scholarly journals Chaos as a symmetry-breaking phenomenon

2019 ◽  
Vol 33 (24) ◽  
pp. 1950287 ◽  
Author(s):  
Igor V. Ovchinnikov ◽  
Massimiliano Di Ventra
Keyword(s):  
Continuous Time ◽  
Initial Conditions ◽  
Deterministic Chaos ◽  
General Definition ◽  
Stochastic Dynamical Systems ◽  
Topological Transitivity ◽  
Wide Range ◽  
Fundamental Phenomenon ◽  
Definition Of ◽  
Low Dimensional

Chaos is an ubiquitous and fundamental phenomenon with a wide range of features pointing to a similar phenomenology. Although apparently distinct, it is natural to ask if all these features emerge from a unifying principle. Recently, it was realized that all continuous-time stochastic dynamical systems (DSs) — the most relevant in physics because natural DSs are always subject to noise and time is continuous — possess a topological supersymmetry (TS). It was then suggested that its spontaneous breakdown could be interpreted as the stochastic generalization of deterministic chaos. This conclusion stems from the fact that such phenomenon encompasses features that are traditionally associated with chaotic dynamics such as non-integrability, positive topological entropy, sensitivity to initial conditions and the Poincaré–Bendixson theorem. Here, we strengthen and complete this picture by showing that the remaining hallmarks of deterministic chaos — topological transitivity/mixing and dense periodic orbits — while being consistent with the TS breaking, do not actually admit a stochastic generalization. This is a major limitation, since all physical systems are always noisy to some extent. We, therefore, conclude that spontaneous TS breaking can be considered as the most general definition of continuous-time dynamical chaos. Contrary to the common perception and semantics of the word “chaos,” this phenomenon should then be truly interpreted as the low-symmetry, or ordered phase of the DSs that manifest it. We also argue that the concept of chaos in low-dimensional, discrete-time DSs that do not obey the Poincaré–Bendixson theorem, is related to the explicit TS breaking.

scholarly journals Dynamic Analysis and Cryptographic Application of a Sinusoidal-polynomial Composite Chaotic System

2021 ◽  
Author(s):  
Hegui Zhu ◽  
Jiangxia Ge ◽  
Wentao Qi ◽  
Xiangde Zhang ◽  
Xiaoxiong Lu
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Encryption Algorithm ◽  
Topological Transitivity ◽  
Detailed Simulation ◽  
Definition Of ◽  
Image Encryption Algorithm ◽  
Sensitivity To Initial Conditions

Abstract Owning to complex properties of ergodicity, non-periodic ability and sensitivity to initial states, chaotic systems are widely used in cryptography. In this paper, we propose a sinusoidal--polynomial composite chaotic system (SPCCS), and prove that it satisfies Devaney's definition of chaos: the sensitivity to initial conditions, topological transitivity and density of periodic points. The experimental results show that the SPCCS has better unpredictability and more complex chaotic behavior than the classical chaotic maps. Furthermore, we provide a new image encryption algorithm combining pixel segmentation operation, block chaotic matrix confusing operation, and pixel diffusion operation with the SPCCS. Detailed simulation results verify effectiveness of the proposed image encryption algorithm.

Effect of Ratio of Liquid Pigment on Colouring Cement Matrix

2019 ◽  
Vol 296 ◽  
pp. 3-8
Author(s):  
David Bujdoš ◽  
Lucia Bulíková
Keyword(s):  
Colour Change ◽  
High Ratio ◽  
General Definition ◽  
Cement Matrix ◽  
Future Research ◽  
Colour Space ◽  
Cement Mortars ◽  
Wide Range ◽  
Definition Of ◽  
Cie Lab

Nowadays, the colouring is used in wide range of architectural concrete. Therefore, determination efficiency of pigments in case of particular combination of input materials is necessary. The research deals with influence of concentration of liquid inorganic pigments on the resulting colour of cement mortars. Two liquid pigments (yellow, red) were used for measurement purposes to verify their optimal ratio to achieve the best colouring of cement specimens. Pigments were mixed in the mortars of two types of cements used for architectural and decorative design. The colour change was determined using Konica Minolta spectrophotometer in colour space CIE Lab (1976). General definition of deviation in the colour space ΔELab was applied for calculating of colour deviation. From the results of the laboratory tests is obvious that significant change of the colour of cement specimens do not show between the concentration of 6% and 9% of the pigment per cement weight yet. Consequently, using of high ratio of pigment than 9% is not profitable neither for purchaser, nor builder. Future research will focus on trials with a more elaborate share of pigment and it will have importance for price optimization in the construction industry.

