Generation of large-scale magnetic fields due to fluctuating α\alpha in shearing systems

We explore the growth of large-scale magnetic fields in a shear flow, due to helicity fluctuations with a finite correlation time, through a study of the Kraichnan-Moffatt model of zero-mean stochastic fluctuations of the $\alpha$ parameter of dynamo theory. We derive a linear integro-differential equation for the evolution of large-scale magnetic field, using the first-order smoothing approximation and the Galilean invariance of the $\alpha$-statistics. This enables construction of a model that is non-perturbative in the shearing rate $S$ and the $\alpha$-correlation time $\tau_\alpha$. After a brief review of the salient features of the exactly solvable white-noise limit, we consider the case of small but non-zero $\tau_\alpha$. When the large-scale magnetic field varies slowly, the evolution is governed by a partial differential equation. We present modal solutions and conditions for the exponential growth rate of the large-scale magnetic field, whose drivers are the Kraichnan diffusivity, Moffatt drift, Shear and a non-zero correlation time. Of particular interest is dynamo action when the $\alpha$-fluctuations are weak; i.e. when the Kraichnan diffusivity is positive. We show that in the absence of Moffatt drift, shear does not give rise to growing solutions. But shear and Moffatt drift acting together can drive large scale dynamo action with growth rate $\gamma \propto |S|$.Comment: 19 pages, 4 figures, Accepted in Journal of Plasma Physic

Properties of pp- and ff-modes in hydromagnetic turbulence

With the ultimate aim of using the fundamental or $f$-mode to study helioseismic aspects of turbulence-generated magnetic flux concentrations, we use randomly forced hydromagnetic simulations of a piecewise isothermal layer in two dimensions with reflecting boundaries at top and bottom. We compute numerically diagnostic wavenumber-frequency diagrams of the vertical velocity at the interface between the denser gas below and the less dense gas above. For an Alfv\'en-to-sound speed ratio of about 0.1, a 5% frequency increase of the $f$-mode can be measured when $k_xH_{\rm p}=3$-$4$, where $k_x$ is the horizontal wavenumber and $H_{\rm p}$ is the pressure scale height at the surface. Since the solar radius is about 2000 times larger than $H_{\rm p}$, the corresponding spherical harmonic degree would be 6000-8000. For weaker fields, a $k_x$-dependent frequency decrease by the turbulent motions becomes dominant. For vertical magnetic fields, the frequency is enhanced for $k_xH_{\rm p}\approx4$, but decreased relative to its nonmagnetic value for $k_xH_{\rm p}\approx9$.Comment: 17 pages, 22 figures, Version accepted in MNRA

Transport coefficients for the shear dynamo problem at small Reynolds numbers

We build on the formulation developed in Sridhar & Singh (JFM, 664, 265, 2010), and present a theory of the \emph{shear dynamo problem} for small magnetic and fluid Reynolds numbers, but for arbitrary values of the shear parameter. Specializing to the case of a mean magnetic field that is slowly varying in time, explicit expressions for the transport coefficients, $\alpha_{il}$ and $\eta_{iml}$, are derived. We prove that, when the velocity field is non helical, the transport coefficient $\alpha_{il}$ vanishes. We then consider forced, stochastic dynamics for the incompressible velocity field at low Reynolds number. An exact, explicit solution for the velocity field is derived, and the velocity spectrum tensor is calculated in terms of the Galilean--invariant forcing statistics. We consider forcing statistics that is non helical, isotropic and delta-correlated-in-time, and specialize to the case when the mean-field is a function only of the spatial coordinate $X_3$ and time $\tau\,$; this reduction is necessary for comparison with the numerical experiments of Brandenburg, R{\"a}dler, Rheinhardt & K\"apyl\"a (ApJ, 676, 740, 2008). Explicit expressions are derived for all four components of the magnetic diffusivity tensor, $\eta_{ij}(\tau)\,$. These are used to prove that the shear-current effect cannot be responsible for dynamo action at small \re and \rem, but for all values of the shear parameter.Comment: 27 pages, 5 figures, Published in Physical Review

The shear dynamo problem for small magnetic Reynolds numbers

We study large-scale dynamo action due to turbulence in the presence of a linear shear flow, in the low conductivity limit. Our treatment is nonperturbative in the shear strength and makes systematic use of both the shearing coordinate transformation and the Galilean invariance of the linear shear flow. The velocity fluctuations are assumed to have low magnetic Reynolds number (Rm) but could have arbitrary fluid Reynolds number. The magnetic fluctuations are determined to lowest order in Rm by explicit calculation of the resistive Green's function for the linear shear flow. The mean electromotive force is calculated and an integro-differential equation is derived for the time evolution of the mean magnetic field. In this equation, velocity fluctuations contribute to two different kinds of terms, the C and D terms, in which first and second spatial derivatives of the mean magnetic field, respectively, appear inside the spacetime integrals. The contribution of the D terms is such that the time evolution of the cross-shear components of the mean field do not depend on any other components excepting themselves. Therefore, to lowest order in Rm but to all orders in the shear strength, the D terms cannot give rise to a shear-current assisted dynamo effect. Casting the integro-differential equation in Fourier space, we show that the normal modes of the theory are a set of shearing waves, labelled by their sheared wavevectors. The integral kernels are expressed in terms of the velocity spectrum tensor, which is the fundamental quantity that needs to be specified to complete the integro-differential equation description of the time evolution of the mean magnetic field.Comment: Near-final version; Accepted for publication in the Journal of Fluid Mechanics; References added; 22 pages, 2 figure

