Morphology of two-dimensional MRI in axial symmetry

In this paper, we analyse the linear stability of a stellar accretion disk having a stratified morphology. The study is performed in the framework of ideal magneto-hydrodynamics and therefore results in a characterization of the linear unstable magneto-rotational modes. The peculiarity of the present scenario consists of adopting the magnetic flux function as the basic dynamical variable. Such a representation of the dynamics allows us to take account of the co-rotation theorem as a fundamental feature of the ideal plasma equilibrium and to evaluate its impact on the perturbation evolution. According to the Alfvenic nature of the magneto-rotational instability, we consider an incompressible plasma profile and perturbations propagating along the background magnetic field. Furthermore, we develop a local perturbation analysis around fiducial coordinates of the background configuration and deal with very small-scale linear dynamics in comparison to the background inhomogeneity size. The main issue of the present study is that the condition for the emergence of unstable modes is the same in the stratified plasma disk as in the case of a thin configuration. Such a feature is the result of the cancellation of the vertical derivative of the disk angular frequency from the dispersion relation, which implies that only the radial profile of the differential rotation is responsible for the trigger of the growing modes.

Design of Digital Binoculars Image Stabilizing Optical System

Digital binoculars is the combination of digital cameras and telescopes, it not only can observe the details of the long distance target but also can record it. The field of view between photographic field lens and telescope system is the same. This paper designs the telescope system on basis of the theory of dynamic optics. The system works in visual light waveband. The field of view is , the magnification is eight and the entrance pupil diameter is 32mm. prism is selected as the image rotation prism and image stabilization prism. In order to obtain clear images in a dynamic circumstance, we utilize the rotation theorem of prism to analyze the relation between jitter compensated lens and luminous beam angle. We can calculate the position of compensated lens. So it can achieve the jitter compensation. Finally, this paper takes an application as an example. If the jittered angle is , the displacement of pixel is calculated to 1.061mm. The displacement of the compensated lens is 2.84mm. At the same time, the light still arrives to the eyepiece by the original track. So image stabilization is relative to the reference coordinate, as a result we can get the stable image.

Convex functions and the rolling circle criterion

Given0≤R1≤R2≤∞,CVG(R1,R2)denotes the class of normalized convex functionsfin the unit discU, for which∂f(U)satisfies a Blaschke Rolling Circles Criterion with radiiR1andR2. Necessary and sufficient conditions forR1=R2, growth and distortion theorems forCVG(R1,R2)and rotation theorem for the class of convex functions of bounded type, are found.

Onα-convex functions of orderβwithm-fold symmetry

This note is a continuation of the previous work [1,2,3]. First we get a new subordination forα-convex functions of orderβwhenα=1−2β, which implies the rotation theorem for(1−2β)/m-convex functions of orderβwithm-fold symmetry. Then we extend the known results onα-convex functions of orderβto the functions withm-fold symmetry. In particular, we give the sharp order of convexity ofα-convex functions of orderβwithm-fold symmetry forα≥1, which is analogous in sharpness to a result given by Miller, Mocanu and Reade [1].

Modeling of Photoelastic Constant Dependent on Arbitrary Crystal Orientation

A mathematical model is proposed to determine the photoelastic constants in arbitrary crystal orientation of Zincblende crystal structure. Tensor rotation technique is applied using Euler’s rotation theorem to develop the model. The model is applicable to evaluate photoelastic constants in terms of P11-P12 and P44 in any crystal plane by controlling the rotation angle using the model. P11-P12 and P44 are calculated for Silicon crystal and found that the values of these constants are strongly dependent on crystal orientations. The outcome of this research enables us to evaluate quantitative amount of strain in polycrystalline silicon material (solar cell material) using Scanning Infrared Polariscope. KEY WORDS - . DOI: http://dx.doi.org/10.3329/mist.v3i0.8055