transdisciplinary framework that unites these different perspectives (quantitative–qualitative, individual–group based) from the starting point of exploratory–falsificatory aims. We discuss the implications of this transdisciplinary approach to applied linguistics research and illustrate how such an integrated approach might be implemented in the field.

scholarly journals Self-similar resistive circuits as fractal-like structures

2017 ◽  
Vol 40 (1) ◽  
Author(s):  
Claudio Xavier Mendes dos Santos ◽  
Carlos Molina Mendes ◽  
Marcelo Ventura Freire
Keyword(s):  
Scale Invariance ◽  
Self Similarity ◽  
General Properties ◽  
Modern Physics ◽  
Resistive Networks ◽  
Self Similar ◽  
And Mathematics ◽  
Definition Of ◽  
The Individual

Fractals play a central role in several areas of modern physics and mathematics. In the present work we explore resistive circuits where the individual resistors are arranged in fractal-like patterns. These circuits have some of the characteristics typically found in geometric fractals, namely self-similarity and scale invariance. Considering resistive circuits as graphs, we propose a definition of self-similar circuits which mimics a self-similar fractal. General properties of the resistive circuits generated by this approach are investigated, and interesting examples are commented in detail. Specifically, we consider self-similar resistive series, tree-like resistive networks and Sierpinski’s configurations with resistors.

TUBE FORMULAS FOR GRAPH-DIRECTED FRACTALS

Fractals ◽  
2010 ◽  
Vol 18 (03) ◽  
pp. 349-361 ◽  
Author(s):  
BÜNYAMIN DEMÍR ◽  
ALI DENÍZ ◽  
ŞAHIN KOÇAK ◽  
A. ERSIN ÜREYEN
Keyword(s):  
The Self ◽  
Self Similarity ◽  
Complex Dimensions ◽  
Tubular Neighborhoods ◽  
Self Similar ◽  
Tube Formulas

Lapidus and Pearse proved recently an interesting formula about the volume of tubular neighborhoods of fractal sprays, including the self-similar fractals. We consider the graph-directed fractals in the sense of graph self-similarity of Mauldin-Williams within this framework of Lapidus-Pearse. Extending the notion of complex dimensions to the graph-directed fractals we compute the volumes of tubular neighborhoods of their associated tilings and give a simplified and pointwise proof of a version of Lapidus-Pearse formula, which can be applied to both self-similar and graph-directed fractals.

scholarly journals On the scaling of shear-driven entrainment: a DNS study

2013 ◽  
Vol 732 ◽  
pp. 150-165 ◽  
Author(s):  
Harm J. J. Jonker ◽  
Maarten van Reeuwijk ◽  
Peter P. Sullivan ◽  
Edward G. Patton
Keyword(s):  
Reynolds Number ◽  
Lower Boundary ◽  
Square Root ◽  
Simulation Design ◽  
Self Similarity ◽  
Original Experiment ◽  
Turbulent Layer ◽  
Entrainment Velocity ◽  
Constant Shear Stress ◽  
Self Similar

AbstractThe deepening of a shear-driven turbulent layer penetrating into a stably stratified quiescent layer is studied using direct numerical simulation (DNS). The simulation design mimics the classical laboratory experiments by Kato & Phillips (J. Fluid Mech., vol. 37, 1969, pp. 643–655) in that it starts with linear stratification and applies a constant shear stress at the lower boundary, but avoids sidewall and rotation effects inherent in the original experiment. It is found that the layers universally deepen as a function of the square root of time, independent of the initial stratification and the Reynolds number of the simulations, provided that the Reynolds number is large enough. Consistent with this finding, the dimensionless entrainment velocity varies with the bulk Richardson number as$R{i}^{- 1/ 2} $. In addition, it is observed that all cases evolve in a self-similar fashion. A self-similarity analysis of the conservation equations shows that only a square root growth law is consistent with self-similar behaviour.

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