602 research outputs found
Anomalous dissipation and regularization in isotropic Gaussian turbulence
No full textIn this work we rigorously establish a number of properties of "turbulent" solutions to the stochastic transport and the stochastic continuity equations constructed by Le Jan and Raimond in [Ann. Probab. 30(2): 826-873, 2002]. The advecting velocity field, not necessarily incompressible, is Gaussian and white-in-time, space-homogeneous and isotropic, with -Hölder regularity in space, . We cover the full range of compressibility ratios giving spontaneous stochasticity of particle trajectories. For the stochastic transport equation, we prove that generic data experience anomalous dissipation of the mean energy, and study basic properties of the resulting anomalous dissipation measure. Moreover, we show that starting from such irregular data, the solution immediately gains regularity and enters into a fractional Sobolev space . The proof of the latter is obtained as a consequence of a new sharp regularity result for the degenerate parabolic PDE satisfied by the associated two-point self-correlation function, which is of independent interest. In the incompressible case, a Duchon-Robert-type formula for the anomalous dissipation measure is derived, making a precise connection between this self-regularizing effect and a limit on the flux of energy in the turbulent cascade. Finally, for the stochastic continuity equation, we prove that solutions starting from a Dirac delta initial condition undergo an average squared dispersion growing with respect to time as , rigorously establishing the analogue of Richardson's law of particle separations in fluid dynamics
The statistical geometry of material loops in turbulence
No full textMaterial elements - which are lines, surfaces, or volumes behaving as
passive, non-diffusive markers - provide an inherently geometric window into
the intricate dynamics of chaotic flows. Their stretching and folding dynamics
has immediate implications for mixing in the oceans or the atmosphere, as well
as the emergence of self-sustained dynamos in astrophysical settings. Here, we
uncover robust statistical properties of an ensemble of material loops in a
turbulent environment. Our approach combines high-resolution direct numerical
simulations of Navier-Stokes turbulence, stochastic models, and dynamical
systems techniques to reveal predictable, universal features of these complex
objects. We show that the loop curvature statistics become stationary through a
dynamical formation process of high-curvature folds, leading to distributions
with power-law tails whose exponents are determined by the large-deviations
statistics of finite-time Lyapunov exponents of the flow. This prediction
applies to advected material lines in a broad range of chaotic flows. To
complement this dynamical picture, we confirm our theory in the analytically
tractable Kraichnan model with an exact Fokker-Planck approach
MANOVA modelling of a chiropractic longitudinal study using multiple imputation
No full textThe purpose of this report is to present the detailed statistical analysis of a randomised, placebo-controlled trial comparing two different treatment modalities to an intervention of no known benefit for people with acute or subacute thoracic spine pain.
The therapy arms consist of Spinal Manipulative Therapy (SMT) and Graston Technique (GT) and the placebo is a non-functional ultrasound. A placebo group was utilised because at present there are no proven treatments for non-specific thoracic pain. This trial is registered with the Australia and New Zealand Clinical Trials Registry. Ethics approval has been granted by Murdoch University Human Research and Ethics Committee, number 2007/274.
The aim of this three arm trial was to test the efficacy of SMT and GT as independent modalities compared to detuned ultrasound for the outcomes of pain and disability. The latter were measured using the Visual Analogue Scale (VAS) and a modified Oswestry Back Pain Disability Index. The study was conducted at the Murdoch University Chiropractic student clinic in Perth, Australia, and the protocol published in Crothers et al (2008).
