Dynamics of a small neutrally buoyant sphere in a fluid and targeting in Hamiltonian systems

We show that, even in the most favorable case, the motion of a small spherical tracer suspended in a fluid of the same density may differ from the corresponding motion of an ideal passive particle. We demonstrate furthermore how its dynamics may be applied to target trajectories in Hamiltonian systems.Comment: See home page http://lec.ugr.es/~julya

Aquifer recharge in the Piedmont Alpine zone: Historical trends and future scenarios

The spatial and temporal variability of air temperature, precipitation, actual evapotranspiration (AET) and their related water balance components, as well as their responses to anthropogenic climate change, provide fundamental information for an effective management of water resources and for a proactive involvement of users and stakeholders, in order to develop and apply adaptation and mitigation strategies at the local level. In this study, using an interdisciplinary research approach tailored to water management needs, we evaluate the past, present and future quantity of water potentially available for drinking supply in the water catchments feeding the about 2.3 million inhabitants of the Turin metropolitan area (the former Province of Turin, north-western Italy), considering climatologies at the quarterly and yearly timescales. Observed daily maximum surface air temperature and precipitation data from 1959 to 2017 were analysed to assess historical trends, their significance and the possible cross-correlations between the water balance components. Regional climate model (RCM) simulations from a small ensemble were analysed to provide mid-century projections of the difference between precipitation and AET for the area of interest in the future CMIP5 scenarios RCP4.5 (stabilization) and RCP8.5 (business as usual). Temporal and spatial variations in recharge were approximated with variations of drainage. The impact of irrigation, and of snowpack variability, on the latter was also assessed. The other terms of water balance were disregarded because they are affected by higher uncertainty. The analysis over the historical period indicated that the driest area of the study region displayed significant negative annual (and spring) trends of both precipitation and drainage. Results from field experiments were used to model irrigation, and we found that relatively wetter watersheds in the northern and in the southern parts behave differently, with a significant increase of AET due to irrigation. The analysis of future projections suggested almost stationary conditions for annual data. Regarding quarterly data, a slight decrease in summer drainage was found in three out of five models in both emission scenarios. The RCM ensemble exhibits a large spread in the representation of the future drainage trends. The large interannual variability of precipitation was also quantified and identified as a relevant risk factor for water management, expected to play a major role also in future decades

Sensitivity of snow models to the accuracy of meteorological forcings in mountain environments

Snow models are usually evaluated at sites providing high-quality meteorological data, so that the uncertainty in the meteorological input data can be neglected when assessing model performances. However, high-quality input data are rarely available in mountain areas and, in practical applications, the meteorological forcing used to drive snow models is typically derived from spatial interpolation of the available in situ data or from reanalyses, whose accuracy can be considerably lower. In order to fully characterize the performances of a snow model, the model sensitivity to errors in the input data should be quantified. In this study we test the ability of six snow models to reproduce snow water equivalent, snow density and snow depth when they are forced by meteorological input data with gradually lower accuracy. The SNOWPACK, GEOTOP, HTESSEL, UTOPIA, SMASH and S3M snow models are forced, first, with high-quality measurements performed at the experimental site of Torgnon, located at 2160ma.s.l. in the Italian Alps (control run). Then, the models are forced by data at gradually lower temporal and/or spatial resolution, obtained by (i) sampling the original Torgnon 30 min time series at 3, 6, and 12 h, (ii) spatially interpolating neighbouring in situ station measurements and (iii) extracting information from GLDAS, ERA5 and ERA-Interim reanalyses at the grid point closest to the Torgnon site. Since the selected models are characterized by different degrees of complexity, from highly sophisticated multi-layer snow models to simple, empirical, single-layer snow schemes, we also discuss the results of these experiments in relation to the model complexity. The results show that, when forced by accurate 30 min resolution weather station data, the single-layer, intermediatecomplexity snow models HTESSEL and UTOPIA provide similar skills to the more sophisticated multi-layer model SNOWPACK, and these three models show better agreement with observations and more robust performances over different seasons compared to the lower-complexity models SMASH and S3M. All models forced by 3-hourly data provide similar skills to the control run, while the use of 6- A nd 12-hourly temporal resolution forcings may lead to a reduction in model performances if the incoming shortwave radiation is not properly represented. The SMASH model generally shows low sensitivity to the temporal degradation of the input data. Spatially interpolated data from neighbouring stations and reanalyses are found to be adequate forcings, provided that temperature and precipitation variables are not affected by large biases over the considered period. However, a simple bias-adjustment technique applied to ERA-Interim temperatures allowed all models to achieve similar performances to the control run. Regardless of their complexity, all models show weaknesses in the representation of the snow density

