Toward detailed prominence seismology - II. Charting the continuous magnetohydrodynamic spectrum

Starting from accurate MHD flux rope equilibria containing prominence condensations, we initiate a systematic survey of their linear eigenoscillations. To quantify the full spectrum of linear MHD eigenmodes, we require knowledge of all flux-surface localized modes, charting out the continuous parts of the MHD spectrum. We combine analytical and numerical findings for the continuous spectrum for realistic prominence configurations. The equations governing all eigenmodes for translationally symmetric, gravitating equilibria containing an axial shear flow, are analyzed, along with their flux-surface localized limit. The analysis is valid for general 2.5D equilibria, where either density, entropy, or temperature vary from one flux surface to another. We analyze the mode couplings caused by the poloidal variation in the flux rope equilibria, by performing a small gravity parameter expansion. We contrast the analytical results with continuous spectra obtained numerically. For equilibria where the density is a flux function, we show that continuum modes can be overstable, and we present the stability criterion for these convective continuum instabilities. Furthermore, for all equilibria, a four-mode coupling scheme between an Alfvenic mode of poloidal mode number m and three neighboring (m-1, m, m+1) slow modes is identified, occurring in the vicinity of rational flux surfaces. For realistically prominence equilibria, this coupling is shown to play an important role, from weak to stronger gravity parameter g values. The analytic predictions for small g are compared with numerical spectra, and progressive deviations for larger g are identified. The unstable continuum modes could be relevant for short-lived prominence configurations. The gaps created by poloidal mode coupling in the continuous spectrum need further analysis, as they form preferred frequency ranges for global eigenoscillations.Comment: Accepted by Astronmy & Astrophysics, 21 pages, 15 figure

Anomalous Diffusion Induced by Cristae Geometry in the Inner Mitochondrial Membrane

Diffusion of inner membrane proteins is a prerequisite for correct functionality of mitochondria. The complicated structure of tubular, vesicular or flat cristae and their small connections to the inner boundary membrane impose constraints on the mobility of proteins making their diffusion a very complicated process. Therefore we investigate the molecular transport along the main mitochondrial axis using highly accurate computational methods. Diffusion is modeled on a curvilinear surface reproducing the shape of mitochondrial inner membrane (IM). Monte Carlo simulations are carried out for topologies resembling both tubular and lamellar cristae, for a range of physiologically viable crista sizes and densities. Geometrical confinement induces up to several-fold reduction in apparent mobility. IM surface curvature per se generates transient anomalous diffusion (TAD), while finite and stable values of projected diffusion coefficients are recovered in a quasi-normal regime for short- and long-time limits. In both these cases, a simple area-scaling law is found sufficient to explain limiting diffusion coefficients for permeable cristae junctions, while asymmetric reduction of the junction permeability leads to strong but predictable variations in molecular motion rate. A geometry-based model is given as an illustration for the time-dependence of diffusivity when IM has tubular topology. Implications for experimental observations of diffusion along mitochondria using methods of optical microscopy are drawn out: a non-homogenous power law is proposed as a suitable approach to TAD. The data demonstrate that if not taken into account appropriately, geometrical effects lead to significant misinterpretation of molecular mobility measurements in cellular curvilinear membranes

From surfaces to objects : Recognizing objects using surface information and object models.

