366 research outputs found

    Complex systems methods characterizing nonlinear processes in the near-Earth electromagnetic environment: recent advances and open challenges

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    Learning from successful applications of methods originating in statistical mechanics, complex systems science, or information theory in one scientific field (e.g., atmospheric physics or climatology) can provide important insights or conceptual ideas for other areas (e.g., space sciences) or even stimulate new research questions and approaches. For instance, quantification and attribution of dynamical complexity in output time series of nonlinear dynamical systems is a key challenge across scientific disciplines. Especially in the field of space physics, an early and accurate detection of characteristic dissimilarity between normal and abnormal states (e.g., pre-storm activity vs. magnetic storms) has the potential to vastly improve space weather diagnosis and, consequently, the mitigation of space weather hazards. This review provides a systematic overview on existing nonlinear dynamical systems-based methodologies along with key results of their previous applications in a space physics context, which particularly illustrates how complementary modern complex systems approaches have recently shaped our understanding of nonlinear magnetospheric variability. The rising number of corresponding studies demonstrates that the multiplicity of nonlinear time series analysis methods developed during the last decades offers great potentials for uncovering relevant yet complex processes interlinking different geospace subsystems, variables and spatiotemporal scales

    The Self The Soul and The World: Affect Reason and Complexity

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    This book looks at the affective-cognitive roots of how the human mind inquires into the workings of nature and, more generally, how the mind confronts reality. Reality is an infinitely complex system, in virtue of which the mind can comprehend it only in bits and pieces, by making up interpretations of the myriads of signals received from the world by way of integrating those with information stored from the past. This constitutes a piecemeal interpretation by which we assemble our phenomenal reality. In perceiving the complex world and responding to it, the mind invokes the logic of affect and the logic of reason, the former mostly innate and implicit, and the latter generated consciously in explicit terms with reference to mind-independent relations between entities in nature. It is a strange combination of affect and reason that enables us to make decisions and inferences, --- the latter mostly of the inductive type --- thereby making possible the development of theories. Theories are our tool-kits for explaining and predicting phenomena, guiding us along in our journey in life. Theories, however, are defeasible, and need to be constantly updated, at times even radically. In this, the self and the soul are of enormous relevance. The former is the affect-based psychological engine driving all our mental processes, while the latter is the capacity of the conscious mind to examine and reconstruct the self by modulating repressed conflicts. If the soul remains inoperative, all our theories become misdirected and a rot spreads inexorably all around us

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    Lattice Boltzmann Methods for Partial Differential Equations

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    Lattice Boltzmann methods provide a robust and highly scalable numerical technique in modern computational fluid dynamics. Besides the discretization procedure, the relaxation principles form the basis of any lattice Boltzmann scheme and render the method a bottom-up approach, which obstructs its development for approximating broad classes of partial differential equations. This work introduces a novel coherent mathematical path to jointly approach the topics of constructability, stability, and limit consistency for lattice Boltzmann methods. A new constructive ansatz for lattice Boltzmann equations is introduced, which highlights the concept of relaxation in a top-down procedure starting at the targeted partial differential equation. Modular convergence proofs are used at each step to identify the key ingredients of relaxation frequencies, equilibria, and moment bases in the ansatz, which determine linear and nonlinear stability as well as consistency orders of relaxation and space-time discretization. For the latter, conventional techniques are employed and extended to determine the impact of the kinetic limit at the very foundation of lattice Boltzmann methods. To computationally analyze nonlinear stability, extensive numerical tests are enabled by combining the intrinsic parallelizability of lattice Boltzmann methods with the platform-agnostic and scalable open-source framework OpenLB. Through upscaling the number and quality of computations, large variations in the parameter spaces of classical benchmark problems are considered for the exploratory indication of methodological insights. Finally, the introduced mathematical and computational techniques are applied for the proposal and analysis of new lattice Boltzmann methods. Based on stabilized relaxation, limit consistent discretizations, and consistent temporal filters, novel numerical schemes are developed for approximating initial value problems and initial boundary value problems as well as coupled systems thereof. In particular, lattice Boltzmann methods are proposed and analyzed for temporal large eddy simulation, for simulating homogenized nonstationary fluid flow through porous media, for binary fluid flow simulations with higher order free energy models, and for the combination with Monte Carlo sampling to approximate statistical solutions of the incompressible Euler equations in three dimensions

    Colloquium: Quantum and Classical Discrete Time Crystals

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    The spontaneous breaking of time translation symmetry has led to the discovery of a new phase of matter - the discrete time crystal. Discrete time crystals exhibit rigid subharmonic oscillations, which result from a combination of many-body interactions, collective synchronization, and ergodicity breaking. This Colloquium reviews recent theoretical and experimental advances in the study of quantum and classical discrete time crystals. We focus on the breaking of ergodicity as the key to discrete time crystals and the delaying of ergodicity as the source of numerous phenomena that share many of the properties of discrete time crystals, including the AC Josephson effect, coupled map lattices, and Faraday waves. Theoretically, there exists a diverse array of strategies to stabilize time crystalline order in both closed and open systems, ranging from localization and prethermalization to dissipation and error correction. Experimentally, many-body quantum simulators provide a natural platform for investigating signatures of time crystalline order; recent work utilizing trapped ions, solid-state spin systems, and superconducting qubits will be reviewed. Finally, this Colloquium concludes by describing outstanding challenges in the field and a vision for new directions on both the experimental and theoretical fronts.Comment: 29 pages, 13 figures; commissioned review for Reviews of Modern Physic

    2018 GREAT Day Program

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    SUNY Geneseo’s Twelfth Annual GREAT Day.https://knightscholar.geneseo.edu/program-2007/1012/thumbnail.jp

    Naval Postgraduate School Academic Catalog - February 2023

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    Classifying 1D elementary cellular automata with the 0-1 test for chaos

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    We utilise the 0-1 test to automatically classify elementary cellular automata. The quantitative results of the 0-1 test reveal a number of advantages over Wolfram’s qualitative classification. For instance, while almost all rules classified as chaotic by Wolfram were confirmed as such by the 0-1 test, there were two rules which were revealed to be non-chaotic. However, their periodic nature is hidden by the high complexity of their spacetime patterns and not easy to see without looking very carefully. Comparing each rule’s chaoticity (as quantified by the 0-1 test) against its intrinsic complexity (as quantified by its Chua complexity index) also reveals a number of counter-intuitive discoveries; i.e. non-chaotic dynamics are not only found in simpler rules, but also in rules as complex as chaos
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