Statistical Properties of Nonlinear Shell Models of Turbulence from Linear Advection Models: Rigorous Results

In a recent paper it was proposed that for some nonlinear shell models of turbulence one can construct a linear advection model for an auxiliary field such that the scaling exponents of all the structure functions of the linear and nonlinear fields coincide. The argument depended on an assumption of continuity of the solutions as a function of a parameter. The aim of this paper is to provide a rigorous proof for the validity of the assumption. In addition we clarify here when the swap of a nonlinear model by a linear one will not work.Comment: 7 pages, 4 figures, submitted to Nonlinearit

A Note on the Regularity of Inviscid Shell Model of Turbulence

In this paper we continue the analytical study of the sabra shell model of energy turbulent cascade initiated in \cite{CLT05}. We prove the global existence of weak solutions of the inviscid sabra shell model, and show that these solutions are unique for some short interval of time. In addition, we prove that the solutions conserve the energy, provided that the components of the solution satisfy $|{u_n}| \le C k_n^{-1/3} (\sqrt{n} \log(n+1))^{-1}$, for some positive absolute constant $C$, which is the analogue of the Onsager's conjecture for the Euler's equations. Moreover, we give a Beal-Kato-Majda type criterion for the blow-up of solutions of the inviscid sabra shell model and show the global regularity of the solutions in the ``two-dimensional'' parameters regime

Sharp Lower Bounds for the Dimension of the Global Attractor of the Sabra Shell Model of Turbulence

In this work we derive a lower bounds for the Hausdorff and fractal dimensions of the global attractor of the Sabra shell model of turbulence in different regimes of parameters. We show that for a particular choice of the forcing and for sufficiently small viscosity term $\nu$, the Sabra shell model has a global attractor of large Hausdorff and fractal dimensions proportional to $\log_\lambda \nu^{-1}$ for all values of the governing parameter $\epsilon$, except for $\epsilon=1$. The obtained lower bounds are sharp, matching the upper bounds for the dimension of the global attractor obtained in our previous work. Moreover, we show different scenarios of the transition to chaos for different parameters regime and for specific forcing. In the ``three-dimensional'' regime of parameters this scenario changes when the parameter $\epsilon$ becomes sufficiently close to 0 or to 1. We also show that in the ``two-dimensional'' regime of parameters for a certain non-zero forcing term the long-time dynamics of the model becomes trivial for any value of the viscosity

Counter and Complicit Masculine Discourse Among Men’s Shed Members

Men’s Sheds is a growing international movement aimed at providing men with places and activities that facilitate social connectedness. Despite Men’s Sheds’ focus on males, little attention has been paid to masculinities within the specific context of these settings. The current study used a gender relations framework to explore the ways in which attendees discussed Men’s Sheds, with particular attention to discussions that were complicit and counter to traditional, hegemonic views of masculinity, and diverse positions in between these binaries. The data consisted of transcripts and field notes from four focus groups comprised of mostly older, White, retired male members of a Canadian shed (N = 22). The analysis revealed three overall themes: (1) focus on work, (2) independence, and (3) need for male-focused spaces. These themes and associated subthemes suggest that shed members ascribe to dominant masculine values and ideals, but also support more fluid and flexible views of masculinity. Implications are discussed for how working with an array of masculinities within the Men’s Sheds movement will be helpful with respect to their future growth in Canada and internationally

A framework for mixing methods in quantitative measurement development, validation, and revision: A case study

A framework for quantitative measurement development, validation, and revision that incorporates both qualitative and quantitative methods is introduced. It extends and adapts Adcock and Collier’s work, and thus, facilitates understanding of quantitative measurement development, validation, and revision as an integrated and cyclical set of procedures best achieved through mixed methods research. It also offers a systematic guide concerning how these procedures may be undertaken through detailing key “stages,” “levels,” and practical “tasks.” A case study illustrates how qualitative and quantitative methods may be mixed through the use of the proposed framework in the cross-cultural content- and construct-related validation and subsequent revision of a quantitative measure.The contribution of this article to mixed methods research literature is briefly discussed

A Qualitative Analysis of Experiential Challenges Associated with Meditation Practice

Although empirical interest in meditation has flourished in recent years, few studies have addressed possible downsides of meditation practice, particularly in community populations. In-depth interviews were conducted with 30 male meditators in London, UK, recruited using principles of maximum variation sampling, and analysed using a modified constant comparison approach. Having originally set out simply to inquire about the impact of various meditation practices (including but not limited to mindfulness) on men’s wellbeing, we uncovered psychological challenges associated with its practice. While meditation was generally reported to be conducive to wellbeing, substantial difficulties accounted for approximately one quarter of the interview data. Our paper focuses specifically on these issues in order to alert health professionals to potential challenges associated with meditation. Four main problems of increasing severity were uncovered: Meditation was a difficult skill to learn and practise; participants encountered troubling thoughts and feelings which were hard to manage; meditation reportedly exacerbated mental health issues, such as depression and anxiety; and in a few cases, meditation was associated with psychotic episodes. Our paper raises important issues around safeguarding those who practise meditation, both within therapeutic settings and in the community