On the dynamics of the Tent function - Phase diagrams

2016 ◽  
Vol 7 (4) ◽  
pp. 261
Author(s):  
Prince Amponsah Kwabi ◽  
William Obeng Denteh ◽  
Richard Kena Boadi
Keyword(s):  
Dynamical Systems ◽  
Phase Diagrams ◽  
Initial Conditions ◽  
Asymptotic Properties ◽  
Topological Dynamical System ◽  
Topological Transitivity ◽  
Tent Map ◽  
One Dimensional ◽  
Definition Of ◽  
Topological Dynamical Systems

This paper focuses on the study of a one-dimensional topological dynamical system, the tent function. We give a good background to the theory of dynamical systems while establishing the important asymptotic properties of topological dynamical systems that distinguishes it from other fields by way of an example - the tent function. A precise definition of the tent function is given and iterates are clearly shown using the phase diagrams. By this same method, chaos in the tent map is shown as iterates become higher. We also show that the tent map has infinitely many chaotic orbits and also express some important features of chaos such as topological transitivity, boundedness and sensitivity to change in initial conditions from a topological viewpoint.

Numerical Analysis of Conservative Maps: A Possible Foundation of Nonextensive Phenomena

2004 ◽  
Author(s):  
Fulvio Baldovin
Keyword(s):  
Statistical Mechanics ◽  
High Energy Physics ◽  
Financial Analysis ◽  
Initial Conditions ◽  
Research Area ◽  
Distribution Functions ◽  
Point Of View ◽  
Dissipative Systems ◽  
Definition Of ◽  
Low Dimensional

We discuss the sensitivity to initial conditions and the entropy production of low-dimensional conservative maps, focusing on situations where the phase space presents complex (fractal-like) structures. We analyze numerically the standard map as a specific example and we observe a scenario that presents appealing analogies with anomalies detected in long-range Hamiltonian systems. We see how the Tsallis nonextensive formalism handles this situation both from a dynamical and from a statistical mechanics point of view…. In recent years, the Tsallis extension of the Boltzmann-Gibbs (BG) statistical mechanics [9, 26], usually referred to as nonextensive (NE) statistical mechanics, has become an intense and exciting research area (see, e.g., Tsallis [25]). The q-exponential distribution functions that emerge as a consequence of the NE formalism have been applied to an impressive variety of problems, ranging from turbulence, to high-energy physics, epilepsy, protein folding, and financial analysis. Yet, the foundation of this formalism, as well as the definition of its area of applicability, is still not completely understood, and it stands as a present challenge in the affirmation of the whole proposal. An intensive effort is currently being made to investigate this point, precisely in trying to understand: (1) which mechanisms lead to a crisis of the BG formalism; and (2) in these cases, does the NE formalism provide a "way out" to some of the problems? A possible approach to these questions comes from the study of the underlying dynamics that gives the basis for a statistical mechanic treatment of the system. This idea is not new. Einstein, in his critical remark about the validity of the Boltzmann principle [10], was one of the first to call attention to the relevance of a dynamical foundation of statistical mechanics. Another fundamental contribution is Krylov's seminal work [14] on the mixing properties of dynamical systems. In one-dimensional (dissipative) systems, intensive effort has been made to analyze the properties of the systems at the edge of chaos, i.e., at the critical poin that marks the transition between chaoticity and regularity [6, 8, 16, 19, 18, 23, 27].

scholarly journals ART OF JACKSON POLLOCK IN URBAN PLANNING AND DESIGN - NOTION OF "LIFE" IN CITY SPACE

2018 ◽  
Vol 13 (1) ◽  
Author(s):  
Valentina Milovanović
Keyword(s):  
Specific Activity ◽  
Complex Form ◽  
General Definition ◽  
Urban Structure ◽  
Jackson Pollock ◽  
Planning And Design ◽  
Wide Range ◽  
City Space ◽  
Urban Planning And Design ◽  
Definition Of

There are different definitions of what constitutes the term "life". The background of most of these definitions is appropriate theories: starting with the notion that everything that exists is matter, and life is only its complex form, up to vitalism which considers the principle of life as purely intangible. Forming the general definition of life has always been a major challenge for many experts. The situation is still unchanged. The question is, how in a wide range of different ideas and attitudes, evidence and experiments, to take a stand when it comes to the phenomenon of life in the context of the urban structure of today? Is it possible to use an expressive structure of the painting as a specific activity that is simultaneously based on previously established principles and techniques, but also on a freedom of the artist, as a good example for translating into the urbanistic domain? The paper explores wide connection between "life", urban structure of today's city and painting of Jackson Pollock.

