Elliptical Geometry Research Articles

Hybrid Cardiac Imaging Integrating Elliptical Orbit SPECT With CT

The cardiac single photon emission computed tomography (SPECT) is an important research topic because of the large clinical demand and the need for improving image quality. It usually suffers from low count sensitivity and poor spatial resolution due to patient radiation safety concerns. In this study, hybrid cardiac imaging integrating elliptical orbit SPECT (E-SPECT) with computed tomography (CT) is proposed to better obtain the anatomical and physiological information of the cardiac and vascular systems. The geometric structure of this proposed hybrid imaging system is similar to that of an ellipse, containing multiple detectors with slit-slat collimation. The hybrid imaging system utilizes the elliptical geometry and multi-detectors to improve the sensitivity and signal to noise ratio (SNR), and incorporates a CT scanner into the system to obtain an accurate attenuation mapping matrix of the patient for image reconstruction. The iterative reconstruction algorithm with some constraints is used to reconstruct images. The constraint-based body contour is introduced to deal with severely truncated data from E-SPECT. The feasibility and advantage of the system is validated by simulations. Simulation results show that it is optimal for system design and the quality of reconstructed images are greatly improved. With an optimal sampling coverage angle between 210° and 240°, the hybrid cardiac imaging system proposed in the paper can achieves significant improvements in image spatial resolution, SNR and image fidelity.

Biomechanical Modeling of Wounded Skin

Skin injury is the most common type of injury, which manifests itself in the form of wounds and cuts. A minor wound repairs itself within a short span of time. However, deep wounds require adequate care and sometime clinical interventions such as surgical suturing for their timely closure and healing. In literature, mechanical properties of skin and other tissues are well known. However, the anisotropic behavior of wounded skin has not been studied yet, specifically with respect to localized overstraining and possibilities of rupture. In the current work, the biomechanics of common skin wound geometries were studied with a biofidelic skin phantom, using uniaxial mechanical testing and Digital Image Correlation (DIC). Global and local mechanical properties were investigated, and possibilities of rupture due to localized overstraining were studied across different wound geometries and locations. Based on the experiments, a finite element (FE) model was developed for a common elliptical skin wound geometry. The fidelity of this FE model was evaluated with simulation of uniaxial tension tests. The induced strain distributions and stress-stretch responses of the FE model correlated very well with the experiments (R2 > 0.95). This model would be useful for prediction of the mechanical response of common wound geometries, especially with respect to their chances of rupture due to localized overstraining. This knowledge would be indispensable for pre-surgical planning, and also in robotic surgeries, for selection of appropriate wound closure techniques, which do not overstrain the skin tissue or initiate tearing.

Investigating the impact models for nanoparticles manipulation based on atomic force microscope (according to contact mechanics)

The impact in the nano scale, especially for the softer nanoparticles, is very important. As a result, the effect of different loadings on the contact process of nanoparticles and nanoparticles impact before initiation of contact are studied in this paper. To investigate the nanoparticles impact before contact begins, three theories including Hertz, JKR and Jamari are investigated. Regarding the impact, cubic and elliptical geometries are selected for nanoparticles. In order to study the contact process more comprehensively, the contact of nanoparticles is studied using the governing equations of elasticity. To validate the results, the developed models and an experimental sample are compared with each other. The sample has a relatively soft polystyrene surface. In comparison between the experimental results for force – displacement graph shows that by considering the initial impact the results accuracy improves up to 2.23%.

Effect of leading-edge geometry on the aerodynamics and heat transfer in the stagnation region of uncooled turbine blades

The flow in the leading-edge stagnation region of uncooled turbine aerofoils is studied. The stagnation region is modelled based on the Hiemenz flow solution, following Holley and Langston (J. Turbomach. 130: 021001, 2008). These results are applied to the JT9D turbine blade and confirmed by computations. It is also shown that the heat transfer at the stagnation point is bounded by the Hiemenz flow and plane stagnation-point potential flow heat transfer solutions. The computations are further extended for a range of Reynolds numbers and freestream turbulence intensities. It is seen that for a wide range of these parameters considered in the present study and data collected from published literature, a majority of the data points are within these bounds. The leading-edge geometry of the JT9D turbine blade is modified with elliptical geometries. Blunter-leading-edge geometries have lower values of heat transfer at the stagnation region; however, their blade profile loss coefficients are higher. The off-design performance characteristics of the turbine blades are also computed. The results presented in this paper will be useful in designing leading-edge geometries for reduced heat transfer in the stagnation region of uncooled turbine blades.

