Search results for: ellipticity

Authors: M. Abdelmalek

Abstract:

In this work, we study the hypersurfaces of constant weighted mean curvature embedded in weighted manifolds. We give a condition about these hypersurfaces to be minimal. This condition is given by the ellipticity of the weighted Newton transformations. We especially prove that two compact hypersurfaces of constant weighted mean curvature embedded in space forms and with the intersection in at least a point of the boundary must be transverse. The method is based on the calculus of the matrix of the second fundamental form in a boundary point and then the matrix associated with the Newton transformations. By equality, we find the weighted elementary symmetric function on the boundary of the hypersurface. We give in the end some examples and applications. Especially in Euclidean space, we use the above result to prove the Alexandrov spherical caps conjecture for the weighted case.

Keywords: weighted mean curvature, weighted manifolds, ellipticity, Newton transformations

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Authors: Naveed Ahmad Fazili

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More than 20 human diseases involve the fibrillation of a specific protein/peptide which forms pathological deposits at various sites. Hereditary lysozyme amyloidosis is a systemic disorder which mostly affects liver, spleen and kidney. This conformational disorder is featured by lysozyme fibril formation. In vivo lysozyme fibrillation was simulated under in vitro conditions using a strong denaturant GdHCl at 3M concentration. Sharp decline in the ANS fluorescence intensity compared to the partially unfolded states, almost 20 fold increase in ThT fluorescence intensity, increase in absorbance at 450 nm suggesting turbidity, negative ellipticity peak in the far-UVCD at 217 nm, red shift of 50 nm compared to the native state in congo red assay and appearance of a network of long rope like fibrils in TEM analysis suggested HEWL fibrillation. Anti-fibrillation potency of baicalein against the preformed fibrils of HEWL was investigated following ThT assay in which there was a dose dependent decrease in ThT fluorescence intensity compared to the fibrillar state of HEWL with the maximum effect observed at 150 μM baicalein concentration, loss of negative ellipticity peak in the far-UVCD region, dip in the Rayleigh scattering intensity and absorbance at 350 nm and 450 nm respectively together with a reduction in the density of fibrillar structure in TEM imaging. Thus, it could be suggested that baicalein could prove to be a positive therapeutics for hereditary human lysozyme amyloidosis.

Keywords: amyloid fibrils, baicalein, congo red, negative ellipticity, therapeutics

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Authors: Marco Tulio C. Faria

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Fixed-geometry hydrodynamic journal bearings are one of the best supporting systems for several applications of rotating machinery. Cylindrical journal bearings present excellent load-carrying capacity and low manufacturing costs, but they are subjected to the oil-film instability at high speeds. An attempt of overcoming this instability problem has been the development of non-circular journal bearings. This work deals with an analysis of oil-lubricated elliptical journal bearings using the finite element method. Steady-state and dynamic performance characteristics of elliptical bearings are rendered by zeroth- and first-order lubrication equations obtained through a linearized perturbation method applied on the classical Reynolds equation. Four-node isoparametric rectangular finite elements are employed to model the bearing thin film flow. Curves of elliptical bearing load capacity and dynamic force coefficients are rendered at several operating conditions. The results presented in this work demonstrate the influence of the bearing ellipticity on its performance at different loading conditions.

Keywords: elliptical journal bearings, non-circular journal bearings, hydrodynamic bearings, finite element method

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Authors: G. Akgun, I. Algul, H. Kurtaran

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In this paper geometrically nonlinear static behavior of laminated composite hollow super-elliptic beams is investigated using generalized differential quadrature method. Super-elliptic beam can have both oval and elliptic cross-sections by adjusting parameters in super-ellipse formulation (also known as Lamé curves). Equilibrium equations of super-elliptic beam are obtained using the virtual work principle. Geometric nonlinearity is taken into account using von-Kármán nonlinear strain-displacement relations. Spatial derivatives in strains are expressed with the generalized differential quadrature method. Transverse shear effect is considered through the first-order shear deformation theory. Static equilibrium equations are solved using Newton-Raphson method. Several composite super-elliptic beam problems are solved with the proposed method. Effects of layer orientations of composite material, boundary conditions, ovality and ellipticity on bending behavior are investigated.

