Fractal analysis: Annual rainfall in Chennai

The annual rainfall data of Chennai is analyzed using the Fractal Construction Technique. According to Mandelbrot the dimension of any line including nautical lines may not be Euclidean but Fractional, Mandelbrot, 1982. This fractional dimension leads to a repetitive appearance of any pattern. Climate which is usually periodic by nature can be analyzed through this technique. Efforts are on to search the fractal geometry of climate and to predict its periodicity on different temporal scales. This paper estimates the various parameters like Lyapunov exponent, Maximum Lyapunov characteristic exponent, Lyapunov time, Kaplan-Yorke dimension for the annual rainfall of Chennai.

Characteristic Times for the Fermi–Ulam Model

The mean Poincaré recurrence time as well as the Lyapunov time are measured for the Fermi–Ulam model. It is confirmed that the mean recurrence time is dependent on the size of the window chosen in the phase space where particles are allowed to return. The fractal dimension of the region is determined by the slope of the recurrence time against the size of the window and two numerical values are measured: (i) [Formula: see text] confirming normal diffusion for chaotic regions far from periodic domains and (ii) [Formula: see text] leading to anomalous diffusion measured inside islands of stability and invariant curves corresponding to regular orbits, a signature of local trapping of an ensemble of particles. The Lyapunov time is the inverse of the Lyapunov exponent. Therefore, the Lyapunov time is measured over different domains in the phase space through a direct determination of the Lyapunov exponent.

Toward Ubimus Philosophical Frameworks

We tackle the philosophical implications of post-2020 music practices. To situate our discussion, we address pending issues in current definitions of music-making. Our analysis indicates that post-2020 definitions of music should feature sonic information and events, framed through social interactions and through the material grounding of the musical activity. Ubiquitous music (ubimus) furnishes a promising playing field for the emerging aspects of creative music-thinking. New frameworks that encompass the dynamic, multimodal and situated characteristics of music while skewing an anthropocentric perspective on creativity may provide meaningful targets for ubimus research toward a new notion of musicality. Three artistic projects serve to exemplify key aspects of this proposal: Atravessamentos, Memory Tree and Lyapunov Time. We address the philosophical implications of these artistic endeavors toward the construction of ubimus philosophical frameworks.

Orbital evolution of Mars-crossing asteroids

ABSTRACT This study is an orbital analysis of the interesting Mars-crossing asteroids (MCAs), also known as Mars-crosser (MC) asteroids or Mars-crossers (MCs). We computed that after 100 million years (Myr), approximately 66 ${{\ \rm per\ cent}}$ of all known MCs are ejected out of the Solar System by collision with the Sun, the planets, Ceres, Pallas, Vesta, or Hygiea. The rate of MC migration is high. Thus, this population of MCs would be supplied by just as many asteroids from outside the Solar System. We estimated the rate at which near-Earth objects were created from MCs throughout a 100 Myr period, with Atiras accounting for nearly 3 ${{\ \rm per\ cent}}$ of these objects, over 2 ${{\ \rm per\ cent}}$ were Atens, nearly 7.5 ${{\ \rm per\ cent}}$ were Apollos, approximately 9${{\ \rm per\ cent}}$ were Amors, and nearly 0.4 ${{\ \rm per\ cent}}$ became Centaurs. These results were calculated with 10 000 yr output intervals. Furthermore, 0.028${{\ \rm per\ cent}}$ of all the starting MCs were in retrograde orbits for at least 10 000 yr. We found that majority of the remaining MCs have migrated into the region of three asteroid families: Phocaea, Hungaria, and Flora. We calculated a small but significant influence of Ceres, Pallas, Vesta, and Hygiea on the orbital evolution of the MCs. From the AstDys catalogue, we found that the largest number of studied numbered MCs have their Lyapunov time (LT) in the range 2–4 kyr. Using the orbfit software, we computed the LT of selected MCs in retrograde orbits, and obtained an LT of between 540 yr (asteroid 2016 DR1) and 71 000 yr (asteroid 42887 1999 RV155).