Shifted Poisson structures and moduli spaces of complexes

In this paper we study the moduli stack of complexes of vector bundles (with chain isomorphisms) over a smooth projective variety X via derived algebraic geometry. We prove that if X is a Calabi–Yau variety of dimension d then this moduli stack has a (1−d)-shifted Poisson structure. In the case d=1, we construct a natural foliation of the moduli stack by 0-shifted symplectic substacks. We show that our construction recovers various known Poisson structures associated to complex elliptic curves, including the Poisson structure on Hilbert scheme of points on elliptic quantum projective planes studied by Nevins and Stafford, and the Poisson structures on the moduli spaces of stable triples over an elliptic curves considered by one of us. We also relate the latter Poisson structures to the semi-classical limits of the elliptic Sklyanin algebras studied by Feigin and Odesskii.

Non-local entropy evolution in heat exchangers with elliptical and circular tube geometries

Numerical simulations of the entropy transportation process inside a plate and tube heat exchanger are presented. Entropy levels around tubes with circular and elliptical cross sections are analyzed and compared. The purpose of the comparison is to determine how the entropy flux contributes to increase, or decrease, the value of the entropy in certain regions of the flow field. This is accomplished by numerically integrating the Reynolds averaged transport equations for the mass, momentum, energy and entropy, in a three dimensional domain. A k-ε-2L model is used to account for the fluctuations appearing in the laminar-to-turbulent transitional regime of the flow. The importance of entropy convection, relative to the generation of entropy, is underlined by means of a direct comparison through a series of visualization maps. This approach allows some useful insights about the evolution of the entropy field in complex geometries. For example, in this case certain troublesome regions where the entropy field reaches high values can be identified and, therefore, design recommendations can be stated in order to increase the thermal efficiencies of the devices under consideration.

Longitudinal fluctuations and decorrelations of anisotropic flows at energies available at the CERN Large Hadron Collider and at the BNL Relativistic Heavy Ion Collider

We perform a systematic study on the decorrelation of anisotropic flows along the pseudorapidity in relativistic heavy-ion collisions at the LHC and RHIC energies. The dynamical evolution of the QGP fireball is simulated via the CLVisc (ideal) (3+1)-dimensional hydrodynamics model, with the fully fluctuating initial condition from A-Multi-Phase-Transport (AMPT) model. Detailed analysis is performed on the longitudinal decorrelations of elliptic, triangular and quadrangular flows in terms of flow vectors, flow magnitudes and flow orientations (event planes). It is found that pure flow magnitudes have smaller longitudinal decorrelation than pure flow orientations, and the decorrelation of flow vectors is a combined effect of both flow magnitudes and orientations. The longitudinal decorrelation of elliptic flow has a strong and non-monotonic centrality dependence due to the initial elliptic collision geometry: smallest decorrelation in mid-central collisions. In contrast, the decorrelations of triangular and quadrangular flows have weak centrality dependence, slightly larger decorrelations in more peripheral collisions. Our numerical results for Pb+Pb collisions at the LHC are in good agreement with the ATLAS data, while our RHIC results predict much larger longitudinal decorrelations as compared to the LHC. We further analyze the longitudinal structures of the AMPT initial conditions and find that the final-state longitudinal decorrelation effects are strongly correlated with the lengths of the initial string structures in the AMPT model. The decorrelation effects are typically larger at lower collision energies and in more peripheral collisions due to shorter lengths of the string structures in the initial states.