This thesis describes research on recognizing partially obscured objects using surface information like Marr's 2D sketch ([MAR82]) and surface-based geometrical object models. The goal of the recognition process is to produce a fully instantiated object hypotheses, with either image evidence for each feature or explanations for their absence, in terms of self or external occlusion. The central point of the thesis is that using surface information should be an important part of the image understanding process. This is because surfaces are the features that directly link perception to the objects perceived (for normal "camera-like" sensing) and because surfaces make explicit information needed to understand and cope with some visual problems (e.g. obscured features). Further, because surfaces are both the data and model primitive, detailed recognition can be made both simpler and more complete. Recognition input is a surface image, which represents surface orientation and absolute depth. Segmentation criteria are proposed for forming surface patches with constant curvature character, based on surface shape discontinuities which become labeled segmentation- boundaries. Partially obscured object surfaces are reconstructed using stronger surface based constraints. Surfaces are grouped to form surface clusters, which are 3D identity-independent solids that often correspond to model primitives. These are used here as a context within which to select models and find all object features. True three-dimensional properties of image boundaries, surfaces and surface clusters are directly estimated using the surface data. Models are invoked using a network formulation, where individual nodes represent potential identities for image structures. The links between nodes are defined by generic and structural relationships. They define indirect evidence relationships for an identity. Direct evidence for the identities comes from the data properties. A plausibility computation is defined according to the constraints inherent in the evidence types. When a node acquires sufficient plausibility, the model is invoked for the corresponding image structure.Objects are primarily represented using a surface-based geometrical model. Assemblies are formed from subassemblies and surface primitives, which are defined using surface shape and boundaries. Variable affixments between assemblies allow flexibly connected objects. The initial object reference frame is estimated from model-data surface relationships, using correspondences suggested by invocation. With the reference frame, back-facing, tangential, partially self-obscured, totally self-obscured and fully visible image features are deduced. From these, the oriented model is used for finding evidence for missing visible model features. IT no evidence is found, the program attempts to find evidence to justify the features obscured by an unrelated object. Structured objects are constructed using a hierarchical synthesis process. Fully completed hypotheses are verified using both existence and identity constraints based on surface evidence. Each of these processes is defined by its computational constraints and are demonstrated on two test images. These test scenes are interesting because they contain partially and fully obscured object features, a variety of surface and solid types and flexibly connected objects. All modeled objects were fully identified and analyzed to the level represented in their models and were also acceptably spatially located. Portions of this work have been reported elsewhere ([FIS83], [FIS85a], [FIS85b], [FIS86]) by the author

The geometric evolution of aortic dissections: Predicting surgical success using fluctuations in integrated Gaussian curvature

Clinical imaging modalities are a mainstay of modern disease management, but the full utilization of imaging-based data remains elusive. Aortic disease is defined by anatomic scalars quantifying aortic size, even though aortic disease progression initiates complex shape changes. We present an imaging-based geometric descriptor, inspired by fundamental ideas from topology and soft-matter physics that captures dynamic shape evolution. The aorta is reduced to a two-dimensional mathematical surface in space whose geometry is fully characterized by the local principal curvatures. Disease causes deviation from the smooth bent cylindrical shape of normal aortas, leading to a family of highly heterogeneous surfaces of varying shapes and sizes. To deconvolute changes in shape from size, the shape is characterized using integrated Gaussian curvature or total curvature. The fluctuation in total curvature (δK) across aortic surfaces captures heterogeneous morphologic evolution by characterizing local shape changes. We discover that aortic morphology evolves with a power-law defined behavior with rapidly increasing δK forming the hallmark of aortic disease. Divergent δK is seen for highly diseased aortas indicative of impending topologic catastrophe or aortic rupture. We also show that aortic size (surface area or enclosed aortic volume) scales as a generalized cylinder for all shapes. Classification accuracy for predicting aortic disease state (normal, diseased with successful surgery, and diseased with failed surgical outcomes) is 92.8±1.7%. The analysis of δK can be applied on any three-dimensional geometric structure and thus may be extended to other clinical problems of characterizing disease through captured anatomic changes

Mechanics of dented orthogonally stiffened cylinders

Imperial Users onl

Poseidon American Society of Civil Engineers/Master Builders Rocky Mountain Regional Concrete Canoe Competition

The concrete canoe team has been selected in behalf of the Utah State University Student Chapter of the American Society of Civil Engineers to prepare an entry for the 1998 ASCE Rocky Mountain Regional Concrete Canoe Competition. This event is co-sponsored by the American Society of Civil Engineers and Master Builders, Inc., and has become a tradition at annual ASCE regional conferences nationwide

Self-Limiting Morphologies in Geometrically Frustrated Assemblies

Geometrically frustrated assembly, where locally preferred motifs are incompatible with constraints on global ordering of the assembly, may result in a super-extensive energy penalty to assembly growth and self-limitation of the assembly size. Using theory and simulation, we study how this mechanism may also shape the assembly\u27s boundary and its interior packing, which are distinct morphological changes. In Chapter 1, we provide some background and a theoretical framework for understanding self-limiting behavior due to geometric frustration. Three distinct projects are detailed in the subsequent chapters: original numerical results are presented on competing responses to frustration in helical bundles made of chiral filaments in Chapter 2, a novel tilt-curvature coupling and its consequences in microphase separated chiral rod membranes are illustrated by both numerical and theoretical results in Chapter 3, and a new particle model for simulation of saddle-wedge membrane assemblies with new theoretical advancement of a continuum model and new numerical results are presented in Chapter 4. In Chapter 5, we conclude by considering lessons from this work for future engineering of self-limiting materials