Manifestation Of Chaos Research Articles

The Order and Chaos in Human Relationships: Objective Grounds and the Ways of Harmonization

Purpose. This article aims to provide a philosophical analysis of disharmonious relations between people in society, to reveal the causes of existing conflicts and to find ways to reduce the manifestations of chaos in human relations. Theoretical basis of the article is socio-cultural anthropology, the principles of the unity of the historical and logical, the ascent from the abstract to the concrete, the unity of analysis and synthesis. To solve the tasks set, authors also used the principles of objectivity, systematicity, and comprehensive development. Originality. The article goes beyond one-sided views on the relationship between people in society, reveals the causes of existing conflicts from a philosophical perspective and searches for ways to reduce chaosogenic manifestations in society. It is assumed that chaos and order in human relations arise not only due to the contradictory interaction between the fundamental components of the Universe – matter and energy, but also due to a lack of understanding of the laws of information use. Therefore, without the discovery and rational use of the basic laws and principles governing the functioning of information in the Universe, it is impossible to overcome chaos in human relations. Conclusions. Given the profound impact of information on human relations, it is possible to help reduce the manifestations of chaos in human relationships. The proper handling of information, along with the rational use of matter and energy, is crucial for overcoming the current state of disharmony and creating a more favourable and orderly future for humanity. Thus, the vector of harmonisation of human relations lies in the plane of comprehensive knowledge of mass-energy and information processes occurring in the Universe, focusing not on subjective, ill-considered short-term goals, but submitting to them for consistent inclusion in these processes.

A Whirling Tempest

Abstract In comparison to research on the Psalms, Isaiah, and other prophetic books, the mythic portrayal of YHWH’s combat of chaotic opposition has received little attention in the study of Jeremiah. By drawing up a holistic profile of Jeremiah’s Chaoskampf, my article demonstrates that this theme is more central to this prophetic book than the scholarly landscape might suggest. Divine mastery of various manifestations of chaos plays a key role in how the book presents YHWH’s work in creation (past), YHWH’s judgment on Israel (present), and YHWH’s defeat of Israel’s enemies and the people’s restoration (future). In conversation with myth and trauma theory, I will argue that the tension between YHWH’s unleashing and quenching of chaotic forces is rooted in the flexible character of the combat myth and that it contributes to the book’s efforts of explaining the crisis of 587 BCE.

A NEW TYPE OF DETERMINISTIC CHAOS: DETERMINISTIC CHAOS OF THE SECOND KIND

Abstract. Currently, the phenomena of deterministic (Dynamic) chaos are widely used in science and technology. Therefore, now the urgent task is to study new phenomena and new manifestations of deterministic chaos. This paper examines a fundamentally new manifestation of deterministic chaos (Deterministic chaos of the second kind). In this regard, previously known manifestations of deterministic chaos should be called manifestations of chaos of the first kind (The previously known type of deterministic chaos, in our terminology, is chaos of the first kind). Deterministic chaos of the first kind is chaos that is directly related to the deterministic - chaotic behavior of the dynamic variables of a given dynamic system. At the same time, our work examines the characteristic features of deterministic chaos of the first kind and methods for generating such chaos. In our work, we considered a fundamentally different type of manifestation of dynamic chaos, namely deterministic chaos of the second kind. Deterministic chaos of the second kind is not directly related to the deterministic chaotic behavior of the dynamic variables of a dynamic system and can only exist in characteristics that are not directly related to the dynamic variables. That is, dynamic chaos of the second kind arises only in second-order manifestations: For example, in the Fourier spectrum. In a more general case, this could be any other type of spectrum (Not Fourier) and even another characteristic different from the spectrum. The paper provides two examples of deterministic chaos of the second kind. The work also proposes a general technique for generating time series demonstrating deterministic chaos of the second kind*. It is very important that dynamic chaos in the examples given in this work manifests itself not in the time series themselves (Which are completely random) but in the Fourier spectrum of these time series. Thus, the original series itself (The original signal itself) can be random, but at the same time, the spectrum of this series, if considered as another time series, can exhibit deterministic chaotic behavior. Thus, for the first time we were able to build a bridge between completely random systems and deterministic chaotic systems. That is, in our work we were the first to show that the same system can be considered both random (From the point of view of the behavior of its variables) and at the same time as deterministic-chaotic (From the point of view of its spectrum or other similar characteristics). Goal of the work. Study of a newtype of deterministic chaos discovered by the authors (Deterministic chaos of the second kind) and the study of its properties and methods for generating this type of chaos.