Symmetry in Regular Polyhedra Seen as 2D Möbius Transformations: Geodesic and Panel Domes Arising from 2D Diagrams

This paper shows a methodology for reducing the complex design process of space structures to an adequate selection of points lying on a plane. This procedure can be directly implemented in a bi-dimensional plane when we substitute (i) Euclidean geometry by bi-dimensional projection of the elliptic geometry and (ii) rotations/symmetries on the sphere by Möbius transformations on the plane. These graphs can be obtained by sites, specific points obtained by homological transformations in the inversive plane, following the analogous procedure defined previously in the three-dimensional space. From the sites, it is possible to obtain different partitions of the plane, namely, power diagrams, Voronoi diagrams, or Delaunay triangulations. The first would generate geo-tangent structures on the sphere; the second, panel structures; and the third, lattice structures.

MECHANICAL PROPERTIES CHANGE IN THE RAT XENOGRAFT MODEL TREATED BY MESENCHYMAL CELLS CULTURED IN AN HYALURONIC ACID-BASED HYDROGEL

This study investigated the efficiency of a cellular therapy with mesenchymal stem cells (MSCs) cultured in an hyaluronic acid-based hydrogel on growth of abdominal aortic aneurysms (AAA) obtained in the rat xenograft model. The experimental model was devoted to create an AAA at D14 after grafting of a decellularized abdominal aorta obtained from guinea pigs before being transplanted into rats. At D21, geometrical measurements as radius and length of AAA were performed on untreated ([Formula: see text]) and treated ([Formula: see text]) arteries. When compared to different cases, it was shown that the proposed cellular treatment significantly reduced the expansion of radius and length of AAA. Furthermore, to explore the mechanical properties change of the arterial wall, an inverse finite element method was performed where AAA is represented by an elliptical geometry with varying thicknesses. To identify the material parameters, the AAA tissue was assumed to behave isochoric and isotropic undergoing large strains and described by the Yeoh’s strain energy function. Although limitations exist in this study such as the time of the experimental protocol, the isotropic behavior law of the AAA wall and the axisymmetric geometry of the artery, the results revealed that arterial wall stiffness change and the maximum effective stress decreased during expansion of AAA when cellular treatment is applied.

Impact of elliptical boreholes on in situ stress estimation from leak-off test data

We developed an inversion technique to determine in situ stresses for elliptical boreholes of arbitrary trajectory. In this approach, borehole geometry, drilling-induced fracture information, and other available leak-off test data were used to construct a mathematical model, which was in turn applied to finding the inverse of an overdetermined system of equations. The method has been demonstrated by a case study in the Appalachian Basin, USA. The calculated horizontal stresses are in reasonable agreement with the reported regional stress study of the area, although there are no field measurement data of the studied well for direct calibration. The results also indicate that 2% of axis difference in the elliptical borehole geometry can cause a 5% difference in minimum horizontal stress calculation and a 10% difference in maximum horizontal stress calculation.

Lie Algebroid Invariants for Subgeometry

We investigate the infinitesimal invariants of an immersed submanifold $\Sigma $ of a Klein geometry $M\cong G/H$, and in particular an invariant filtration of Lie algebroids over $\Sigma $. The invariants are derived from the logarithmic derivative of the immersion of $\Sigma $ into $M$, a complete invariant introduced in the companion article, 'A characterization of smooth maps into a homogeneous space'. Applications of the Lie algebroid approach to subgeometry include a new interpretation of Cartan's method of moving frames and a novel proof of the fundamental theorem of hypersurfaces in Euclidean, elliptic and hyperbolic geometry.

Image processing and data evaluation algorithms for reproducible optical in-plane permeability characterization by radial flow experiments

Textile permeability is one of the dictating factors in the fabrication of fibre-reinforced polymer composites. However, reproducibility of experimental in-plane permeability characterization is still a challenging task due to the lack of standardized test and evaluation procedures. The paper at hand addresses two major sources for discrepancies when characterizing in-plane permeability through optical observation of radial flow experiments: digital image processing and data evaluation algorithms. A digital image processing strategy is presented, which robustly handles varying lightning conditions, optical properties of the materials under test and image occlusions caused by mechanical elements of the test setup. The strategy is of universal validity and independent of the choice of reinforcing material and impregnating fluid. An experimental analysis compares two approaches for fitting elliptic geometry models to data points detected along the fluid flow front. The study reveals the impact of the fitting strategy on the resulting permeability data and the benefit of forcing the ellipse centre to that of the injection opening. The computation algorithm of Chan and Hwang, widely used for calculating in-plane permeability values from experimental data, is critically discussed. A correction of the algorithm is proposed which avoids a violation of isotropic data characteristics while adding robustness to the data reduction. An experimental analysis compares anisotropic in-plane permeability values obtained with different evaluation algorithms. The study highlights the impact of the computational algorithm on the permeability data and reveals discrepancies of up to 6%, which is considerable compared to the scatter typically reported for in-plane permeability data.

