Dynamics of fingering convection II: The formation of thermohaline staircases

Regions of the ocean's thermocline unstable to salt fingering are often observed to host thermohaline staircases, stacks of deep well-mixed convective layers separated by thin stably-stratified interfaces. Decades after their discovery, however, their origin remains controversial. In this paper we use 3D direct numerical simulations to shed light on the problem. We study the evolution of an analogous double-diffusive system, starting from an initial statistically homogeneous fingering state and find that it spontaneously transforms into a layered state. By analysing our results in the light of the mean-field theory developed in Paper I, a clear picture of the sequence of events resulting in the staircase formation emerges. A collective instability of homogeneous fingering convection first excites a field of gravity waves, with a well-defined vertical wavelength. However, the waves saturate early through regular but localized breaking events, and are not directly responsible for the formation of the staircase. Meanwhile, slower-growing, horizontally invariant but vertically quasi-periodic gamma-modes are also excited and grow according to the gamma-instability mechanism. Our results suggest that the nonlinear interaction between these various mean-field modes of instability leads to the selection of one particular gamma-mode as the staircase progenitor. Upon reaching a critical amplitude, this progenitor overturns into a fully-formed staircase. We conclude by extending the results of our simulations to real oceanic parameter values, and find that the progenitor gamma-mode is expected to grow on a timescale of a few hours, and leads to the formation of a thermohaline staircase in about one day with an initial spacing of the order of one to two metres.Comment: 18 pages, 9 figures, associated mpeg file at http://earth.uni-muenster.de/~stellma/movie_small.mp4, submitted to JF

The subgroup growth spectrum of virtually free groups

For a finitely generated group $\Gamma$ denote by $\mu(\Gamma)$ the growth coefficient of $\Gamma$, that is, the infimum over all real numbers $d$ such that $s_n(\Gamma)<n!^d$. We show that the growth coefficient of a virtually free group is always rational, and that every rational number occurs as growth coefficient of some virtually free group. Moreover, we describe an algorithm to compute $\mu$

Searching for an anchor in an unpredictable world: A computational model of obsessive compulsive disorder

In this article, we develop a computational model of obsessive–compulsive disorder (OCD). We propose that OCD is characterized by a difficulty in relying on past events to predict the consequences of patients’ own actions and the unfolding of possible events. Clinically, this corresponds both to patients’ difficulty in trusting their own actions (and therefore repeating them), and to their common preoccupation with unlikely chains of events. Critically, we develop this idea on the basis of the well-developed framework of the Bayesian brain, where this impairment is formalized as excessive uncertainty regarding state transitions. We illustrate the validity of this idea using quantitative simulations and use these to form specific empirical predictions. These predictions are evaluated in relation to existing evidence, and are used to delineate directions for future research. We show how seemingly unrelated findings and phenomena in OCD can be explained by the model, including a persistent experience that actions were not adequately performed and a tendency to repeat actions; excessive information gathering (i.e., checking); indecisiveness and pathological doubt; overreliance on habits at the expense of goal-directed behavior; and overresponsiveness to sensory stimuli, thoughts, and feedback. We discuss the relationship and interaction between our model and other prominent models of OCD, including models focusing on harm-avoidance, not-just-right experiences, or impairments in goal-directed behavior. Finally, we outline potential clinical implications and suggest lines for future research

Spontaneous visual exploration during locomotion in patients with phobic postural vertigo

BACKGROUND Earlier studies on stance and gait with posturographic and EMG-recordings and automatic gait analysis in patients with phobic postural vertigo (PPV) or visual height intolerance (vHI) revealed similar patterns of body stiffening with muscle co-contraction and a slow, cautious gait. Visual exploration in vHI patients was characterized by a freezing of gaze-in-space when standing and reduced horizontal eye and head movements during locomotion. OBJECTIVE Based on the findings in vHI patients, the current study was performed with a focus on visual control of locomotion in patients with PPV while walking along a crowded hospital hallway. METHODS Twelve patients with PPV and eleven controls were recruited. Participants wore a mobile infrared video eye-tracking system that continuously measured eye-in-head movements in the horizontal and vertical planes and head orientation and motion in the yaw, pitch, and roll planes. Visual exploration behavior of participants was recorded at the individually preferred speed for a total walking distance of 200 m. Gaze-in-space directions were determined by combining eye-in-head and head-in-space orientation. Walking speeds were calculated based on the trial duration and the total distance traversed. Participants were asked to rate their feelings of discomfort during the walk on a 4-point numeric rating scale. The examiners rated the crowdedness of the hospital hallway on a 4-point numeric rating scale. RESULTS The major results of visual exploration behavior in patients with PPV in comparison to healthy controls were: eye and head positions were directed more downward in the vertical plane towards the ground ahead with increased frequency of large amplitude vertical orientation movements towards the destination, the end of the ground straight ahead. The self-adjusted speed of locomotion was significantly lower in PPV. Particularly those patients that reported high levels of discomfort exhibited a specific visual exploration of their horizontal surroundings. The durations of fixating targets in the visual surroundings were significantly shorter as compared to controls. CONCLUSION Gaze control of locomotion in patients with PPV is characterized by a preferred deviation of gaze more downward and by horizontal explorations for suitable auxiliary means for potential postural support in order to prevent impending falls. These eye movements have shorter durations of fixation as compared to healthy controls and patients with vHI. Finally, the pathological alterations in eye-head coordination during locomotion correlate with a higher level of discomfort and anxiety about falling