Machine Learning of committor functions for predicting high impact climate events

<p>There is a growing interest in the climate community to improve the prediction of high impact climate events, for instance ENSO (El-Ni\~no--Southern Oscillation) or extreme events, using a combination of model and observation data. In this talk we present a machine learning approach for predicting the committor function, the relevant concept.<span> </span></p><p>Because the dynamics of the climate system is chaotic, one usually distinguishes between time scales much shorter than a Lyapunov time for which a deterministic weather forecast is relevant, and time scales much longer than a mixing times beyond which any deterministic forecast is irrelevant and only climate averaged or probabilistic quantities can be predicted. However, for most applications, the largest interest is for intermediate time scales for which some information, more precise than the climate averages, might be predicted, but for which a deterministic forecast is not relevant. We call this range of time scales \it{the predictability margin}. We stress in this talk that the prediction problem at the predictability margin is of a probabilistic nature. Indeed, such time scales might typically be of the order of the Lyapunov time scale or larger, where errors on the initial condition and model errors limit our ability to compute deterministically the evolution. In this talk we explain that, in a dynamical context, the relevant quantity for predicting a future event at the predictability margin is a committor function. A committor function is the probability that an event will occur or not in the future, as a function of the current state of the system.<span> </span></p><p>We compute and discuss the committor function from data, either through a direct approach or through a machine learning approach using neural networks. We discuss two examples: a) the computation of the Jin and Timmerman model, a low dimensional model proposed to explain the decadal amplitude changes of El-Ni\~no, b) the computation of committor function for extreme heat waves. We compare several machine learning approaches, using neural network or using kernel-based analogue methods.</p><p>From the point of view of the climate extremes, our main conclusion is that one should generically distinguish between states with either intrinsic predictability or intrinsic unpredictability. This predictability concept is markedly different from the deterministic unpredictability arising because of chaotic dynamics and exponential sensivity to initial conditions.<span> </span></p>

The potentially hazardous NEA 2001 BB16

We computed the impact solutions of the potentially dangerous Near Earth Asteroid (NEA) 2001 BB16 based on 47 optical observations from January 20.08316 UTC, 2001, through February 09.15740 UTC, 2016, and one radar observation from January 19.90347 UTC, 2016. We used two methods to sample the starting Line of Variation (LOV). First method, called thereafter LOV1, with the uniform sampling of the LOV parameter, out to LOV = 5 computing 3000 virtual asteroids (VAs) on both sides of the LOV, which gives 6001 VAs and propagated their orbits to JD2525000.5 TDT=February 12, 2201. We computed the non-gravitational parameterA2=(34.55±7.38)·10–14 au/d2 for nominal orbit of 2001 BB16 and possible impacts with the Earth until 2201. For potential impact in 2195 we find A2=20.0·10−14 au/d2. With a positive value of A2, 2001 BB16 can be prograde rotator. Moreover, we computed Lyapunov Time (LT) for 2001 BB16, which for all VAs, has a mean value of about 25 y. We showed that impact solutions, including the calculated probability of a possible collision of a 2001 BB16 asteroid with the Earth depends on how to calculate and take into account the appropriate gravitational model, including the number of perturbing massive asteroids. In some complicated cases, it may depend also on the number of clones calculated for a given sigma LOV1. The second method of computing the impact solutions, called thereafter LOV2, is based on a non-uniformly sampling of the LOV. We showed that different methods of sampling the LOV can give different impact solutions, but all computed dates of possible impacts of the asteroid 2001 BB16 with the Earth occur in accordance at the end of the 22nd century.

N-body chaos, phase-space transport and relaxation in numerical simulations

Using direct N-body simulations of self-gravitating systems we study the dependence of dynamical chaos on the system size N. We find that the N-body chaos quantified in terms of the largest Lyapunov exponent Λmax decreases with N. The values of its inverse (the so-called Lyapunov time tλ) are found to be smaller than the two-body collisional relaxation time but larger than the typical violent relaxation time, thus suggesting the existence of another collective time scale connected to many-body chaos.