Some Remarks on the Significances of Elimination the Manifestations of Chaos and Symbols of Evil in the Scenes of the Greek and Roman Periods

Some Remarks on the Significances of Elimination the Manifestations of Chaos and Symbols of Evil in the Scenes of the Greek and Roman Periods

Some Remarks on the Significances of Elimination the Manifestations of Chaos and Symbols of Evil in the Scenes of the Greek and Roman Periods

Some Remarks on the Significances of Elimination the Manifestations of Chaos and Symbols of Evil in the Scenes of the Greek and Roman Periods

Some Remarks on the Significances of Elimination the Manifestations of Chaos and Symbols of Evil in the Scenes of the Greek and Roman Periods

Some Remarks on the Significances of Elimination the Manifestations of Chaos and Symbols of Evil in the Scenes of the Greek and Roman Periods

Claiming the Wilderness in Late Roman Gaul

The enthusiasm with which Christian authors of late Roman Gaul adopted the ideal of desert asceticism is well known. There is also general agreement that the appeal of the wilderness was, for many of these individuals, more rhetorical than actual. What has not been fully acknowledged is the extent to which their attitudes to wilderness were influenced by classical thought in addition to biblical and hagiographical literature. To the educated classical mind, the cosmos was built on a fundamental dichotomy between order and chaos that permeated the physical and natural world. Wilderness, in its raw natural form, was a manifestation of chaos, while human civilization reflected the principles of order. The argument of this article is that this dichotomy, thanks to a tradition of classical education, helped structure the response of educated Gallo-Romans to the Christian desert tradition as its ideals spread to the west. Despite the appeal of monastic asceticism per se, its association with the desert provoked suspicion among those who had been trained to regard wilderness as the antithesis of civilization and culture. It is, however, possible to detect an evolution in attitudes over the last century of Roman rule in Gaul, as successive generations responded to social and political transformations and, drawing on both Christian and classical tradition, developed new ways of relating to the natural world.

Reduced Variations in Earth’s and Mars’ Orbital Inclination and Earth’s Obliquity from 58 to 48 Myr ago due to Solar System Chaos

The dynamical evolution of the solar system is chaotic with a Lyapunov time of only ∼5 Myr for the inner planets. Due to the chaos it is fundamentally impossible to accurately predict the solar system’s orbital evolution beyond ∼50 Myr based on present astronomical observations. We have recently developed a method to overcome the problem by using the geologic record to constrain astronomical solutions in the past. Our resulting optimal astronomical solution (called ZB18a) shows exceptional agreement with the geologic record to ∼58 Ma (Myr ago) and a characteristic resonance transition around 50 Ma. Here we show that ZB18a and integration of Earth’s and Mars’ spin vector based on ZB18a yield reduced variations in Earth’s and Mars’ orbital inclination and Earth’s obliquity (axial tilt) from ∼58 to ∼48 Ma—the latter being consistent with paleoclimate records. The changes in the obliquities have important implications for the climate histories of Earth and Mars. We provide a detailed analysis of solar system frequencies (g and s modes) and show that the shifts in the variation in Earth’s and Mars’ orbital inclination and obliquity around 48 Ma are associated with the resonance transition and caused by changes in the contributions to the superposition of s modes, plus g–s mode interactions in the inner solar system. The g–s mode interactions and the resonance transition (consistent with geologic data) are unequivocal manifestations of chaos. Dynamical chaos in the solar system hence not only affects its orbital properties but also the long-term evolution of planetary climate through eccentricity and the link between inclination and axial tilt.

