VELOCITY FIELD OF COMPRESSIBLE MAGNETOHYDRODYNAMIC TURBULENCE: WAVELET DECOMPOSITION AND MODE SCALINGS

We study compressible magnetohydrodynamic turbulence, which holds the key to many astrophysical processes, including star formation and cosmic-ray propagation. To account for the variations of the magnetic field in the strongly turbulent fluid, we use wavelet decomposition of the turbulent velocity field into Alfven, slow, and fast modes, which presents an extension of the Cho & Lazarian decomposition approach based on Fourier transforms. The wavelets allow us to follow the variations of the local direction of the magnetic field and therefore improve the quality of the decomposition compared to the Fourier transforms, which are done in the mean field reference frame. For each resulting component, we calculate the spectra and two-point statistics such as longitudinal and transverse structure functions as well as higher order intermittency statistics. In addition, we perform a Helmholtz-Hodge decomposition of the velocity field into incompressible and compressible parts and analyze these components. We find that the turbulence intermittency is different for different components, and we show that the intermittency statistics depend on whether the phenomenon was studied in the global reference frame related to the mean magnetic field or in the frame defined by the local magnetic field. The dependencies of the measures we obtained are different for different components of the velocity; for instance, we show that while the Alfven mode intermittency changes marginally with the Mach number, the intermittency of the fast mode is substantially affected by the change.

Hierarchical spherical model from a geometric point of view

A continuous version of the hierarchical spherical model at dimension d=4 is investigated. Two limit distributions of the block spin variable X(gamma), normalized with exponents gamma = d + 2 and gamma=d at and above the critical temperature, are established. These results are proven by solving certain evolution equations corresponding to the renormalization group (RG) transformation of the O(N) hierarchical spin model of block size L(d) in the limit L down arrow 1 and N ->infinity. Starting far away from the stationary Gaussian fixed point the trajectories of these dynamical system pass through two different regimes with distinguishable crossover behavior. An interpretation of this trajectories is given by the geometric theory of functions which describe precisely the motion of the Lee-Yang zeroes. The large-N limit of RG transformation with L(d) fixed equal to 2, at the criticality, has recently been investigated in both weak and strong (coupling) regimes by Watanabe (J. Stat. Phys. 115:1669-1713, 2004) . Although our analysis deals only with N = infinity case, it complements various aspects of that work.

Gravitational field of a straight cosmic string in the framework of higher-derivative gravity

The gravitational properties of a straight cosmic string are studied in the linear approximation of higher-derivative gravity. These properties are shown to be very different from those found using linearized Einstein gravity: there exists a short range gravitational (anti-gravitational) force in the nonrelativistic limit; in addition, the derection angle of a light ray moving in a plane orthogonal to the string depends on the impact parameter.

Objective Detection and Delineation of Oral Neoplasia Using Autofluorescence Imaging

Although the oral cavity is easily accessible to inspection, patients with oral cancer most often present at a late stage, leading to high morbidity and mortality. Autofluorescence imaging has emerged as a promising technology to aid clinicians in screening for oral neoplasia and as an aid to resection, but current approaches rely on subjective interpretation. We present a new method to objectively delineate neoplastic oral mucosa using autofluorescence imaging. Autofluorescence images were obtained from 56 patients with oral lesions and 11 normal volunteers. From these images, 276 measurements from 159 unique regions of interest (ROI) sites corresponding to normal and confirmed neoplastic areas were identified. Data from ROIs in the first 46 subjects were used to develop a simple classification algorithm based on the ratio of red-to-green fluorescence; performance of this algorithm was then validated using data from the ROIs in the last 21 subjects. This algorithm was applied to patient images to create visual disease probability maps across the field of view. Histologic sections of resected tissue were used to validate the disease probability maps. The best discrimination between neoplastic and nonneoplastic areas was obtained at 405 nm excitation; normal tissue could be discriminated from dysplasia and invasive cancer with a 95.9% sensitivity and 96.2% specificity in the training set, and with a 100% sensitivity and 91.4% specificity in the validation set. Disease probability maps qualitatively agreed with both clinical impression and histology. Autofluorescence imaging coupled with objective image analysis provided a sensitive and noninvasive tool for the detection of oral neoplasia.