Keywords: generalized differential quadrature, geometric nonlinearity, laminated composite, super-elliptic cross-section

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Authors: Marc S. Paolella, Pawel Polak

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The paper proposes a framework for large-scale portfolio optimization which accounts for all the major stylized facts of multivariate financial returns, including volatility clustering, dynamics in the dependency structure, asymmetry, heavy tails, and non-ellipticity. It introduces a so-called risk fear portfolio strategy which combines portfolio optimization with active risk monitoring. The former selects optimal portfolio weights. The latter, independently, initiates market exit in case of excessive risks. The strategy agrees with the stylized fact of stock market major sell-offs during the initial stage of market downturns. The advantages of the new framework are illustrated with an extensive empirical study. It leads to superior multivariate density and Value-at-Risk forecasting, and better portfolio performance. The proposed risk fear portfolio strategy outperforms various competing types of optimal portfolios, even in the presence of conservative transaction costs and frequent rebalancing. The risk monitoring of the optimal portfolio can serve as an early warning system against large market risks. In particular, the new strategy avoids all the losses during the 2008 financial crisis, and it profits from the subsequent market recovery.

Keywords: comfort, financial crises, portfolio optimization, risk monitoring

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Authors: Elisabet Liljeblad, Tomas Karlsson, Torbjorn Sundberg, Anita Kullen

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The magnetospheric magnetic field data from the MESSENGER spacecraft is investigated to establish the presence of ultra-low frequency (ULF) waves in connection to 131 previously observed nonlinear Kelvin-Helmholtz waves (KHWs) at Mercury. Distinct ULF signatures are detected in 44 out of the 131 magnetospheric traversals prior to or after observing a KHW. In particular, 39 of these 44 ULF events are highly coherent at the frequency of maximum power spectral density. The waves observed at the dayside, which appears mainly at the duskside and naturally following the KHW occurrence asymmetry, are significantly different to the events behind the dawn-dusk terminator and have the following distinct wave characteristics: they oscillate clearly in the perpendicular (azimuthal) direction to the mean magnetic field with a wave normal angle more in the parallel than the perpendicular direction, increase in absolute ellipticity with distance from noon, are almost exclusively right-hand polarized, and are observed mainly for frequencies in the range 0.02-0.04 Hz. These results indicate that the dayside ULF waves are likely to shear Alfvén waves driven by KHWs at the magnetopause, which in turn manifests the importance of the Kelvin-Helmholtz instability in terms of mass transport throughout the Mercury magnetosphere.

Keywords: ultra-low frequency waves, kelvin-Helmholtz instability, magnetospheric processes, mercury, messenger, energy and momentum transfer in planetary environments

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Authors: Vinod Kumar, Surjit Angra

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The objective of this theoretical study is to develop simple design formulas for the prediction of minimum film thickness and maximum mean film temperature rise in lightly loaded high-speed rolling/sliding lubricated elliptical contacts incorporating starvation effect. Herein, the reported numerical analysis focuses on thermoelastohydrodynamically lubricated rolling/sliding elliptical contacts, considering the Newtonian rheology of lubricant for wide range of operating parameters, namely load characterized by Hertzian pressure (PH = 0.01 GPa to 0.10 GPa), rolling speed (>10 m/s), slip parameter (S varies up to 1.0), and ellipticity ratio (k = 1 to 5). Starvation is simulated by systematically reducing the inlet supply. This analysis reveals that influences of load, rolling speed, and level of starvation are significant on the minimum film thickness. However, the maximum mean film temperature rise is strongly influenced by slip in addition to load, rolling speed, and level of starvation. In the presence of starvation, reduction in minimum film thickness and increase in maximum mean film temperature are observed. Based on the results of this study, empirical relations are developed for the prediction of dimensionless minimum film thickness and dimensionless maximum mean film temperature rise at the contacts in terms of various operating parameters.