Using correlation diagrams to study the vibrational spectrum of highly nonlinear floppy molecules: The K-CN case

The correlation diagrams of vibrational energy levels considering the Planck constant as a variable parameter have proven as a very useful tool to study vibrational molecular states, and more specifically in relation to the quantum manifestations of chaos in such dynamical systems. In this paper, we consider the highly nonlinear K-CN molecule, showing how the regular classical structures, i.e., Kolmogorov-Arnold-Moser tori, existing in the mixed classical phase space appear in the quantum levels correlation diagram as emerging diabatic states, something that remains hidden when only the actual value of the Planck constant is considered. Additionally, a quantum transition from order to chaos is unveiled with the aid of these correlation diagrams, where it appears as a frontier of scarred functions.

Older Adults' Narratives of Seeking Mental Health Treatment: Making Sense of Mental Health Challenges and "Muddling Through" to Care.

Older adults who experience challenges related to mental health are unlikely to seek professional help. The voices of older adults who have navigated through mental health issues and systems of care to arrive at psychological treatment are less well understood. We conducted individual interviews with 15 adults aged 61 to 86 who sought psychological treatment. Interviews were audio-recorded, transcribed, and analyzed using narrative methods. We identified several main storylines that describe the meaning-making and treatment-seeking journeys of older adults: resistance to being labeled with mental health problems (telling stories of resistance, defining mental health issues in mysterious and uncontrollable terms, and experiencing internal role conflict); muddling through the help-seeking process (manifestations of chaos and system-level barriers); and emotional reactions to psychological treatment (hope, fear, and mistrust). Findings add to the literature base in the area of narrative gerontology, and highlight the complex experiences that older adults face when seeking psychological treatment.

Manifestations of chaos in relativistic quantum systems - A study based on out-of-time-order correlator

Previous work in the field of relativistic quantum chaos has revealed initial evidence that the manifestations of classical chaos in relativistic quantum systems tend to be weakened as compared with those in nonrelativistic quantum systems. To place this finding on a firmer ground, we investigate the relativistic quantum fingerprints of classical chaos using the out-of-time-order correlator (OTOC). OTOC has recently been applied to a number of fields in physics and it holds special promises for the field of quantum chaos, but existing work focused exclusively on nonrelativistic quantum systems. Calculating and analyzing OTOC for relativistic quantum billiard systems described by the massless Dirac equation, we find that the signatures of classical chaos are indeed characteristically less pronounced in relativistic than in nonrelativistic quantum systems. The finding is substantiated by studying four different aspects of OTOC. Firstly, in the energy eigenspace, in the short time regime there is a complete lack of any signature of chaos associated with the evolution of OTOC in the Dirac billiard due to the relativistic quantum phenomenon of Zitterbewegung, in contrast to nonrelativistic quantum billiard systems where chaos leaves behind a quite distinct signature. Secondly, weakening of the relativistic quantum manifestations of classical chaos occurs in the long time regime as well. Thirdly, evolution of the wave packet based OTOC also reveals that the fingerprints of chaos are much less pronounced in the Dirac billiard systems as compared with the Schrödinger billiards. Fourthly, the level spacing statistics of the OTOC operators in systems with classically integrable and chaotic dynamics, which are characteristically distinct in the Schrödinger billiards, bear a strong similarity in the Dirac billiards, indicating again the dwindling effects of chaos. The OTOC based results suggest that the impacts of classical chaos are generally weaker in relativistic than in nonrelativistic quantum systems, a fundamental issue that warrants further investigation.

Quasibound states in a triple Gaussian potential.

We derive the transmission probabilities and delay times, and identify quasibound state structures in an open quantum system consisting of three Gaussian potential energy peaks, a system whose classical scattering dynamics we show to be chaotic. Such open quantum systems can serve as models for nanoscale quantum devices and their wave dynamics are similar to electromagnetic wave dynamics in optical microcavities. We use a quantum web to determine energy regimes for which the system exhibits the quantum manifestations of chaos, and we show that the classical scattering dynamics contains a significant amount of chaos. We also derive an exact expression for the non-Hermitian Hamiltonian whose eigenvalues give quasibound state energies and lifetimes of the system.

