Inhomogeneities and caustics in the sedimentation of noninertial particles in incompressible flows

In an incompressible flow, fluid density remains invariant along fluid element trajectories. This implies that the spatial distribution of non-interacting noninertial particles in such flows cannot develop density inhomogeneities beyond those that are already introduced in the initial condition. However, in certain practical situations, density is measured or accumulated on (hyper-) surfaces of dimensionality lower than the full dimensionality of the flow in which the particles move. An example is the observation of particle distributions sedimented on the floor of the ocean. In such cases, even if the initial distribution of noninertial particles is uniform within a finite support in an incompressible flow, advection in the flow will give rise to inhomogeneities in the observed density. In this paper we analytically derive, in the framework of an initially homogeneous particle sheet sedimenting towards a bottom surface, the relationship between the geometry of the flow and the emerging distribution. From a physical point of view, we identify the two processes that generate inhomogeneities to be the stretching within the sheet, and the projection of the deformed sheet onto the target surface. We point out that an extreme form of inhomogeneity, caustics, can develop for sheets. We exemplify our geometrical results with simulations of particle advection in a simple kinematic flow, study the dependence on various parameters involved, and illustrate that the basic mechanisms work similarly if the initial (homogeneous) distribution occupies a more general region of finite extension rather than a sheet.Comment: 56 pages, 17 figure

Quantifying nonergodicity in nonautonomous dissipative dynamical systems: an application to climate change

In nonautonomous dynamical systems, like in climate dynamics, an ensemble of trajectories initiated in the remote past defines a unique probability distribution, the natural measure of a snapshot attractor, for any instant of time, but this distribution typically changes in time. In cases with an aperiodic driving, temporal averages taken along a single trajectory would differ from the corresponding ensemble averages even in the infinite-time limit: ergodicity does not hold. It is worth considering this difference, which we call the nonergodic mismatch, by taking time windows of finite length for temporal averaging. We point out that the probability distribution of the nonergodic mismatch is qualitatively different in ergodic and nonergodic cases: its average is zero and typically nonzero, respectively. A main conclusion is that the difference of the average from zero, which we call the bias, is a useful measure of nonergodicity, for any window length. In contrast, the standard deviation of the nonergodic mismatch, which characterizes the spread between different realizations, exhibits a power-law decrease with increasing window length in both ergodic and nonergodic cases, and this implies that temporal and ensemble averages differ in dynamical systems with finite window lengths. It is the average modulus of the nonergodic mismatch, which we call the ergodicity deficit, that represents the expected deviation from fulfilling the equality of temporal and ensemble averages. As an important finding, we demonstrate that the ergodicity deficit cannot be reduced arbitrarily in nonergodic systems. We illustrate via a conceptual climate model that the nonergodic framework may be useful in Earth system dynamics, within which we propose the measure of nonergodicity, i.e., the bias, as an order-parameter-like quantifier of climate change

Local characterization of transient chaos on finite times in open systems

To characterize local finite-time properties associated with transient chaos in open dynamical systems, we introduce an escape rate and fractal dimensions suitable for this purpose in a coarse-grained description. We numerically illustrate that these quantifiers have a considerable spread across the domain of the dynamics, but their spatial variation, especially on long but non-asymptotic integration times, is approximately consistent with the relationship that was recognized by Kantz and Grassberger for temporally asymptotic quantifiers. In particular, deviations from this relationship are smaller than differences between various locations, which confirms the existence of such a dynamical law and the suitability of our quantifiers to represent underlying dynamical properties in the non-asymptotic regime.Comment: 23 pages, 8 figures. Revision based on referee reports: minor corrections and a new analysis of the deviation from the Kantz-Grassberger relationshi

Nonlinear forced change and nonergodicity: The case of ENSO-Indian monsoon and global precipitation teleconnections

We study the forced response of the teleconnection between the El Nino-Southern Oscillation (ENSO) and global precipitation in general and the Indian summer monsoon (IM) in particular in the Max Planck Institute Grand Ensemble. The forced response of the teleconnection is defined as the time-dependence of a correlation coefficient evaluated over the ensemble. The ensemble-wise variability is taken either wrt. spatial averages or dominant spatial modes in the sense of Maximal Covariance Analysis or Canonical Correlation Analysis or EOF analysis. We find that the strengthening of the ENSO-IM teleconnection is robustly or consistently featured in view of all four teleconnection representations, whether sea surface temperature (SST) or sea level pressure (SLP) is used to characterise ENSO, and both in the historical period and under the RCP8.5 forcing scenario. The main contributor to this strengthening in terms of a linear regression model is the regression coefficient, which can outcompete even a declining ENSO variability in view of using the SLP. We also find that the forced change of the teleconnection is typically nonlinear by (1) formally rejecting the hypothesis that ergodicity holds, i.e., that expected values of temporal correlation coefficients with respect to the ensemble equal the ensemble-wise correlation coefficient itself, and also showing that (2) the trivial contributions of the forced changes of e.g. the mean SST and/or precipitation to temporal correlations are insignificant here. We also provide, in terms of the test statistics, global maps of the degree of nonlinearity/nonergodicity of the forced change of the teleconnection between local precipitation and ENSO

