A microscopic time scale approximation to the behavior of the local slope on the faceted surface under a nonuniformity in supersaturation

The morphological stability of a growing faceted crystal is discussed. It has been explained hat the interplay between nonuniformity in supersaturation on a growing facet and nisotropy of surface kinetics derived from the lateral motion of steps leads to a faceted nstability. Qualitatively speaking, as long as the nonuniformity in supersaturation on the acet is not too large, it can be compensated by a variation of step density along the facet nd the faceted crystal can grow in a stable manner. The problem can be modeled as a amilton-Jacobi equation for height of the crystal surface. The notion of a maximal stable egion of a growing facet is introduced for microscopic time scale approximation of the riginal Hamilton-Jacobi equation. It is shown that the maximal stable region keeps its hape, determined by profile of the surface supersaturation, with constant growth rate by tudying large time behavior of solution of macroscopic time scale approximation. As a esult, a quantitative criterion for the facet stability is given

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Brain Alterations and Mini-Mental State Examination in Patients with Progressive Supranuclear Palsy: Voxel-Based Investigations Using 18F-Fluorodeoxyglucose Positron Emission Tomography and Magnetic Resonance Imaging

Background/Aims: The aim of this study was to compare differences in morphological and functional changes in brain regions in individual patients with progressive supranuclear palsy (PSP) and correlate their Mini-Mental State Examination (MMSE) score with anatomy and function using magnetic resonance imaging (MRI) and 18F-fluorodeoxyglucose positron emission tomography (FDG-PET). Methods: Sixteen PSP patients and 20 age-matched healthy volunteers underwent FDG-PET and 3-dimensional MRI. Gray matter, white matter and metabolic activity were compared between patients and normal controls. In addition, possible correlations between the MMSE score and brain function/anatomy were examined. Results: The PSP group had reduced cerebral glucose metabolism, and lower gray and white matter volumes in the frontal lobes and midbrain compared with normal controls. In PSP subjects, the metabolic changes observed in the PET scans were greater than the loss in gray and white matter observed in the MRI scans. The MMSE scores were positively correlated with volume and FDG uptake in the frontal lobe. Conclusion: FDG-PET is a more effective tool in the diagnosis of PSP than MRI. Atrophy and hypometabolism in the frontal lobe are as important as in the basal midbrain for differentiating PSP patients who primarily exhibit cognitive dysfunction from normal controls

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