Geometrical Modeling of Scattering Environment for Highways in Umbrella Cell Based MIMO Communication Systems

In this paper, we develop a three-dimensional (3D) eccentricity-based cylindrical geometrical channel model for nonisotropic multiple-input-multiple-output (MIMO) communication systems under umbrella macrocellular environment. We use elliptic cylindrical geometry to model the scattering phenomenon in streets, canyons and highways. The scattering objects like, high-rise building, trees and vegetation that lie along the roadside premises are modeled by the height of an elliptical cylinder. The proposed channel model targets fast moving vehicles on the highways in an umbrella-cell of cellular communication networks. We assume that both ends of the communication link are equipped with multiple antenna arrays, where, mobile-station antenna height is lower than base-station antenna. Utilizing the proposed MIMO communication channel model, we obtain closed-form expressions for the space–time correlation function among the MIMO antenna elements. The obtained theoretical expressions are plotted and analyzed for different values of channel parameters. Finally, we compare the proposed model with the existing models in the literature and prove that our model can be deduced to the existing two-dimensional and 3D channel models.

Differential Transmission Line Loop for RFID Reactive Near-Field Coupling

The differential transmission line loop (DTLL) as an efficient reactive near-field coupling element for programming of radio frequency identification (RFID) inlays is proposed. It is validated, with simulations and measurements, that the differential excitation and the presence of a ground plane are fundamental properties for high performance in coupling while providing high electromagnetic isolation. As a proof of concept, super elliptical loop geometries as coupling elements are investigated for a number of commercially available inlay geometries. From simulations of the DTLL and inlay antenna, coupling efficiencies higher than 80% are predicted. Measurements of the $\Delta \Gamma $ -value indicate a nonlinear input impedance with power, and verify the high values of simulated coupling efficiency. The threshold power levels read from interrogator are below 5 dBm, which are considered as very low in inlay encoding, and hence show that the DTLL is a promising candidate for efficient RFID programming in the reactive near field.

Investigation of shaft stability and anisotropic deformation in a deep shaft in Idaho, United States

During construction of a deep shaft at Hecla's Lucky Friday Mine, excessive anisotropic ground deformation led to significant damage to the shaft liner. This necessitated a major design change during construction, with the excavated shape of the shaft being changed from a circular to an approximately elliptical geometry. This study utilizes extensometer data collected during construction as well as a three-dimensional finite-difference model of stress redistribution around the shaft and a calibrated two-dimensional discontinuum numerical model to develop an understanding of the factors affecting the relative stability of both shaft geometries. Although the focus of the work is the deformation behavior of the foliated rock surrounding the shaft, the role of liner installation in suppressing ground displacements is also considered. The change in shaft geometry was found to be highly effective in improving stability of the shaft, with the maximum time-dependent displacement around the shaft decreasing by approximately an order of magnitude. Additionally, finite-difference models confirmed that increased stress concentrations around the shaft caused by adjacent level developments played a significant role in exacerbating ground deformation in the circular portion of the shaft.