In this report, Section 2 provides an initial exploratory analysis of the data, Section 3 outlines the statistical models used in the final analysis, Section 4 defines these models in mathematical terms, Section 5 discusses the management of missing values via multiple imputation and Section 6 presents the results of the statistical modelling and hypothesis tests. The clinical study will be published in full elsewhere
Q&A with Ted Satterthwaite and Joëlle Bagautdinova
No full textWe at Cell Reports discuss the work, interests, and mentoring experiences of Theodore Satterthwaite (TS) and his graduate student and co-author, Joëlle Bagautdinova (JB). They share with us their recent findings highlighting the relationship between the development of cognitive function and white matter and also talk about the challenges and technical advances in cognitive neuroscience and neuroimaging
Theodore Metochites' Byzantios as a testimony to the cosmological discussions of the early Palaeologan period
No full textAccording to the author, Theodore Metochites, while composing his unpublished laudatio of constantinople entitled Byzantios, utilized one of the cosmological treatises of nikephoros choumnos, referring to the eternal movement of nature, to which the imperial city is compared.Selon l’auteur, Théodore Métochitès utilisa, dans la composition de sa Laudatio inédite de Constantinople intitulée Byzantios, un des traités cosmologiques de Nicéphore Choumnos, concernant le mouvement éternel de la nature, auquel la ville impériale est comparée.Polemis Ioannis D. Theodore Metochites' Byzantios as a testimony to the cosmological discussions of the early Palaeologan period. In: Revue des études byzantines, tome 66, 2008. pp. 241-246
Achilles and the improba virgo. Ovid, Ars am. 1.681-704 and Statius, "Ach." 1.491-552
No full textAnalysis of the modelling influence of Ovid's apostrophai to Achilles in cross-dress at Scyros (Ars am. 1.681-704) on Statius' Achilleid 1.619-639 (Achilles' dialogue with himself in the night he rapes Deidameia) and 1.514-535 (apostrophai to Thetis and Achilles by Calchas, who is asked by the Greeks at Aulis to divine where Achilles is hidden).
Calchas' speech may be read as a more dignified, epic retelling of Ovid's narrative, which had presented the didactic author (mockingly, of course) as the positive influence that ensured Achilles would adhere to his twin destiny as martial hero & great lover. Statius‘ Calchas has the same tone of indignation over the destiny of the character Achilles as Ovid did in the Ars. Like the Ovidian narrator, he also serves as the catalyst that advances the plot towards Achilles' definitive liberation from cross-dressing, in that he provides Odysseus and Diomedes with the necessary information to summon the hidden hero to the war. Calchas‘ assuming this role is well within the limits of the poetics of epic, since his Iliadic alter ego had similarly compelled Agamemnon to radically change his attitude toward Chryseis and thus redirected the story of the war of Troy. Later in my paper, we will see how Statius' re-dignified Achilles follows, in a way, in Calchas‘ and Ovid's footsteps by showing the same indignation and addressing comparable apostrophai to himself (1.619-639) as he himself acknowledges the necessity of stopping his transvestism even before Calchas‘ stand-in Odysseus compelled him to give it up.
The paper concludes with an Ovidian interpretation of the expression improba virgo, with which Statius’ Calchas labels Deidameia (1.535)
Self-Regularization in turbulence from the Kolmogorov 4/5-Law and Alignment
No full textA defining feature of 3D hydrodynamic turbulence is that the rate of energy
dissipation is bounded away from zero as viscosity is decreased (Reynolds
number increased). This phenomenon - anomalous dissipation - is sometimes
called the `zeroth law of turbulence' as it underpins many celebrated
theoretical predictions. Another robust feature observed in turbulence is that
velocity structure functions
exhibit persistent power-law scaling in the inertial range, namely for exponents over an ever-increasing (with
Reynolds) range of scales. This behavior indicates that the velocity field
retains some fractional differentiability uniformly in the Reynolds number. The
Kolmogorov 1941 theory of turbulence predicts that for all
and Onsager's 1949 theory establishes the requirement that
for for consistency with the zeroth law. Empirically, and , suggesting that turbulent
Navier-Stokes solutions approximate dissipative weak solutions of the Euler
equations possessing (nearly) the minimal degree of singularity required to
sustain anomalous dissipation. In this note, we adopt an experimentally
supported hypothesis on the anti-alignment of velocity increments with their
separation vectors and demonstrate that the inertial dissipation provides a
regularization mechanism via the Kolmogorov 4/5-law.Comment: 14 pages, 4 figure
The critical editions, the creation time and the authors of the ancient Vitae of st. Theodore of Studios his curriculum vitae according to Vita A
No full textThe article states that the four ancient Greek lives (A, B, C, D) contain extensive information about the life and activity of St. Theodore of Studios (759-826). The oldest one is Vita S. Theodori Studitae B which was published in 1853 by A. Mai. The document was written in c. 868 and its author was probably a monk Michael or another ascetic who lived in the Studios Monastery in Constantinople; Vita A, which is an extended version of Vita B, was published in 1696. His author was Theodore Daphnopates, who lived in the first half of the 10th century. Vita C (Vita S. Theodori Studitae in codice Mosquensi musei Rumianzoviani No 520) was published in 1915, but it dates back to the 12th century and it is similar in its content to Vita S. Theodori Studitae A and B. Vita D (Codex Monacensis No 467) was not yet published
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