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Register a new userMixing properties in the advection of passive tracers via recurrences and extreme value theory
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In this paper we characterize the mixing properties in the advection of passive tracers by exploiting the extreme value theory for dynamical systems. With respect to classical techniques directly related to the Poincare recurrences analysis, our method provides reliable estimations of the characteristic mixing times and distinguishes between barriers and unstable fixed points. The method is based on a check of convergence for extreme value laws on finite datasets. We define the mixing times in terms of the shortest time intervals such that extremes converge to the asymptotic (known) parameters of the Generalized Extreme Value distribution. Our technique is suitable for applications in the analysis of other systems where mixing time scales need to be determined and limited datasets are available.
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We provide formulas to compute the coefficients entering the affine scaling needed to get a non-degenerate function for the asymptotic distribution of the maxima of some kind of observable computed along the orbit of a randomly perturbed dynamical system. This will give information on the local geometrical properties of the stationary measure. We will consider systems perturbed with additive noise and with observational noise. Moreover we will apply our techniques to chaotic systems and to contractive systems, showing that both share the same qualitative behavior when perturbed.
This study uses the link between extreme value laws and dynamical systems theory to show that important dynamical quantities as the correlation dimension, the entropy and the Lyapunov exponents can be obtained by fitting observables computed along a trajectory of a chaotic systems. All this information is contained in a newly defined Dynamical Extreme Index. Besides being mathematically well defined, it is almost numerically effortless to get as i) it does not require the specification of any additional parameter (e.g. embedding dimension, decorrelation time); ii) it does not suffer from the so-called curse of dimensionality. A numerical code for its computation is provided.
This work reviews the present position of and surveys future perspectives in the physics of chaotic advection: the field that emerged three decades ago at the intersection of fluid mechanics and nonlinear dynamics, which encompasses a range of applications with length scales ranging from micrometers to hundreds of kilometers, including systems as diverse as mixing and thermal processing of viscous fluids, microfluidics, biological flows, and oceanographic and atmospheric flows.
We continue our study of chaotic mixing and transport of passive particles in a simple model of a meandering jet flow [Prants, et al, Chaos {bf 16}, 033117 (2006)]. In the present paper we study and explain phenomenologically a connection between dynamical, topological, and statistical properties of chaotic mixing and transport in the model flow in terms of dynamical traps, singular zones in the phase space where particles may spend arbitrary long but finite time [Zaslavsky, Phys. D {bf 168--169}, 292 (2002)]. The transport of passive particles is described in terms of lengths and durations of zonal flights which are events between two successive changes of sign of zonal velocity. Some peculiarities of the respective probability density functions for short flights are proven to be caused by the so-called rotational-islands traps connected with the boundaries of resonant islands (including those of the vortex cores) filled with the particles moving in the same frame. Whereas, the statistics of long flights can be explained by the influence of the so-called ballistic-islands traps filled with the particles moving from a frame to frame.
Common domain adaptation techniques assume that the source domain and the target domain share an identical label space, which is problematic since when target samples are unlabeled we have no knowledge on whether the two domains share the same label space. When this is not the case, the existing methods fail to perform well because the additional unknown classes are also matched with the source domain during adaptation. In this paper, we tackle the open set domain adaptation problem under the assumption that the source and the target label spaces only partially overlap, and the task becomes when the unknown classes exist, how to detect the target unknown classes and avoid aligning them with the source domain. We propose to utilize an instance-level reweighting strategy for domain adaptation where the weights indicate the likelihood of a sample belonging to known classes and to model the tail of the entropy distribution with Extreme Value Theory for unknown class detection. Experiments on conventional domain adaptation datasets show that the proposed method outperforms the state-of-the-art models.
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