Beckett's Broken Circle: A Literary Fractal

2020 ◽  
Vol 29 (2) ◽  
pp. 196-215
Author(s):  
Luke Connolly
Keyword(s):  
Dynamic Chaos ◽  
Geometric Form ◽  
Self Similarity ◽  
Collision Point ◽  
Stable Order ◽  
Structural Principle ◽  
Recent Interest ◽  
Viable Solution ◽  
Specific Shape

This essay proposes that the picture of a broken circle encountered by Watt during the second part of his tale marks a crucial collision point between Beckett's literary and mathematical interests and triggers a process of fractal scaling self-similarity. Building on recent interest concerning the role of the mathematics and mathematical forms found in Beckett's work, I argue that the broken circle depicted in the picture from Watt is a geometric form which (re)appears within at least three interlocking scales throughout Beckett's novel-length prose: (i) its moment of arrival in the picture from Watt, (ii) a macroscopic reinscription in the names of the protagonists populating the five novels spanning Watt through to The Unnamable and (iii) buried within the narratological depths of How It Is. As a structural principle, the interminable irregularity of fractals offered Beckett a viable solution for what he considered the defining task of the modern artist: ‘to find a form to accommodate the mess’. Moreover, the specific shape selected for his fractal is shown to contain within its geometry one of Beckett's most universal and pressing concerns: the inevitable insufficiency of language. Therefore, although this essay restricts itself to examining Beckett's novel-length prose, the idea of a broken circle fractal promises to provide a valuable heuristic through which to reassess the author's other generic avenues. Fractals thus offer a means through which one can bind together the length and breadth of Beckett's oeuvre without ever reducing dynamic chaos to stable order.

scholarly journals Topographic Analysis of Wetlandscapes: Fractal Dimension and Scaling Properties

10.29007/c7r5 ◽  
2018 ◽  
Author(s):  
Leonardo Enrico Bertassello ◽  
P. Suresh Rao ◽  
Gianluca Botter ◽  
Antoine Aubeneau
Keyword(s):  
Fractal Dimension ◽  
The United States ◽  
Self Similarity ◽  
Topographic Analysis ◽  
Scaling Properties ◽  
Dem Analysis ◽  
Water Filling ◽  
Topographic Depressions ◽  
And Storage

Wetlands are ubiquitous topographic depressions on landscapes and form criticalelements of the mosaic of aquatic habitats. The role of wetlands in the global hydrological and biogeochemical cycles is intimately tied to their geometric characteristics. We used DEM analysis and local search algorithms to identify wetland attributes (maximum stage, surface area and storage volume) in four wetlandscapes across the United States. We then derived the exceedance cumulative density functions (cdfs) of these attributes for the identified wetlands, applied the concept of fractal dimension to investigate the variability in wetland’ shapes. Exponentially tempered Pareto distributions were fitted to DEM derived wetland attributes. In particular, the scaling exponents appear to remain constant through the progressive water-filling of the landscapes, suggesting self-similarity of wetland geometrical attributes. This tendency is also reproduced by the fractal dimension (D) of wetland shorelines, which remains constant across different water-filling levels. In addition, the variability in D is constrained within a narrow range (1 <D < 1.33) in all the four wetlandscapes. Finally, the comparison between wetlands identified by the DEM-based model are consistentwith actual data.

Increasing Penetration of DERs in Smart Grid Framework: A State-of-the-Art Review on Challenges, Mitigation Techniques and Role of Smart Inverters

2020 ◽  
Vol 29 (16) ◽  
pp. 2030014
Author(s):  
Sumeet Kumar Wankhede ◽  
Priyanka Paliwal ◽  
Mukesh K. Kirar
Keyword(s):  
Smart Grid ◽  
Renewable Energy Sources ◽  
Mitigation Measures ◽  
Electrical Grid ◽  
Functional Capabilities ◽  
Viable Solution ◽  
Advanced Control ◽  
Vital Component ◽  
Smart Inverters

The world is witnessing a transformation from the conventional electrical grid into the smart grid. The smart grid can provide an effective solution to alarming problems associated with a conventional grid with increased reliability, efficiency, and sustainability. Integration of distributed energy resources (DERs) comprising of renewable energy sources (RESs) is a vital component of the smart grid. DERs not only can provide a viable solution for environmental concerns arising due to conventional fossil fuel-based plants, but can also contribute towards the system reliability. However, the integration of DERs is associated with several challenges.  Thus, the successful deployment of DERs in smart grid framework calls for a comprehensive analysis. This paper presents an exhaustive review of various challenges associated with increased penetration of DERs. An organized classification of various technical challenges along with their mitigation measures has been critically reviewed. Smart inverters equipped with advanced control structure are emerging as a potential solution to address these challenges effectively. Hence, a review of smart inverter along with its functional capabilities has also been discussed in this paper.

scholarly journals On the concept of international disorder

2020 ◽  
pp. 004711782092228
Author(s):  
Aaron McKeil
Keyword(s):  
International Relations ◽  
Research Agenda ◽  
International Order ◽  
World Politics ◽  
International Affairs ◽  
Order And Disorder ◽  
Recent Interest ◽  
History Of ◽  
International Systems

