The signature of laminar instabilities in the zone of transition to turbulence

We demonstrate that the space-time statistics of the birth of turbulent spots in boundary layers can be reconstructed qualitatively from the average behavior of macroscopic measures in the transition zone. The conclusion in \cite{vg04} that there exists a connection between the patterns in laminar instability and the birth of turbulent spots is strengthened. We examine why the relationship between instability and transition to turbulence is manifest in some cases and appears to be totally absent in others. Novel cellular automaton type simulations of the transition zone are conducted, and the pattern of spot birth is obtained from secondary instability analysis. The validity of the hypothesis of concentrated breakdown, according to which most turbulent spots originate at a particular streamwise location, is assessed. The predictions made lend themselves to straightforward experimental verification.Comment: 12 pages, 25 figures, submitted to PR

Novel black hole bound states and entropy

We solve for the spectrum of the Laplacian as a Hamiltonian on $\mathbb{R}^{2}-\mathbb{D}$ and in $\mathbb{R}^{3}-\mathbb{B}$. A self-adjointness analysis with $\partial\mathbb{D}$ and $\partial\mathbb{B}$ as the boundary for the two cases shows that a general class of boundary conditions for which the Hamiltonian operator is essentially self-adjoint are of the mixed (Robin) type. With this class of boundary conditions we obtain "bound state" solutions for the Schroedinger equation. Interestingly, these solutions are all localized near the boundary. We further show that the number of bound states is finite and is in fact proportional to the perimeter or area of the removed \emph{disc} or \emph{ball}. We then argue that similar considerations should hold for static black hole backgrounds with the horizon treated as the boundary.Comment: 13 pages, 3 figures, approximate formula for energy spectrum added at the end of section 2.1 along with additional minor changes to comply with the version accepted in PR

Games in Tholkappiyam and Aganaanooru

Tamil culture places a high value on grammar and literature. A sport thought of as a hobby  that  focuses on the civilization and culture of every people. From the sangam era to the present, the contribution of games has dominted grammar and literature. The greatest treasure that can never be destroyed is the world of games. Humans benefit greatly from sport in terms of agility and fun. The best medicine for the human body and for life is sports. Additionally, it is clamied to rejuvenate peoples life. They provide the body with the necessary energy, health, and sense of community. The game improves navigation and speaking skills for both kids and adults. As a result, every ones capacity for rational, in-depth thought improves.The lyrics allusions to the games played in Tholkappiaym and Aganaanooru are dispersed through Sout and arranged harmoniously. Tamil community values sport as a significant aspect

Structure Space of Model Proteins --A Principle Component Analysis

We study the space of all compact structures on a two-dimensional square lattice of size $N=6\times6$. Each structure is mapped onto a vector in $N$-dimensions according to a hydrophobic model. Previous work has shown that the designabilities of structures are closely related to the distribution of the structure vectors in the $N$-dimensional space, with highly designable structures predominantly found in low density regions. We use principal component analysis to probe and characterize the distribution of structure vectors, and find a non-uniform density with a single peak. Interestingly, the principal axes of this peak are almost aligned with Fourier eigenvectors, and the corresponding Fourier eigenvalues go to zero continuously at the wave-number for alternating patterns ($q=\pi$). These observations provide a stepping stone for an analytic description of the distribution of structural points, and open the possibility of estimating designabilities of realistic structures by simply Fourier transforming the hydrophobicities of the corresponding sequences.Comment: 14 pages, 12 figures, Conclusion has been modifie

Neuromuscular Complications With SARS-COV-2 Infection: A Review

© Copyright © 2020 Katyal, Narula, Acharya and Govindarajan. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) cases were first reported in Wuhan, Hubei province of China in December, 2019. SARS- COV-2 primarily affects the cardio-respiratory system. Over the last few months, several studies have described various neurological sequelae of SARS-COV-2 infection. Neurological complications are more frequent in patients with severe respiratory infections. In this review, we have analyzed the current literature on neuromuscular complications associated with SARS-COV-2 and highlighted possible mechanisms of neuromuscular invasion. We reviewed 11 studies describing 11 cases of Guillain Barre syndrome (GBS), and 1 case each of Miller Fisher syndrome, Polyneuritis Cranialis, Acute myelitis, Oculomotor paralysis and Bell\u27s Palsy associated with SARS-COV-2 infection. Mean age of patients with GBS was 61.54 years, with standard deviation (SD) 14.18 years. Majority patients had fever and cough as the first symptom of SARS COV-2 infection. Mean time for onset of neurological symptoms from initial symptoms in 11 patients was 8.18 days, with SD of 2.86 days. Mean time to performing electrodiagnostic study from onset of neurological symptom was 6 days with standard deviation of 3.25. Six patients had demyelinating pattern, three had acute sensory motor axonal neuropathy, and one had acute motor axonal neuropathy on electrodiagnostic studies

Stability analysis of an axisymmetric boundary layer

A linear stability analysis of the boundary layer over an axisymmetric body shows that transverse curvature has a significant effect on the stability. Depending on the curvature axisymmetric or nonaxisymmetric modes may be dominant. Detailed computations of energy balance are also done. The disturbance kinetic energy production indicates that several modes can co-exist giving rise to possibilities for different routes to transition