Indexed fast network proximity querying

Node proximity queries are among the most common operations on network databases. A common measure of node proximity is random walk based proximity, which has been shown to be less susceptible to noise and missing data. Real-time processing of random-walk based proximity queries poses significant computational challenges for larger graphs with over billions of nodes and edges, since it involves solution of large linear systems of equations. Due to the importance of this operation, significant effort has been devoted to developing efficient methods for random-walk based node proximity computations. These methods either aim to speed up iterative computations by exploiting numerical properties of random walks, or rely on computation and storage of matrix inverses to avoid computation during query processing. Although both approaches have been well studied, the speedup achieved by iterative approaches does not translate to real-time query processing, and the storage requirements of inversion-based approaches prohibit their use on very large graph databases. We present a novel approach to significantly reducing the computational cost of random walk based node proximity queries with scalable indexing. Our approach combines domain graph-partitioning based indexing with fast iterative computations during query processing using Chebyshev polynomials over the complex elliptic plane. This approach combines the query processing benefits of inversion techniques with the memory and storage benefits of iterative approache. Using real-world networks with billions of nodes and edges, and top- k proximity queries as the benchmark problem, we show that our algorithm, I-C hopper , significantly outperforms existing methods. Specifically, it drastically reduces convergence time of the iterative procedure, while also reducing storage requirements for indexing.

Elliptical Shape Hole-Pattern Seals Performance Evaluation Using Design of Experiments Technique1

Hole-pattern annular gas seals have two distinct flow regions: an annular jet-flow region between the rotor and stator, and cylindrical indentions in the stator that serve as cavities where flow recirculation occurs. As the working fluid enters the cavities and recirculates, its kinetic energy is reduced, resulting in a reduction of leakage flow rate through the seal. The geometry of the cylindrical cavities has a significant effect on the overall performance of the seal. In this study, the effects of elliptical shape hole pattern geometry on the leakage and dynamic response performance of an industry-relevant hole-pattern seal design are investigated using a combination of computational fluid dynamics (CFD), hybrid bulk flow-CFD analysis, and design of experiments (DOEs) technique. The design space was defined by varying the values of five geometrical characteristics: the major and minor radius of hole, the angle between the major axis and the axis of the seal, the spacing between holes along the seal axis, and hole spacing in the circumferential direction. This detailed analysis allowed for a greater understanding of the interaction effects from varying all of these design parameters together as opposed to studying them one variable at a time. Response maps generated from the calculated results demonstrate the effects of each design parameter on seal leakage as well as the co-dependence between the design parameters. The data from this analysis were also used to generate linear regression models that demonstrate how these parameters affect the leakage rate and the dynamic coefficients, including the effective damping.

Two-point mean value formulas for some elliptic equations spaces with constant curvature

An analogue of the consequence of Bitsadze & Nakhushev’s mean value formula was obtained in the Lobachevskiy space and on a sphere.

Stepwise Luneburg Lens for Bloch Surface Waves

In order to enlarge the capability for in-plane manipulation of the Bloch surface wave (BSW), we investigate 2D gradient index (GRIN) optical components using a finite-difference time-domain (FDTD) numerical method. To ease difficulties in fabrication to acquire a continuous index profile of GRIN optical components, we propose a stepwise index profile. For 2D surface wave devices, such discrete index steps can be achieved by stepwise structuring of the top layer, also called the device layer. For the demonstration of the stepwise GRIN optics concept, we consider a Luneburg lens, which is a good example of the GRIN optical component that produces a strong focal spot on the shadow-side curvature of the lens. The limited index contrast of the BSW systems loosens the confinement of the focal spot. A mitigation plan is to elongate the circular geometry to the prolate ellipse. BSW-based Luneburg lenses with a relatively small number of steps and an elliptical geometry are demonstrated with comparable performances to a standard Luneburg lens.

Assessment of ground vehicle tankers interacting with liquid sloshing dynamics

This paper presents an assessment of the problems encountered with the design, dynamics and stability of road tankers. Generally, the research activities pertaining to these problems may be classified into three groups, liquid sloshing dynamics in moving containers, trucks dynamics carrying solids, and dynamic coupling of liquid-vehicle systems. The modal analysis of liquid free surface for circular, elliptic and generic cross-section geometries is presented together with the corresponding equivalent mechanical models. Considering popularity of horizontal elliptic cross-section tanks, the trammel equivalent pendulum received extensive research activities and the main results are discussed. Design optimisation of the liquid container cross-section and the passive and active control of liquid sloshing approaches are used by engineers to minimise rollover problem. The most difficult problem of road tankers is the coupling dynamics of liquid and vehicle dynamics under different conditions such as braking and lateral acceleration; in this view, computer numerical simulations have been developed.