International relations today are widely considered to be experiencing deepening disorder and the topic of international disorder is gaining increased attention. Yet, despite this recent interest in international disorder, in and beyond the academy, and despite the decades-long interest in international order, there is still little agreement on the concept of international disorder, which is often used imprecisely and with an alarmist rather than analytical usage. This is a problem if international disorder is to be understood in theory, towards addressing its concomitant problems and effects in practice. As such, this article identifies and explores two ways international order studies can benefit from a clearer and more precise conception of international disorder. First, it enables a more complete picture of how orderly international orders have been. Second, a greater understanding of the problem of international order is illuminated by a clearer grasp of the relation between order and disorder in world politics. The article advances these arguments in three steps. First, an analytical concept of international disorder is developed and proposed. Second, applying it to the modern history of international order, the extent to which there is a generative relationship between order and disorder in international systems is explored. Third, it specifies the deepening international disorder in international affairs today. It concludes by indicating a research agenda for International Relations and international order studies that takes the role of international disorder more seriously.

The Role of Self-Similarity in Fractal Photoconductive THz Emitters

2011 ◽  
Vol 32 (11) ◽  
pp. 1285-1290 ◽  
Author(s):  
Pouya Maraghechi ◽  
Abdulhakem Y. Elezzabi
Keyword(s):  
Self Similarity

scholarly journals Magnetic collimation of relativistic jets: the role of the black hole spin

2010 ◽  
Vol 6 (S274) ◽  
pp. 246-248
Author(s):  
N. Globus ◽  
C. Sauty ◽  
V. Cayatte
Keyword(s):  
Black Hole ◽  
Kerr Black Hole ◽  
Polar Axis ◽  
Kerr Metric ◽  
Relativistic Jets ◽  
Self Similarity ◽  
Simple Criterion ◽  
Frame Dragging ◽  
Grmhd Equations

AbstractAn ideal engine for producing ultrarelativistic jets is a rapidly rotating black hole threaded by a magnetic field. Following the 3+1 decomposion of spacetime of Thorne et al. (1986), we use a local inertial frame of reference attached to an observer comoving with the frame-dragging of the Kerr black hole (ZAMO) to write the GRMHD equations. Assuming θ-self similarity, analytical solutions for jets can be found for which the streamline shape is calculated exactly. Calculating the total energy variation between a non polar streamline and the polar axis, we have extended to the Kerr metric the simple criterion for the magnetic collimation of jets developed by Sauty et al. (1999). We show that the black hole rotation induces a more efficient magnetic collimation of the jet.

scholarly journals Generalized Finite-Length Fibonacci Sequences in Healthy and Pathological Human Walking: Comprehensively Assessing Recursivity, Asymmetry, Consistency, Self-Similarity, and Variability of Gaits

2021 ◽  
Vol 15 ◽  
Author(s):  
Cristiano Maria Verrelli ◽  
Marco Iosa ◽  
Paolo Roselli ◽  
Antonio Pisani ◽  
Franco Giannini ◽  
...  
Keyword(s):  
Finite Length ◽  
Golden Ratio ◽  
Point Of View ◽  
Human Walking ◽  
General Definition ◽  
Self Similarity ◽  
Time Intervals ◽  
Double Support ◽  
Fibonacci Sequences

Healthy and pathological human walking are here interpreted, from a temporal point of view, by means of dynamics-on-graph concepts and generalized finite-length Fibonacci sequences. Such sequences, in their most general definition, concern two sets of eight specific time intervals for the newly defined composite gait cycle, which involves two specific couples of overlapping (left and right) gait cycles. The role of the golden ratio, whose occurrence has been experimentally found in the recent literature, is accordingly characterized, without resorting to complex tools from linear algebra. Gait recursivity, self-similarity, and asymmetry (including double support sub-phase consistency) are comprehensively captured. A new gait index, named Φ-bonacci gait number, and a new related experimental conjecture—concerning the position of the foot relative to the tibia—are concurrently proposed. Experimental results on healthy or pathological gaits support the theoretical derivations.

scholarly journals Life Cycle of a Military Product

2018 ◽  
Vol 23 (2) ◽  
pp. 103-111
Author(s):  
Nicolae Moro
Keyword(s):  
Decision Making ◽  
North Atlantic ◽  
Second Life ◽  
Life Goal ◽  
The North ◽  
Select Group ◽  
Viable Solution ◽  
Technical Systems ◽  
The North Atlantic

Abstract Romania’s membership of the select group of states belonging to the North Atlantic Treaty Organization brings, in addition to the expected security benefits and assurances and commitments and obligations that we have to assume. The participation of politicians, militaries and Romanian experts in the decision-making within the specialized committees of the NATO structures is an extremely important element for the assertion of Romania as a security guarantor in the area, a hypostasis that was only a vision a few years ago. This role of our country must be supported by strong and powerful military capabilities, capabilities that are hard to reach for many of the countries in Eastern Europe. The economically advantageous and technologically viable solution for a period of time is to acquire advanced military technical systems that are equipped with the great economic powers of NATO, systems used and verified by these armies, revitalized and upgraded, a second life goal.