On the p-length of some finite p-soluble groups

The main aim of this paper is to give structural information of a finite group of minimal order belonging to a subgroup-closed class of finite groups and whose p-length is greater than 1, p a prime number. Alternative proofs and improvements of recent results about the influence of minimal p-subgroups on the p-nilpotence and p-length of a finite group arise as consequences of our study

Reverse undercompressive shock structures in driven thin film flow

We show experimental evidence of a new structure involving an undercompressive and reverse undercompressive shock for draining films driven by a surface tension gradient against gravity. The reverse undercompressive shock is unstable to transverse perturbations while the leading undercompressive shock is stable. Depending on the pinch-off film thickness, as controlled by the meniscus, either a trailing rarefaction wave or a compressive shock separates from the reverse undercompressive shock

How do neural processes give rise to cognition? Simultaneously predicting brain and behavior with a dynamic model of visual working memory

There is consensus that activation within distributed functional brain networks underlies human thought. The impact of this consensus is limited, however, by a gap that exists between data-driven correlational analyses that specify where functional brain activity is localized using functional magnetic resonance imaging (fMRI), and neural process accounts that specify how neural activity unfolds through time to give rise to behavior. Here, we show how an integrative cognitive neuroscience approach may bridge this gap. In an exemplary study of visual working memory, we use multilevel Bayesian statistics to demonstrate that a neural dynamic model simultaneously explains behavioral data and predicts localized patterns of brain activity, outperforming standard analytic approaches to fMRI. The model explains performance on both correct trials and incorrect trials where errors in change detection emerge from neural fluctuations amplified by neural interaction. Critically, predictions of the model run counter to cognitive theories of the origin of errors in change detection. Results reveal neural patterns predicted by the model within regions of the dorsal attention network that have been the focus of much debate. The model-based analysis suggests that key areas in the dorsal attention network such as the intraparietal sulcus play a central role in change detection rather than working memory maintenance, counter to previous interpretations of fMRI studies. More generally, the integrative cognitive neuroscience approach used here establishes a framework for directly testing theories of cognitive and brain function using the combined power of behavioral and fMRI data. (PsycInfo Database Record (c) 2021 APA, all rights reserved)

Brief cognitive assessment in a UK population sample -- distributional properties and the relationship between the MMSE and an extended mental state examination.

BACKGROUND: Despite the MMSE's known flaws, it is still used extensively as both a screening instrument for dementia and a population measure of cognitive ability. The aim of this paper is to provide data on the distribution of MMSE scores in a representative sample from the UK population and to compare it with an extended cognitive assessment (EMSE) which covers a wider range of cognitive domains and provides a wider range of difficulty levels. METHODS: The MMSE and the EMSE were administered to over 12,000 participants at the screening stage of the MRC Cognitive Function and Ageing Study (MRC CFAS). MRC CFAS is a multi-centre population-based study in England and Wales with respondents aged 65 years and older. RESULTS: Normative values on the MMSE and EMSE are presented by age group, sex and level of education. There are very large differences between age groups, with smaller differences seen between the sexes and by level of education. The EMSE extends the scores at the high end of the ability range, but is no better than the MMSE at differentiating between dementia and non-dementia. CONCLUSION: Population-derived norms are valuable for comparing an individual's score to the score that would be expected among the general population, given the individual's specific demographic characteristics.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are

Lava channel formation during the 2001 eruption on Mount Etna: evidence for mechanical erosion

We report the direct observation of a peculiar lava channel that was formed near the base of a parasitic cone during the 2001 eruption on Mount Etna. Erosive processes by flowing lava are commonly attributed to thermal erosion. However, field evidence strongly suggests that models of thermal erosion cannot explain the formation of this channel. Here, we put forward the idea that the essential erosion mechanism was abrasive wear. By applying a simple model from tribology we demonstrate that the available data agree favorably with our hypothesis. Consequently, we propose that erosional processes resembling the wear phenomena in glacial erosion are possible in a volcanic environment.Comment: accepted for publication in Physical Review Letter