Symmetric space description of carbon nanotubes

Using an innovative technique arising from the theory of symmetric spaces, we obtain an approximate analytic solution of the Dorokhov-Mello-Pereyra-Kumar (DMPK) equation in the insulating regime of a metallic carbon nanotube with symplectic symmetry and an odd number of conducting channels. This symmetry class is characterized by the presence of a perfectly conducting channel in the limit of infinite length of the nanotube. The derivation of the DMPK equation for this system has recently been performed by Takane, who also obtained the average conductance both analytically and numerically. Using the Jacobian corresponding to the transformation to radial coordinates and the parameterization of the transfer matrix given by Takane, we identify the ensemble of transfer matrices as the symmetric space of negative curvature SO^*(4m+2)/[SU(2m+1)xU(1)] belonging to the DIII-odd Cartan class. We rederive the leading-order correction to the conductance of the perfectly conducting channel and its variance Var(log(delta g)). Our results are in complete agreement with Takane's. In addition, our approach based on the mapping to a symmetric space enables us to obtain new universal quantities: a universal group theoretical expression for the ratio Var(log(delta g)/ and as a byproduct, a novel expression for the localization length for the most general case of a symmetric space with BC_m root system, in which all three types of roots are present.Comment: 23 pages. Text concerning symmetric space description augmented, table and references added. Version to be published on JSTA

Multiparametric Imaging and MR Image Texture Analysis in Brain Tumors

Discrimination of tumor from radiation injured (RI) tissues and differentiation of tumor types using noninvasive imaging is essential for guiding surgical and radiotherapy treatments are some of the challenges that clinicians face in the course of treatment of brain tumors. The first objective in this thesis was to develop a method to discriminate between glioblastoma tumor recurrences and radiation injury using multiparametric characterization of the tissue incorporating conventional magnetic resonance imaging signal intensities and diffusion tensor imaging parameters. Our results show significant correlations in the RI that was missing in the tumor regions. These correlations may aid in differentiating between tumor recurrence and RI. The second objective of was to investigate whether texture based image analysis of routine MR images would provide quantitative information that could be used to differentiate between glioblastoma and metastasis. Our results demonstrate that first-order texture feature of standard deviation and second-order texture features of entropy, inertia, homogeneity, and energy show significant differences between the two groups. The third objective was to investigate whether quantitative measurements of tumor size and appearance on MRI scans acquired prior to helical tomotherapy (HT) type whole brain radiotherapy with simultaneous infield boost treatment could be used to differentiate responder and non-responder patient groups. Our results demonstrated that smaller size lesions may respond better to this type of radiation therapy. Measures of appearance provided limited added value over measures of size for response prediction. Quantitative measurements of rim enhancement and core necrosis performed separately did not provide additional predictive value

Effects of orbital exposure on Halar during the LDEF mission

Thermomechanical Analysis (TMA), Differential Scanning Calorimetry (DSC), and Thermogravimetric Analysis (TGA) were performed on samples of Halar exposed on the LDEF Mission for 6 years in orbit and unexposed Halar control samples. Sections 10-100 microns thick were removed from the exposed surface down to a depth of 1,000 microns through the 3 mm thick samples. The TMA and DSC results, which arise from the entire slice and not just its surface, showed no differences between the LDEF and the control samples. TMA scans were run from ambient to 300 C; results were compared by a tabulation of the glass transition temperatures. DSC scans were run from ambient to 700 C; the enthalpy of melting was compared for the samples as a function of section depth with the sample. The TGA results, which arise from the surface of the sample initially, showed a sharp increase in the topmost 50 micron section (the exposed, discolored side) in the weight loss of 170 C in oxygen. This weight loss dropped to bulk values in the range of depth of 50-200 microns. The control sample showed only a slight increase in weight loss as the top surface was approached. The LDEF Halar sample appears to be mechanically undamaged, with a surface layer which oxidizes faster as a result of orbital exposure

Novel spectral kurtosis technology for adaptive vibration condition monitoring of multi-stage gearboxes

In this paper, the novel wavelet spectral kurtosis (WSK) technique is applied for the early diagnosis of gear tooth faults. Two variants of the wavelet spectral kurtosis technique, called variable resolution WSK and constant resolution WSK, are considered for the diagnosis of pitting gear faults. The gear residual signal, obtained by filtering the gear mesh frequencies, is used as the input to the SK algorithm. The advantages of using the wavelet-based SK techniques when compared to classical Fourier transform (FT)-based SK is confirmed by estimating the toothwise Fisher's criterion of diagnostic features. The final diagnosis decision is made by a three-stage decision-making technique based on the weighted majority rule. The probability of the correct diagnosis is estimated for each SK technique for comparison. An experimental study is presented in detail to test the performance of the wavelet spectral kurtosis techniques and the decision-making technique