scholarly journals Elementary & Secondary Education Department Mardan, KP Pakistan

2020 ◽  
pp. 53-62
Author(s):  
Amir ZAMAN ◽  
◽  
Riaz AHMAD ◽  
Keyword(s):  
Presidential Elections ◽  
Political Stability ◽  
Power Sharing ◽  
Education Department ◽  
Peace Agreement ◽  
Viable Solution ◽  
The Us ◽  
Us Government ◽  
Great Development

Afghanistan that remained the epicenter of terrorism and insurgency in the post 9/11 incident, suffered irreparable loss in both human and infrastructure, is now heading towards an era of peace and political stability. The signing of the peace agreement on February 29, 2020 by both the US government and the Taliban is a great development for strengthening democratization and power-sharing among the stakeholders in Afghanistan. However, certain hurdles stand in the way of peace and stability. This paper discusses some of the key areas such as the dilemma of Afghan presidential elections, Pakistan’s controversial role, role of neighboring countries and the Indo-Afghan Nexus. Lacunae in the US-Taliban agreement to the exclusion of the Afghan government in the agreement and the threat of the ISIS are some of the other hurdles in bringing peace and stability in the country. Bargaining among the US and Taliban and the various stakeholders of Afghanistan is the only viable solution to the problem which provides the basis for theoretical framework. Keywords: Peace, Hurdles, Afghanistan, Taliban, US

scholarly journals MODELING OF VIBRATIONAL PROCESSES IN DISCRETE MATRIX STRUC-TURES APPROACH

2020 ◽  
pp. 67-79
Author(s):  
Yuriy Penkin ◽  
Georgi Hara ◽  
Alina Fedoseeva
Keyword(s):  
Discrete System ◽  
Latin Square ◽  
Matrix Transformations ◽  
Self Similarity ◽  
Linear Type ◽  
Type Group ◽  
Structural Principle ◽  
The Matrix ◽  
Radio Signals ◽  
Discrete Structures

In the article are presented general principles of modeling vibrations in discrete structures formed in the form of special matrix forms of the Latin square (Sudoku type) are presented. The signs of structural and functional self-similarity for the matrix structures of standard Sudoku grids are formulated. It is shown that the structural principle can be interpreted as the implementation of the second iteration in the scale scaling algorithm characteristic of fractal objects. The signs of functional self-similarity of structures include the property of additive conservation of grid shapes to the requirements of Sudoku, which is formulated as a theorem. It is proved that the matrix sums of Sudoku constants and grids of arbitrary sizes, obtained taking into account the introduced cyclic ranking rule, will satisfy the three required Sudoku requirements. It is determined that by performing a given sequence of group shift operators, it is possible to establish a specific scenario for dynamically changing the state of a structure on a discrete time scale. It has been established that the evolution operators of linear-type group translations lead to matrix transformations of Sudoku grids from the set of equivalent ones (concerning the original ones), and the vortex-type group shifts operators to matrix transformations from many essentially different networks. The modes of harmonic, chaotic, and hybrid vibrations for structures of arbitrary size are considered. The requirements for transformations of the operators of the evolution of structures that provide the implementation of the considered modes are formulated. The results of modeling chaotic oscillatory processes by cycles of states of a discrete system that form similarities of attractor paths are analyzed. The principle of synchronization of chaotic states of matrix structures is established. The possibility of simulating the modes of beatings of oscillations in discrete cellular structures organized in the form of two-level matrix forms is substantiated. Specific examples show the results of simulating beatings of oscillations in cycles of changing states of a discrete system for two types of beats: similar to the result of a superposition of harmonic vibrations at multiple frequencies in the theory of radio signals, as well as noise-like beats.

scholarly journals On the Role of Hazard and Particle Failure Statistics on the Variation of Fracture Parameters of Ductile-Brittle Composites

Metals ◽  
2019 ◽  
Vol 9 (6) ◽  
pp. 633
Author(s):  
Mikhail Lebyodkin ◽  
Tatiana Lebedkina
Keyword(s):  
Spherical Particles ◽  
Average Value ◽  
Strain Behavior ◽  
Hard Particles ◽  
Failure Statistics ◽  
Specific Shape ◽  
Probabilistic Nature ◽  
Brittle Composites

The behavior of a simple computer model considering a random distribution of brittle spherical particles in a ductile matrix is examined in order to highlight the intrinsic variations of the fracture conditions due to the probabilistic nature of the particle cleavage. The model is qualitatively supported by experimental data on stress-strain behavior and damage accumulation in an Al-Si alloy with unconnected equiaxed Si particles. It is used to evaluate the effect of the particle failure statistics on the fracture characteristics (strength, ductility, and fraction of cracked particles) and their scatter, which occur to be strongly dependent on the specific shape of the probabilistic law. In particular, it is found that the variations of the fracture conditions may depend non-monotonously on its sharpness, in the case of the well-known Weibull statistics controlled by the value of the respective modulus of the material of hard particles. The existence of a maximum scatter leads to a suggestion that the choice of the reinforcements may influence not only on the average value of the fracture resistance but also on the quality of its prediction.

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