13 research outputs found
OBLIQUE MAGNETIC FIELDS AND THE ROLE OF FRAME DRAGGING NEAR ROTATING BLACK HOLE
Magnetic null points can develop near the ergosphere boundary of a rotating black hole by the combined effects of strong gravitational field and the frame-dragging mechanism. The induced electric component does not vanish in the magnetic null and an efficient process of particle acceleration can occur in its immediate vicinity. Furthermore, the effect of imposed (weak) magnetic field can trigger an onset of chaos in the motion of electrically charged particles. The model set-up appears to be relevant for low-accretion-rate nuclei of some galaxies which exhibit episodic accretion events (such as the Milky Way's supermassive black hole) embedded in a large-scale magnetic field of external origin with respect to the central black hole. In this contribution we summarise recent results and we give an outlook for future work with the focus on the role of gravito-magnetic effects caused by rotation of the black hole
Entropy in Dynamic Systems
In order to measure and quantify the complex behavior of real-world systems, either novel mathematical approaches or modifications of classical ones are required to precisely predict, monitor, and control complicated chaotic and stochastic processes. Though the term of entropy comes from Greek and emphasizes its analogy to energy, today, it has wandered to different branches of pure and applied sciences and is understood in a rather rough way, with emphasis placed on the transition from regular to chaotic states, stochastic and deterministic disorder, and uniform and non-uniform distribution or decay of diversity. This collection of papers addresses the notion of entropy in a very broad sense. The presented manuscripts follow from different branches of mathematical/physical sciences, natural/social sciences, and engineering-oriented sciences with emphasis placed on the complexity of dynamical systems. Topics like timing chaos and spatiotemporal chaos, bifurcation, synchronization and anti-synchronization, stability, lumped mass and continuous mechanical systems modeling, novel nonlinear phenomena, and resonances are discussed
Obtención de funciones multivariables para el estudio generalizado de la estabilidad y estabilidad asintótica de los puntos de equilibrio de un sistema autónomo no lineal, en el Departamento de Física – UNJBG en el año 2013
El propósito de esta tesis, es determinar la estabilidad y la estabilidad asintótica de los puntos de equilibrio de los sistemas autónomos no lineales, ya que no teníamos hasta ahora de ningún medio para establecer la estabilidad, salvo que hallemos efectivamente todas las soluciones del sistema, lo que puede resultar difícil si no imposible. Se investigó que la estabilidad y estabilidad asintótica de los puntos de equilibrio de un sistema autónomo no lineal es posible determinarlo por medio de las propiedades de una función de Liapunov. La función de Liapunov es una función real de variable vectorial que en un punto de equilibrio se anula, y tiene un mínimo local estricto. Además, la función decrece a lo largo de la solución del sistema autónomo no lineal. Finalmente, la idea central es detectar estabilidad para un sistema autónomo no lineal por medio de las propiedades de una función, denominada Liapunov y esto se hace sin conocer las soluciones del sistema, solo la función.Tesi
Chaos and Relaxation in Classical and Quantum Spin Systems
The problems of chaos and relaxation have a fundamental importance in the study of many-body classical and quantum systems. We investigate some of the issues related to these problems numerically in classical and quantum spin systems. New results reported in this thesis include: (i) A remarkably simple algorithm for discriminating chaotic from nonchaotic behavior in classical systems using a time series of one macroscopic observable. The effectiveness of this algorithm stems from the qualitative differences in the power spectra of chaotic and nonchaotic systems. (ii) A modified version of the Onsager regression relation applicable to pure quantum states. (iii) An efficient algorithm for computing the infinitetemperature time correlation functions in systems with large Hilbert spaces. (iv) Absence of exponential sensitivity to small perturbations in macroscopic nonintegrable systems of spins 1/2 . Such a behavior is contrasted with the exponential sensitivity to small perturbations in chaotic classical spin systems. (v) Accurate numerical investigations of free induction decay and spin diffusion in certain spin lattices. The consequences of these results have implications for the foundations of statistical mechanics or practical problems such as computing the long-time behavior of the free induction decay in solids
Diffusive models and chaos indicators for non-linear betatron motion in circular hadron accelerators
Understanding the complex dynamics of beam-halo formation and evolution in circular particle accelerators is crucial for the design of current and future rings, particularly those utilizing superconducting magnets such as the CERN Large Hadron Collider (LHC), its luminosity upgrade HL-LHC, and the proposed Future Circular Hadron Collider (FCC-hh).
A recent diffusive framework, which describes the evolution of the beam distribution by means of a Fokker-Planck equation, with diffusion coefficient derived from the Nekhoroshev theorem, has been proposed to describe the long-term behaviour of beam dynamics and particle losses.
In this thesis, we discuss the theoretical foundations of this framework, and propose the implementation of an original measurement protocol based on collimator scans in view of measuring the Nekhoroshev-like diffusive coefficient by means of beam loss data.
The available LHC collimator scan data, unfortunately collected without the proposed measurement protocol, have been successfully analysed using the proposed framework. This approach is also applied to datasets from detailed measurements of the impact on the beam losses of so-called long-range beam-beam compensators also at the LHC.
Furthermore, dynamic indicators have been studied as a tool for exploring the phase-space properties of realistic accelerator lattices in single-particle tracking simulations.
By first examining the classification performance of known and new indicators in detecting the chaotic character of initial conditions for a modulated Hénon map and then applying this knowledge to study the properties of realistic accelerator lattices, we tried to identify a connection between the presence of chaotic regions in the phase space and Nekhoroshev-like diffusive behaviour, providing new tools to the accelerator physics community
15th Conference on Dynamical Systems Theory and Applications DSTA 2019 ABSTRACTS
From Preface: This is the fifteen time when the conference „Dynamical Systems – Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and the Ministry of Science and Higher Education. It is a great pleasure that our invitation has been accepted by so many people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to
participate in the conference for the first time. With proud and satisfaction we welcome nearly 255 persons from 47 countries all over the world. They decided to share the results of their research and many years experiences in the discipline of dynamical systems by submitting many very interesting papers. This booklet contains a collection of 338 abstracts, which have gained the acceptance of referees and have been qualified for publication in the conference edited books.Technical editor and cover design: Kaźmierczak, MarekCover design: Ogińska, Ewelina; Kaźmierczak, Mare
References, Appendices & All Parts Merged
Includes: Appendix MA: Selected Mathematical Formulas; Appendix CA: Selected Physical Constants; References; EGP merged file (all parts, appendices, and references)https://commons.library.stonybrook.edu/egp/1007/thumbnail.jp