Estimating long term behavior of flows without trajectory integration: the infinitesimal generator approach

The long-term distributions of trajectories of a flow are described by invariant densities, i.e. fixed points of an associated transfer operator. In addition, global slowly mixing structures, such as almost-invariant sets, which partition phase space into regions that are almost dynamically disconnected, can also be identified by certain eigenfunctions of this operator. Indeed, these structures are often hard to obtain by brute-force trajectory-based analyses. In a wide variety of applications, transfer operators have proven to be very efficient tools for an analysis of the global behavior of a dynamical system. The computationally most expensive step in the construction of an approximate transfer operator is the numerical integration of many short term trajectories. In this paper, we propose to directly work with the infinitesimal generator instead of the operator, completely avoiding trajectory integration. We propose two different discretization schemes; a cell based discretization and a spectral collocation approach. Convergence can be shown in certain circumstances. We demonstrate numerically that our approach is much more efficient than the operator approach, sometimes by several orders of magnitude

Teológiai és rituális horror

Gabor M. Koltai’s essay is an excerpt from his book on the world view of Renaissance stage horror. Jacobean drama was sensitive to the changes taking place in the concepts that framed the audience’s everyday lives. The abolition of Catholic rituals had shaken confidence in familiar notions of marriage and the mourning of the dead, or in the certainty of what would happen to us after we die. John Webster’s theatre responded to these changes with dramaturgical and visual constructs similar to the Freudian notion of the ’Unheimlich’: religious ceremonies and sacraments are blurred on his stage as ghosts’ features in a horror film. Webster’s characters articulate doubts akin to the questions of Faustus and Don Juan. They regurgitate the emblems of their cultural past to fill the gaps in the fabric of death and salvation. The supernatural does not exist; it is only the work of their haunted imagination. In Calvin’s new universe, no one is safe from having their waking decisions lead to a nightmarish future

Markov-chain-inspired search for MH370

Markov-chain models are constructed for the probabilistic description of the drift of marine debris from Malaysian Airlines flight MH370. En route from Kuala Lumpur to Beijing, the MH370 mysteriously disappeared in the southeastern Indian Ocean on 8 March 2014, somewhere along the arc of the 7th ping ring around the Inmarsat-3F1 satellite position when the airplane lost contact. The models are obtained by discretizing the motion of undrogued satellite-tracked surface drifting buoys from the global historical data bank. A spectral analysis, Bayesian estimation, and the computation of most probable paths between the Inmarsat arc and confirmed airplane debris beaching sites are shown to constrain the crash site, near 25$^{\circ}$S on the Inmarsat arc.Comment: Submitted to Chao

SPORTS, EXERCISE ONLINE? THE OPINION OF SPORT MAJORS ON THE NON-ATTENDANCE TUITION

Aim of the study: The aim of our research is to map out the new aspect of life, in one section of higher education, created by the epidemiological situation, to get to know the methodics used by the teachers of the two sport science institutes (ESI, STI) in our faculty, and get to know our student's opinion on the topic. Methods: We worked with our own questionnaire, which includes the following groups of questions: demographic data, questions about the students' availability of tools, students' opinions about the requirements, communication with the instructor, the completion of the courses, changes in their own learning habits and their physical and practical preparation capabilities. The members of sample was studied at the Eötvös Loránd University PPK in Szombathely and Budapest by students majoring in sport field. Results: No difficulties were reported by our students, 90% had adequate tools. Their workload was much higher than in previous periods, which was reflected in a strong increase in time spent with studying (p <0.01). The lessons, tasks and dissertations carried out in the online learning space were a bigger challenge for the lecturers, based on the opinion of our students, the education did not seem more exciting or creative (2.8 on a 6-point scale). Opinions about the educational platforms used were evenly distributed, they did not find it difficult to navigate between the different surfaces (3.66 on a scale of 6.).Conclusion: The virtue of problem solving could be practiced in recent times. It is advisable to incorporate the experience of the recent period into the solutions of the important tasks aheadAim of the study: The aim of our research is to map out the new aspect of life, in one section of higher education, created by the epidemiological situation, to get to know the methodics used by the teachers of the two sport science institutes (ESI, STI) in our faculty, and get to know our student's opinion on the topic. Methods: We worked with our own questionnaire, which includes the following groups of questions: demographic data, questions about the students' availability of tools, students' opinions about the requirements, communication with the instructor, the completion of the courses, changes in their own learning habits and their physical and practical preparation capabilities. The members of sample was studied at the Eötvös Loránd University PPK in Szombathely and Budapest by students majoring in sport field. Results: No difficulties were reported by our students, 90% had adequate tools. Their workload was much higher than in previous periods, which was reflected in a strong increase in time spent with studying (p <0.01). The lessons, tasks and dissertations carried out in the online learning space were a bigger challenge for the lecturers, based on the opinion of our students, the education did not seem more exciting or creative (2.8 on a 6-point scale). Opinions about the educational platforms used were evenly distributed, they did not find it difficult to navigate between the different surfaces (3.66 on a scale of 6.).Conclusion: The virtue of problem solving could be practiced in recent times. It is advisable to incorporate the experience of the recent period into the solutions of the important tasks ahea

Fine-tuning the functional properties of carbon nanotubes via the interconversion of encapsulated molecules

Tweaking the properties of carbon nanotubes is a prerequisite for their practical applications. Here we demonstrate fine-tuning the electronic properties of single-wall carbon nanotubes via filling with ferrocene molecules. The evolution of the bonding and charge transfer within the tube is demonstrated via chemical reaction of the ferrocene filler ending up as secondary inner tube. The charge transfer nature is interpreted well within density functional theory. This work gives the first direct observation of a fine-tuned continuous amphoteric doping of single-wall carbon nanotubes

Electron spin resonance signal of Luttinger liquids and single-wall carbon nanotubes

A comprehensive theory of electron spin resonance (ESR) for a Luttinger liquid (LL) state of correlated metals is presented. The ESR measurables such as the signal intensity and the line-width are calculated in the framework of Luttinger liquid theory with broken spin rotational symmetry as a function of magnetic field and temperature. We obtain a significant temperature dependent homogeneous line-broadening which is related to the spin symmetry breaking and the electron-electron interaction. The result crosses over smoothly to the ESR of itinerant electrons in the non-interacting limit. These findings explain the absence of the long-sought ESR signal of itinerant electrons in single-wall carbon nanotubes when considering realistic experimental conditions.Comment: 5 pages, 1 figur

From Metastable to Coherent Sets – time-discretization schemes

Given a time-dependent stochastic process with trajectories x(t) in a space \Omega, there may be sets such that the corresponding trajectories only very rarely cross the boundaries of these sets. We can analyze such a process in terms of metastability or coherence. Metastable sets M are defined in space M \subset \Omega, coherent sets M(t) \subset \Omega are defined in space and time. Hence, if we extend the space \Omega by the time-variable t, coherent sets are metastable sets in \Omega \times [0,\infty). This relation can be exploited, because there already exist spectral algorithms for the identification of metastable sets. In this article we show that these well-established spectral algorithms (like PCCA+) also identify coherent sets of non-autonomous dynamical systems. For the identification of coherent sets, one has to compute a discretization (a matrix T) of the transfer operator of the process using a space-time-discretization scheme. The article gives an overview about different time-discretization schemes and shows their applicability in two different fields of application