Tonic

2015 ◽  
pp. 105-135
Author(s):  
Steven Rings
Keyword(s):  
Hard Rock ◽  
General Definition ◽  
Rust Belt ◽  
Avant Garde ◽  
Wide Range ◽  
Musical Cultures ◽  
Intellectual Traditions ◽  
Narrow Definition ◽  
The Common ◽  
Definition Of

This article proposes a general definition of tonic and explores its ramifications across repertories and intellectual traditions (cognitive, historical, ethnomusicological, music analytical, and phenomenological). The proposed definition admits of both wide and narrow applications: from broad conceptions that detect tonics in a wide range of world musics to a more narrow definition that limits the term (and its theoretical entailments) to bourgeois musical cultures in the West. These ideas are illustrated through discussions of diverse musical examples, from the “common practice” (Bach, Schubert) to the postwar avant-garde (Lutosławski), French house (Daft Punk), and rust-belt hard rock (Akron-based band Dia Pason).

Typologization of security regulation

2020 ◽  
pp. 20-27
Author(s):  
Denis Tikhomirov
Keyword(s):  
Social Relations ◽  
Scientific Literature ◽  
Legal Regulation ◽  
Procedural Understanding ◽  
Limited Ability ◽  
Methodological Basis ◽  
Wide Range ◽  
The Subject ◽  
Definition Of ◽  
Legal Understanding

The purpose of the article is to typologize terminological definitions of security, to find out the general, to identify the originality of their interpretations depending on the subject of legal regulation. The methodological basis of the study is the methods that made it possible to obtain valid conclusions, in particular, the method of comparison, through which it became possible to correlate different interpretations of the term "security"; method of hermeneutics, which allowed to elaborate texts of normative legal acts of Ukraine, method of typologization, which made it possible to create typologization groups of variants of understanding of the term "security". Scientific novelty. The article analyzes the understanding of the term "security" in various regulatory acts in force in Ukraine. Typological groups were understood to understand the term "security". Conclusions. The analysis of the legal material makes it possible to confirm that the issues of security are within the scope of both legislative regulation and various specialized by-laws. However, today there is no single conception on how to interpret security terminology. This is due both to the wide range of social relations that are the subject of legal regulation and to the relativity of the notion of security itself and the lack of coherence of views on its definition in legal acts and in the scientific literature. The multiplicity of definitions is explained by combinations of material and procedural understanding, static - dynamic, and conditioned by the peculiarities of a particular branch of legal regulation, limited ability to use methods of one or another branch, the inter-branch nature of some variations of security, etc. Separation, common and different in the definition of "security" can be used to further standardize, in fact, the regulatory legal understanding of security to more effectively implement the legal regulation of the security direction.

Music after the Fall

2017 ◽  
Author(s):  
Tim Rutherford-Johnson
Keyword(s):  
New Media ◽  
Contemporary Music ◽  
The United States ◽  
Art Music ◽  
Sound Art ◽  
Musical Composition ◽  
Western Art ◽  
Wide Range ◽  
Definition Of ◽  
The Cold War

By the start of the 21st century many of the foundations of postwar culture had disappeared: Europe had been rebuilt and, as the EU, had become one of the world’s largest economies; the United States’ claim to global dominance was threatened; and the postwar social democratic consensus was being replaced by market-led neoliberalism. Most importantly of all, the Cold War was over, and the World Wide Web had been born. Music After The Fall considers contemporary musical composition against this changed backdrop, placing it in the context of globalization, digitization, and new media. Drawing on theories from the other arts, in particular art and architecture, it expands the definition of Western art music to include forms of composition, experimental music, sound art, and crossover work from across the spectrum, inside and beyond the concert hall. Each chapter considers a wide range of composers, performers, works, and institutions are considered critically to build up a broad and rich picture of the new music ecosystem, from North American string quartets to Lebanese improvisers, from South American electroacoustic studios to pianos in the Australian outback. A new approach to the study of contemporary music is developed that relies less on taxonomies of style and technique, and more on the comparison of different responses to common themes, among them permission, fluidity, excess, and loss.

Geometry and Physics: Volume II

2018 ◽  
Keyword(s):  
Moduli Spaces ◽  
Mirror Symmetry ◽  
Geometric Analysis ◽  
Mathematical Physics ◽  
Poisson Geometry ◽  
Special Holonomy ◽  
Low Dimensional Topology ◽  
Generalized Complex Structures ◽  
Wide Range ◽  
Low Dimensional

These volumes contain the proceedings of the conference held at Aarhus, Oxford and Madrid in September 2016 to mark the seventieth birthday of Nigel Hitchin, one of the world’s foremost geometers and Savilian Professor of Geometry at Oxford. The proceedings contain twenty-nine articles, including three by Fields medallists (Donaldson, Mori and Yau). The articles cover a wide range of topics in geometry and mathematical physics, including the following: Riemannian geometry, geometric analysis, special holonomy, integrable systems, dynamical systems, generalized complex structures, symplectic and Poisson geometry, low-dimensional topology, algebraic geometry, moduli spaces, Higgs bundles, geometric Langlands programme, mirror symmetry and string theory. These volumes will be of interest to researchers and graduate students both in geometry and mathematical physics.

Sign in / Sign up

Export Citation Format

Share Document