98 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
Bridging the gap: Defining the molecular mechanisms of CEP290 disease pathogenesis
No full textMutations in the gene CEP290 cause an array of debilitating and phenotypically distinct human diseases, ranging in severity from the devastating blinding disease Leber congenital amaurosis (LCA) to Senior Løken Syndrome, Joubert syndrome, and the embryonically lethal Meckel-Grüber syndrome. The pathology observed in these diseases is thought to be due to CEP290\u27s essential role in the development and maintenance of the primary cilium, but despite its critical role in biology and disease we know only little about CEP290\u27s function. Here we identify four novel functional domains of the protein, showing that CEP290 directly binds to cellular membranes through an N-terminal domain that includes a highly conserved amphipathic helix motif, and to microtubules through a domain located within its myosin-tail homology domain. Furthermore, CEP290 activity was found to be regulated by two novel autoinhibitory domains within its N- and C-termini, both of which were also found to play critical roles in regulating ciliogenesis. Disruption of the microtubule-binding domain in the rd16 mouse LCA model was found to be sufficient to induce significant deficits in cilium formation leading to retinal degeneration. Taking these findings into account, we developed a novel model that accurately predicts patient CEP290 protein levels in a mutation-specific fashion. Predicted CEP290 protein levels were found to robustly correlate with disease severity for all reported CEP290 patients. All these data implicate CEP290 as an integral structural and regulatory component of the primary cilium and provide insight into the pathological mechanisms of LCA and related ciliopathies. Our findings also suggest novel strategies for therapeutic intervention in the treatment of CEP290-based disease that, if fully realized, would be the first treatment available for the many patients suffering the devastating effects of CEP290 dysfunction
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
O38: Universal exome sequencing in critically-ill adults: A diagnostic yield of 25% and race-based disparities in access to genetic testing
No full textThe Bionic Retina: A Small Molecule with Big Potential for Visual Restoration
No full textIn this issue of Neuron, Polosukhina et al. (2012) intravitreally deliver the light-activatable molecule acrylamide-azobenzene-quaternary ammonium (AAQ) to the eyes of mice with end-stage retinal degeneration. Results show that, with the appropriate illumination, AAQ restores light sensitivity and visual behavior
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