General structure of gauge boson propagator and its spectra in a hot magnetized medium

Based on transversality condition of gauge boson self-energy we have systematically constructed the general structure of the gauge boson two-point functions using four linearly independent basis tensors in presence of a nontrivial background, i.e., hot magnetized material medium. The hard thermal loop approximation has been used for the heat bath to compute various form factors associated with the gauge boson's two point functions both in strong and weak field approximation. We have also analyzed the dispersion of a gauge boson (e.g., gluon) using the effective propagator both in strong and weak magnetic field approximation. The formalism is also applicable to QED. The presence of only thermal background leads to a longitudinal (plasmon) mode and a two-fold degenerate transverse mode. In presence of a hot magnetized background medium the degeneracy of the two transverse modes is lifted and one gets three quasiparticle modes. In weak field approximation one gets two transverse modes and one plasmon mode. On the other hand, in strong field approximation also one gets the three modes in Lowest Landau Level. The general structure of two-point function may be useful for computing the thermo-magnetic correction of various quantities associated with a gauge boson.Comment: 39 pages, 7 figure

Fuzzy image segmentation of generic shaped clusters

The segmentation performance of any clustering algorithm is very sensitive to the features in an image, which ultimately restricts their generalisation capability. This limitation was the primary motivation in our investigation into using shape information to improve the generality of these algorithms. Fuzzy shape-based clustering techniques already consider ring and elliptical profiles in segmentation, though most real objects are neither ring nor elliptically shaped. This paper addresses this issue by introducing a new shape-based algorithm called fuzzy image segmentation of generic shaped clusters (FISG) that incorporates generic shape information into the framework of the fuzzy c-means (FCM) algorithm. Both qualitative and quantitative analyses confirm the superiority of FISG compared to other shape-based fuzzy clustering methods including, Gustafson-Kessel algorithm, ring-shaped, circular shell, c-ellipsoidal shells and elliptic ring-shaped clusters. The new algorithm has also been shown to be application independent so it can be applied in areas such as video object plane segmentation in MPEG-4 based coding

Three dimensional filamentary structures of a relativistic electron beam in Fast Ignition plasmas

The filamentary structures and associated electromagnetic fields of a relativistic electron beam have been studied by three dimensional particle-in-cell (PIC) simulations in the context of Fast Ignition fusion. The simulations explicitly include collisions in return plasma current and distinctly examine the effects of beam temperature and collisions on the growth of filamentary structures generated.Comment: 4 pages, 6 figures, submitted to Physics of Plasma

Do Athermal Amorphous Solids Exist?

We study the elastic theory of amorphous solids made of particles with finite range interactions in the thermodynamic limit. For the elastic theory to exist one requires all the elastic coefficients, linear and nonlinear, to attain a finite thermodynamic limit. We show that for such systems the existence of non-affine mechanical responses results in anomalous fluctuations of all the nonlinear coefficients of the elastic theory. While the shear modulus exists, the first nonlinear coefficient B_2 has anomalous fluctuations and the second nonlinear coefficient B_3 and all the higher order coefficients (which are non-zero by symmetry) diverge in the thermodynamic limit. These results put a question mark on the existence of elasticity (or solidity) of amorphous solids at finite strains, even at zero temperature. We discuss the physical meaning of these results and propose that in these systems elasticity can never be decoupled from plasticity: the nonlinear response must be very substantially plastic.Comment: 11 pages, 11 figure

A generic fuzzy rule based technique for image segmentation

Many fuzzy clustering based techniques do not incorporate the spatial relationships of the pixels, while all fuzzy rule based image segmentation techniques tend to be very much application dependent. In most techniques, the structure of the membership functions are predefined and their parameters are either automatically or manually determined. This paper addresses the aforementioned problems by introducing a general fuzzy rule based image segmentation technique, which is application independent and can also incorporate the spatial relationships of the pixels. It also proposes the automatic defining of the structure of the membership functions. A qualitative comparison is made between the segmentation results using this method and the popular fuzzy c-means (FCM) applied to two types of images: light intensity (LI) and an X-ray of the human vocal tract. The results clearly show that this method exhibits significant improvements over FCM for both types of image

Extended fuzzy rules for image segmentation

The generic fuzzy rule-based image segmentation (GFRIS) technique does not produce good results for non-homogeneous regions that possess abrupt changes in pixel intensity, because it fails to consider two important properties of perceptual grouping, namely surroundedness and connectedness. A new technique called extended fuzzy rules for image segmentation (EFRIS) is proposed, which includes a second rule to that defined already in GFRIS, that incorporates both the surroundedness and connectedness properties of a region's pixels. This additional rule is based on a split-and-merge algorithm and refines the output from the GFRIS technique. Two different classes of image, namely light intensity and medical X-rays are empirically used to assess the performance of the new technique. Quantitative evaluation of the performance of EFRIS is discussed and contrasted with GFRIS using one of the standard segmentation evaluation methods. Overall, EFRIS exhibits significantly improved results compared with the GFRIS approac

Finite Size Scaling for the Glass Transition: the Role of a Static Length Scale

Over the last decade computer simulations have had an increasing role in shedding light on difficult statistical physical phenomena and in particular on the ubiquitous problem of the glass transition. Here in a wide variety of materials the viscosity of a super-cooled liquid increases by many orders of magnitude upon decreasing the temperature over a modest range. A natural concern in these computer simulation is the very small size of the simulated systems compared to experimental ones, raising the issue of how to assess the thermodynamic limit. Here we offer a theory for the glass transition based on finite size scaling, a method that was found very useful in the context of critical phenomena and other interesting problems. As is known, the construction of such a theory rests crucially on the existence of a growing {\em static} length scale upon decreasing the temperature. We demonstrate that the static length scale that was discovered in Ref. \cite{12KLP} fits the bill extremely well, allowing us to provide a finite size scaling theory for the $\alpha$ relaxation time of the glass transition, including predictions for the thermodynamic limit based on simulations in small systems.Comment: 6 pages and 6 figure