Chaos or Noise - Difficulties of a Distinction

In experiments, the dynamical behavior of systems is reflected in time series. Due to the finiteness of the observational data set it is not possible to reconstruct the invariant measure up to arbitrary fine resolution and arbitrary high embedding dimension. These restrictions limit our ability to distinguish between signals generated by different systems, such as regular, chaotic or stochastic ones, when analyzed from a time series point of view. We propose to classify the signal behavior, without referring to any specific model, as stochastic or deterministic on a certain scale of the resolution $\epsilon$, according to the dependence of the $(\epsilon,\tau)$-entropy, $h(\epsilon, \tau)$, and of the finite size Lyapunov exponent, $\lambda(\epsilon)$, on $\epsilon$.Comment: 24 pages RevTeX, 9 eps figures included, two references added, minor corrections, one section has been split in two (submitted to PRE

Signature of chaos in gravitational waves from a spinning particle

A spinning test particle around a Schwarzschild black hole shows a chaotic behavior, if its spin is larger than a critical value. We discuss whether or not some peculiar signature of chaos appears in the gravitational waves emitted from such a system. Calculating the emitted gravitational waves by use of the quadrupole formula, we find that the energy emission rate of gravitational waves for a chaotic orbit is about 10 times larger than that for a circular orbit, but the same enhancement is also obtained by a regular "elliptic" orbit. A chaotic motion is not always enhance the energy emission rate maximally. As for the energy spectra of the gravitational waves, we find some characteristic feature for a chaotic orbit. It may tell us how to find out a chaotic behavior of the system. Such a peculiar behavior, if it will be found, may also provide us some additional informations to determine parameters of a system such as a spin.Comment: 14 pages, LaTeX, to appear in Phys. Rev.

Fractals vs. halos: Asymptotic scaling without fractal properties

Precise analyses of the statistical and scaling properties of galaxy distribution are essential to elucidate the large-scale structure of the universe. Given the ongoing debate on its statistical features, the development of statistical tools permitting to discriminate accurately different spatial patterns is highly desiderable. This is specially the case when non-fractal distributions have power law two-point correlation functions, which are usually signatures of fractal properties. Here we review some possible methods used in the literature and introduce a new variable called "scaling gradient". This tool and the conditional variance are shown to be effective in providing an unambiguous way for such a distinction. Their application is expected to be of outmost importance in the analysis of upcoming galaxy catalogues.Comment: 7 pages, 3 figure

Can we identify non-stationary dynamics of trial-to-trial variability?"

Identifying sources of the apparent variability in non-stationary scenarios is a fundamental problem in many biological data analysis settings. For instance, neurophysiological responses to the same task often vary from each repetition of the same experiment (trial) to the next. The origin and functional role of this observed variability is one of the fundamental questions in neuroscience. The nature of such trial-to-trial dynamics however remains largely elusive to current data analysis approaches. A range of strategies have been proposed in modalities such as electro-encephalography but gaining a fundamental insight into latent sources of trial-to-trial variability in neural recordings is still a major challenge. In this paper, we present a proof-of-concept study to the analysis of trial-to-trial variability dynamics founded on non-autonomous dynamical systems. At this initial stage, we evaluate the capacity of a simple statistic based on the behaviour of trajectories in classification settings, the trajectory coherence, in order to identify trial-to-trial dynamics. First, we derive the conditions leading to observable changes in datasets generated by a compact dynamical system (the Duffing equation). This canonical system plays the role of a ubiquitous model of non-stationary supervised classification problems. Second, we estimate the coherence of class-trajectories in empirically reconstructed space of system states. We show how this analysis can discern variations attributable to non-autonomous deterministic processes from stochastic fluctuations. The analyses are benchmarked using simulated and two different real datasets which have been shown to exhibit attractor dynamics. As an illustrative example, we focused on the analysis of the rat's frontal cortex ensemble dynamics during a decision-making task. Results suggest that, in line with recent hypotheses, rather than internal noise, it is the deterministic trend which most likely underlies the observed trial-to-trial variability. Thus, the empirical tool developed within this study potentially allows us to infer the source of variability in in-vivo neural recordings