Global and regional brain metabolic scaling and its functional consequences

Background: Information processing in the brain requires large amounts of metabolic energy, the spatial distribution of which is highly heterogeneous reflecting complex activity patterns in the mammalian brain. Results: Here, it is found based on empirical data that, despite this heterogeneity, the volume-specific cerebral glucose metabolic rate of many different brain structures scales with brain volume with almost the same exponent around -0.15. The exception is white matter, the metabolism of which seems to scale with a standard specific exponent -1/4. The scaling exponents for the total oxygen and glucose consumptions in the brain in relation to its volume are identical and equal to $0.86\pm 0.03$, which is significantly larger than the exponents 3/4 and 2/3 suggested for whole body basal metabolism on body mass. Conclusions: These findings show explicitly that in mammals (i) volume-specific scaling exponents of the cerebral energy expenditure in different brain parts are approximately constant (except brain stem structures), and (ii) the total cerebral metabolic exponent against brain volume is greater than the much-cited Kleiber's 3/4 exponent. The neurophysiological factors that might account for the regional uniformity of the exponents and for the excessive scaling of the total brain metabolism are discussed, along with the relationship between brain metabolic scaling and computation.Comment: Brain metabolism scales with its mass well above 3/4 exponen

Sensorimotor Behavioral Tests for Use in a Juvenile Rat Model of Traumatic Brain Injury: Assessment of Sex Differences

Modeling juvenile traumatic brain injury (TBI) in rodents presents several unique challenges compared to adult TBI, one of which is selecting appropriate sensorimotor behavioral tasks that enable the assessment of the extent of injury and recovery over time in developing animals. To address this challenge, we performed a comparison of common sensorimotor tests in Long-Evans rats of various sizes and developmental stages (postnatal days 16–45, 35–190 g). Tests were compared and selected for their developmental appropriateness, scalability for growth, pre-training requirements, and throughput capability. Sex differences in response to TBI were also assessed. Grid walk, automated gait analysis, rotarod, beam walk, spontaneous forelimb elevation test, and measurement of motor activity using the force-plate actometer were evaluated. Grid walk, gait analysis, and rotarod failed to meet one or more of the evaluation criteria. Beam walk, spontaneous forelimb elevation test, and measurement of motor activity using the force-plate actometer satisfied all criteria and were capable of detecting motor abnormalities in rats subjected to controlled cortical impact on postnatal day 17. No sex differences were detected in the acute effects of TBI or functional recovery during the 28 days after injury using these tests. This demonstrates the utility of these tests for the evaluation of sensorimotor function in studies using rat models of pediatric TBI, and suggest that pre-pubertal males and females respond similarly to TBI with respect to sensorimotor outcomes

Dopamine receptor alterations in female rats with diet-induced decreased brain docosahexaenoic acid (DHA): interactions with reproductive status

Decreased tissue levels of n-3 (omega-3) fatty acids, particularly docosahexaenoic acid (DHA), are implicated in the etiologies of non-puerperal and postpartum depression. This study examined the effects of a diet-induced loss of brain DHA content and concurrent reproductive status on dopaminergic parameters in adult female Long–Evans rats. An α-linolenic acid-deficient diet and breeding protocols were used to produce virgin and parous female rats with cortical phospholipid DHA levels 20–22% lower than those fed a control diet containing adequate α-linolenic acid. Decreased brain DHA produced a significant main effect of decreased density of ventral striatal D2-like receptors. Virgin females with decreased DHA also exhibited higher density of D1-like receptors in the caudate nucleus than virgin females with normal DHA. These receptor alterations are similar to those found in several rodent models of depression, and are consistent with the proposed hypodopaminergic basis for anhedonia and motivational deficits in depression

Reaction rate reconstruction from biomass concentration measurement in bioreactors using modified second-order sliding mode algorithms

This paper deals with the estimation of unknown signals in bioreactors using sliding observers. Particular attention is drawn to estimate the specific growth rate of microorganisms from measurement of biomass concentration. In a recent article, notions of high-order sliding modes have been used to derive a growth rate observer for batch processes. In this paper we generalize and refine these preliminary results. We develop a new observer with a different error structure to cope with other types of processes. Furthermore, we show that these observers are equivalent, under coordinate transformations and time scaling, to the classical super-twisting differentiator algorithm, thus inheriting all its distinctive features. The new observers’ family achieves convergence to timevarying unknown signals in finite time, and presents the best attainable estimation error order in the presence of noise. In addition, the observers are robust to modeling and parameter uncertainties since they are based on minimal assumptions on bioprocess dynamics. In addition, they have interesting applications in fault detection and monitoring. The observers performance in batch, fed-batch and continuous bioreactors is assessed by experimental data obtained from the fermentation of Saccharomyces Cerevisiae on glucose.This work was supported by the National University of La Plata (Project 2012-2015), the Agency for the Promotion of Science and Technology ANPCyT (PICT2007-00535) and the National Research Council CONICET (PIP112-200801-01052) of Argentina; the Technical University of Valencia (PAID-02-09), the CICYT (DPI2005-01180) and AECID (A/024186/09) of Spain; and by the project FEDER of the European Union.De Battista, H.; Picó Marco, JA.; Garelli, F.; Navarro Herrero, JL. (2012). 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