Keywords: starvation, lubrication, elliptical contact, traction, minimum film thickness

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Authors: Anton V. Bourdine, Vladimir A. Burdin, Oleg R. Delmukhametov

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This work presents a fast and simple method for the design of large core silica optical fibers with differential mode delay (DMD) management. Some results are reported concerned with refractive index profile optimization for 42 µm core 16-LP-mode optical fiber for next-generation optical networks. Here special refractive index profile form provides total DMD reducing over all mode staff under desired enhanced mode effective area. Method for the simulation of 'real manufactured' few-mode optical fiber (FMF) core geometry differing from the desired optimized structure by core non-symmetrical ellipticity and refractive index profile deviation including local fluctuations is proposed. Results of the following analysis of optimized FMF with inserted geometry distortions performed by earlier on developed modification of rigorous mixed finite-element method showed strong DMD degradation that requires additional higher-order mode management. In addition, this work also presents a method for design mode division multiplexer channel precision spatial positioning scheme at FMF core end that provides one of the potentiality solutions of described DMD degradation problem concerned with 'distorted' core geometry due to features of optical fiber manufacturing techniques.

Keywords: differential mode delay, few-mode optical fibers, nonlinear Shannon limit, optical fiber non-circularity, ‘real manufactured’ optical fiber core geometry simulation, refractive index profile optimization

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Authors: Jonathon Bailey, Neil Bressloff, Nick Curzen

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Transcatheter Aortic Valve Implantation (TAVI) devices are stent-like frames with prosthetic leaflets on the inside, which are percutaneously implanted. The device in a crimped state is fed through the arteries to the aortic root, where the device frame is opened through either self-expansion or balloon expansion, which reveals the prosthetic valve within. The frequency at which TAVI is being used to treat aortic stenosis is rapidly increasing. In time, TAVI is likely to become the favoured treatment over Surgical Valve Replacement (SVR). Mortality after TAVI has been associated with severe Paravalvular Aortic Regurgitation (PAR). PAR occurs when the frame of the TAVI device does not make an effective seal against the internal surface of the aortic root, allowing blood to flow backwards about the valve. PAR is common in patients and has been reported to some degree in as much as 76% of cases. Severe PAR (grade 3 or 4) has been reported in approximately 17% of TAVI patients resulting in post-procedural mortality increases from 6.7% to 16.5%. TAVI devices, like SVR devices, are circular in cross-section as the aortic root is often considered to be approximately circular in shape. In reality, however, the aortic root is often non-circular. The ascending aorta, aortic sino tubular junction, aortic annulus and left ventricular outflow tract have an average ellipticity ratio of 1.07, 1.09, 1.29, and 1.49 respectively. An elliptical aortic root does not severely affect SVR, as the leaflets are completely removed during the surgical procedure. However, an elliptical aortic root can inhibit the ability of the circular Balloon-Expandable (BE) TAVI devices to conform to the interior of the aortic root wall, which increases the risk of PAR. Self-Expanding (SE) TAVI devices are considered better at conforming to elliptical aortic roots, however the valve leaflets were not designed for elliptical function, furthermore the incidence of PAR is greater in SE devices than BE devices (19.8% vs. 12.2% respectively). If a patient’s aortic root is too severely elliptical, they will not be suitable for TAVI, narrowing the treatment options to SVR. It therefore follows that in order to increase the population who can undergo TAVI, and reduce the risk associated with TAVI, non-circular devices should be developed. Computational simulations were employed to further advance our understanding of non-circular TAVI devices. Radial stiffness of the TAVI devices in multiple directions, frame bending stiffness and resistance to balloon induced expansion are all computationally simulated. Finally, a simulation has been developed that demonstrates the expansion of TAVI devices into a non-circular patient specific aortic root model in order to assess the alterations in deployment dynamics, PAR and the stresses induced in the aortic root.

Keywords: tavi, tavr, fea, par, fem

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