Neuroadaptive Model Following Controller Design for a Nonaffine UAV Model

This paper proposes a new model-following adaptive control design technique for nonlinear systems that are nonaffine in control. The adaptive controller uses online neural networks that guarantee tracking in the presence of unmodeled dynamics and/or parameter uncertainties present in the system model through an online control adaptation procedure. The controller design is carried out in two steps: (i) synthesis of a set of neural networks which capture the unmodeled (neglected) dynamics or model uncertainties due to parametric variations and (ii) synthesis of a controller that drives the state of the actual plant to that of a reference model. This method is tested using a three degree of freedom model of a UAV. Numerical results which demonstrate these features and clearly bring out the potential of the proposed approach are presented in this paper

Trichoscopic findings in cicatricial alopecias and hair shaft disorders and its application in histopathology

Background: Many studies have been published on dermoscopy of hair and scalp disorders in the past few years, but these have been mainly carried out in western countries. Indian skin is mainly type IV and V and has its own unique set of problems and pathological findings. Hence, we conducted a study at our institute to study the dermoscopic patterns of various cicatricial alopecias.Methods: This was a descriptive study conducted in the Dermatology outpatient department, Skinaccess clinics, Nashik, between August 2014 to June 2016. The most common and characteristic feature seen in patients with cicatricial alopecia was hair follicle effacement seen in all 24 patients (100%). Hair follicle plugging was seen in 6 (25%) patients with DLE, and one patient with idiopathic scarring. Hyperkeratotic perifollicular scaling was seen in 2 patients with lichen plano pilaris. Perifollicular hyperpigmentation was seen in one patient of discoid lupus erythematosus (DLE) and 2 patients with idiopathic scarring. Hair casts were seen in 2 patients with lichen plano pilaris, and in one patient with idiopathic scarring. Patchy depigmentation was seen in 4 patients with discoid lupus erythematosus, 3 patients with idiopathic scarring, and one patient with lichen plano pilaris.Results: The most common and characteristic feature seen in patients with cicatricial alopecia was hair follicle effacement seen in all 24 patients (100%). Hair follicle plugging was seen in 6 (25%) patients with DLE, and one patient with idiopathic scarring. Hyperkeratotic perifollicular scaling was seen in 2 patients with lichen plano pilaris. Perifollicular hyperpigmentation was seen in one patient of discoid lupus erythematosus (DLE) and 2 patients with idiopathic scarring. Hair casts were seen in 2 patients with lichen plano pilaris, and in one patient with idiopathic scarring. Patchy depigmentation was seen in 4 patients with discoid lupus erythematosus, 3 patients with idiopathic scarring, and one patient with lichen plano pilaris.Conclusions: Hair follicle effacement is a characteristic dermoscopic feature of cicatricial alopecia. Hair follicle plugging, patchy depigmentation and red dots are seen in DLE. In lichen plano pilaris the dermoscopic findings of blue dots, white dots and perifollicular scaling were found to be useful for making an accurate diagnosis. Perifollicular scaling and tufting of hair is characteristically seen in patients with folliculitis decalvans. Dermoscopy is very useful in differentiating cicatricial from non-cicatricial alopecias. A biopsy obtained from the peripheral edge of the patch is more likely to show diagnostic features than the central portion. Dermoscopic guided biopsies were shown to yield definitive pathological diagnosis in 95% of the cases. Hair shaft disorders can be easily diagnosed by dermoscopy, without the need for hair

Angiotensin II blockade and aortic-root dilation in Marfan's syndrome

Background: Progressive enlargement of the aortic root, leading to dissection, is the main cause of premature death in patients with Marfan's syndrome. Recent data from mouse models of Marfan's syndrome suggest that aortic-root enlargement is caused by excessive signaling by transforming growth factor (beta) (TGF-(beta)) that can be mitigated by treatment with TGF-(beta) antagonists, including angiotensin II-receptor blockers (ARBs). We evaluated the clinical response to ARBs in pediatric patients with Marfan's syndrome who had severe aortic-root enlargement. Methods: We identified 18 pediatric patients with Marfan's syndrome who had been followed during 12 to 47 months of therapy with ARBs after other medical therapy had failed to prevent progressive aortic-root enlargement. The ARB was losartan in 17 patients and irbesartan in 1 patient. We evaluated the efficacy of ARB therapy by comparing the rates of change in aortic-root diameter before and after the initiation of treatment with ARBs. Results: The mean (+/-SD) rate of change in aortic-root diameter decreased significantly from 3.54+/-2.87 mm per year during previous medical therapy to 0.46+/-0.62 mm per year during ARB therapy (P<0.001). The deviation of aortic-root enlargement from normal, as expressed by the rate of change in z scores, was reduced by a mean difference of 1.47 z scores per year (95% confidence interval, 0.70 to 2.24; P<0.001) after the initiation of ARB therapy. The sinotubular junction, which is prone to dilation in Marfan's syndrome as well, also showed a reduced rate of change in diameter during ARB therapy (P<0.05), whereas the distal ascending aorta, which does not normally become dilated in Marfan's syndrome, was not affected by ARB therapy. Conclusions: In a small cohort study, the use of ARB therapy in patients with Marfan's syndrome significantly slowed the rate of progressive aortic-root dilation. These findings require confirmation in a randomized trial

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