The theory of parallel climate realizations as a new framework for teleconnection analysis

Teleconnections are striking features of the Earth climate system which appear as statistically correlated climate-related patterns between remote geographical regions of the globe. In a changing climate, however, the strength of teleconnections might change, and an appropriate characterization of these correlations and their change (more appropriate than detrending the time series) is lacking in the literature. Here we present a novel approach, based on the theory of snapshot attractors, corresponding in our context to studying parallel climate realizations. Imagining an ensemble of parallel Earth systems, instead of the single one observed (i.e., the real Earth), the ensemble, after some time, characterizes the appropriate probabilities of all options permitted by the climate dynamics, reflecting the internal variability of the climate. We claim that the relevant quantities for characterizing teleconnections in a changing climate are correlation coefficients taken over the temporally evolving ensemble in any time instant. As a particular example, we consider the teleconnections of the North Atlantic Oscillation (NAO). In a numerical climate model, we demonstrate that this approach provides the only statistically correct characterization, in contrast to commonly used temporal correlations evaluated along single detrended time series. The teleconnections of the NAO are found to survive the climate change, but their strength might be time-dependent

The impact of intermediate-term alcohol abstinence on memory retrieval and suppression

Background: The nature of episodic memory deficit in intermediate-term abstinence from alcohol in alcohol dependence (AD) is not yet clarified. Deficits in inhibitory control are commonly reported in substance use disorders. However, much less is known about cognitive control suppressing interference from memory. The Think/No-think (TNT) paradigm is a well established method to investigate inhibition of associative memory retrieval.Methods: Thirty-six unmedicated alcohol dependent (AD) patients and 36 healthy controls (HC) performed the TNT task. Thirty image-word pairs were trained up to a predefined accuracy level. Cued recall was examined in three conditions: Think (T) for items instructed to-be-remembered, No-think (NT) assessing the ability to suppress retrieval and Baseline (B) for general relational memory. Premorbid IQ, clinical variables and impulsivity measures were quantified. Results: AD patients had a significantly increased demand for training. Baseline memory abilities and effect of practice on retrieval were not markedly different between the groups. We found a significant main effect of group (HC vs AD) x condition (B, T and NT) and a significant difference in mean NT-B scores for the two groups. Discussion: AD and HC groups did not differ essentially in their baseline memory abilities. Also, the instruction to focus on retrieval improved episodic memory performance in both groups. Crucially, control participants were able to suppress relational words in the NT condition supporting the critical effect of cognitive control processes over inhibition of retrieval. In contrast to this, the ability of AD patients to suppress retrieval was found to be impaired

On the importance of the convergence to climate attractors

Ensemble approaches are becoming widely used in climate research. In contrast to weather forecast, however, in the climatic context one is interested in long-time properties, those arising on the scale of several decades. The well-known strong internal variability of the climate system implies the existence of a related dynamical attractor with chaotic properties. Under the condition of climate change this should be a snapshot attractor, naturally arising in an ensemble-based framework. Although ensemble averages can be evaluated at any instant of time, results obtained during the process of convergence of the ensemble towards the attractor are not relevant from the point of view of climate. In simulations, therefore, attention should be paid to whether the convergence to the attractor has taken place. We point out that this convergence is of exponential character, therefore, in a finite amount of time after initialization relevant results can be obtained. The role of the time scale separation due to the presence of the deep ocean is discussed from the point of view of ensemble simulations

Alteration of Visuospatial System as an Early Marker of Cognitive Decline: A Double-Center Neuroimaging Study

Amnestic-type mild cognitive impairment (a-MCI) represents the prodromal phase of Alzheimer's disease associated with a high conversion rate to dementia and serves as a potential golden period for interventions. In our study, we analyzed the role of visuospatial (VS) functions and networks in the recognition of a-MCI. We examined 78 participants (32 patients and 46 controls) in a double-center arrangement using neuropsychology, structural, and resting-state functional MRI. We found that imaging of the lateral temporal areas showed strong discriminating power since in patients only the temporal pole (F = 5.26, p = 0.034) and superior temporal gyrus (F = 8.04, p < 0.001) showed reduced cortical thickness. We demonstrated significant differences between controls and patients in various neuropsychological results; however, analysis of cognitive subdomains revealed that the largest difference was presented in VS skills (F = 8.32, p < 0.001). Functional connectivity analysis of VS network showed that patients had weaker connectivity between the left and right frontotemporal areas, while stronger local connectivity was presented between the left frontotemporal structures (FWE corrected p < 0.05). Our results highlight the remarkable potential of examining the VS system in the early detection of cognitive decline. Since resting-state setting of functional MRI simplifies the possible automatization of data analysis, detection of VS system alterations might provide a non-invasive biomarker of a-MCI