Dynamic localization in walking droplets?

In this paper we explore the possibility of localization in the dynamics of walking droplets on a vertically vibrated liquid surface in the presence of a chaotic external potential and the limit of low memory, i.e. considering the effect of the wave generated only in the last bounce. Taking into account the similarity existing between this macroscopic system and de Broglie?s pilot wave theory this study aims at establishing manifestations of chaos in the later theory.

Signatures of chaos in the Brillouin zone.

When the classical dynamics of a particle in a finite two-dimensional billiard undergoes a transition to chaos, the quantum dynamics of the particle also shows manifestations of chaos in the form of scarring of wave functions and changes in energy level spacing distributions. If we "tile" an infinite plane with such billiards, we find that the Bloch states on the lattice undergo avoided crossings, energy level spacing statistics change from Poisson-like to Wigner-like, and energy sheets of the Brillouin zone begin to "mix" as the classical dynamics of the billiard changes from regular to chaotic behavior.

Generalized Lyapunov exponent as a unified characterization of dynamical instabilities.

The Lyapunov exponent characterizes an exponential growth rate of the difference of nearby orbits. A positive Lyapunov exponent (exponential dynamical instability) is a manifestation of chaos. Here, we propose the Lyapunov pair, which is based on the generalized Lyapunov exponent, as a unified characterization of nonexponential and exponential dynamical instabilities in one-dimensional maps. Chaos is classified into three different types, i.e., superexponential, exponential, and subexponential chaos. Using one-dimensional maps, we demonstrate superexponential and subexponential chaos and quantify the dynamical instabilities by the Lyapunov pair. In subexponential chaos, we show superweak chaos, which means that the growth of the difference of nearby orbits is slower than a stretched exponential growth. The scaling of the growth is analytically studied by a recently developed theory of a continuous accumulation process, which is related to infinite ergodic theory.

Relativistic quantum tunneling of a Dirac fermion in nonhyperbolic chaotic systems

Nonhyperbolicity, as characterized by the coexistence of Kolmogorov-Arnold-Moser (KAM) tori and chaos in the phase space, is generic in classical Hamiltonian systems. An open but fundamental question in physics concerns the relativistic quantum manifestations of nonhyperbolic dynamics. We choose the mushroom billiard that has been mathematically proven to be nonhyperbolic, and study the resonant tunneling dynamics of a massless Dirac fermion. We find that the tunneling rate as a function of the energy exhibits a striking ``clustering'' phenomenon, where the majority of the values of the rate concentrate on a narrow region, as a result of the chaos component in the classical phase space. Relatively few values of the tunneling rate, however, spread outside the clustering region due to the integrable component. Resonant tunneling of electrons in nonhyperbolic chaotic graphene systems exhibits a similar behavior. To understand these numerical results, we develop a theoretical framework by combining analytic solutions of the Dirac equation in certain integrable domains and physical intuitions gained from current understanding of the quantum manifestations of chaos. In particular, we employ a theoretical formalism based on the concept of self-energies to calculate the tunneling rate and analytically solve the Dirac equation in one dimension as well as in two dimensions for a circular-ring-type of tunneling systems exhibiting integrable dynamics in the classical limit. Because relatively few and distinct classical periodic orbits are present in the integrable component, the corresponding relativistic quantum states can have drastically different behaviors, leading to a wide spread in the values of the tunneling rate in the energy-rate plane. In contrast, the chaotic component has embedded within itself an infinite number of unstable periodic orbits, which provide far more quantum states for tunneling. Due to the nature of chaos, these states are characteristically similar, leading to clustering of the values of the tunneling rate in a narrow band. The appealing characteristic of our work is a demonstration and physical understanding of the ``mixed'' role played by chaos and regular dynamics in shaping relativistic quantum tunneling dynamics.

Manifestation of resonance-related chaos in coupled Josephson junctions

Manifestation of chaos in the temporal dependence of the electric charge is demonstrated through the calculation of the maximal Lyapunov exponent, phase–charge and charge–charge Lissajous diagrams and correlation functions. It is found that the number of junctions in the stack strongly influences the fine structure in the current–voltage characteristics and a strong proximity effect results from the nonperiodic boundary conditions. The observed resonance-related chaos exhibits intermittency. The criteria for a breakpoint region with no chaos are obtained. Such criteria could clarify recent experimental observations of variations in the power output from intrinsic Josephson junctions in high temperature superconductors.

Deterministic chaos and historical geomorphology: A review and look forward

The study of nonlinear dynamics in geomorphology has been dominated by analytical techniques derived largely from other fields. Ultimately, however, confronting nonlinear complexity requires problematizing from within a geomorphological context. This paper focuses on deterministic chaos. The major classes of techniques for detecting chaos in geomorphic systems are reviewed. While the long time series most amenable to traditional methods of chaos detection are only occasionally available to geomorphologists, there are methods for detecting chaos in spatial data, including qualitative and categorical data. Many of these are similar to, or are adaptations of, familiar techniques for partitioning within- and between-unit variation, and for identifying elementary uniform landscape units. The manifestations of chaos in landforms and landscapes take the form of divergent vs. convergent evolution (increasing vs. decreasing irregularity), disproportionality vs. proportionality of response to perturbations or initial variations, and the (lack of) geographical consistency or commonality of response. These also serve as criteria for distinguishing between achievement of a new steady-state and unstable divergence in interpreting geomorphic changes. Study of nonlinear dynamics in earth science need not be dominated by theoreticians and modellers, as complex nonlinear behaviors can be identified and diagnosed using the types of data, observations, and methods typically available to geomorphologists. Even more important is the need to further inform the study of nonlinear dynamics on the basis of field-based geomorphology.

Chaotic signature in the motion of coupled carbon nanotube oscillators

The motion of coupled oscillators based on multiwalled carbon nanotubes is studied usingrigid-body dynamics simulations. The results show the existence of chaotic and regularbehaviours for a given total energy, indicating the manifestation of chaos in nanoscaledmechanical systems based on carbon nanotube oscillators. Different regular motions areobserved for different total energies, and they can be obtained by appropriatelychoosing the initial conditions. This possibility can allow the construction ofmulti-functional nano-devices based on multiwalled carbon nanotube oscillators.

A Chaotic Mixer for Magnetic Bead-Based Micro Cell Sorter

An efficient magnetic force driven mixer with simple configuration is designed, fabricated, and tested. It is designed to facilitate the mixing of magnetic beads and biomolecules in a microchannel, where mixing is unavoidably inefficient due to its low Reynolds number. With appropriate temporal variations of the force field, chaotic mixing is achieved, hence the mixing becomes effective. The mixing device consists of embedded microconductors as a magnetic field source and a microchannel that guides the streams of working fluid. It is demonstrated that a pair of integrated micro conductors provides a local magnetic field strong enough to attract nearby magnetic beads. Mixing of magnetic beads is accomplished by applying a time-dependent control signal to a row of conductors, at the Reynolds number of as low as 10/sup -2/. Two-dimensional numerical simulation has been performed to design the configuration of the channel and electrodes, which creates chaotic motion of beads. It is found that a simple two-dimensional serpentine channel geometry with the transverse electrodes is able to create the stretching and folding of material lines, which is a manifestation of chaos. The mixing pattern predicted by the simulation has been confirmed by both flow visualization and PTV (particle tracking velocimetry) in the chaotic mixer fabricated, which should greatly increase the attachment of beads onto the target biomolecules. The optimum frequency of applied control signal is searched by evaluating the Lyapunov exponent in both numerical and experimental particle tracking. It is found that the range of optimum Strouhal number is 5<St<12, which is defined by the channel width and the mean velocity.