Computation of eigenvalues and solutions of regular Sturm–Liouville problems using Haar wavelets

The paper presents a novel method for the computation of eigenvalues and solutions of Sturm–Liouville eigenvalue problems (SLEPs) using truncated Haar wavelet series. This is an extension of the technique proposed by Hsiao to solve discretized version of variational problems via Haar wavelets. The proposed method aims to cover a wider class of problems, by applying it to historically important and a very useful class of boundary value problems, thereby enhancing its applicability. To demonstrate the effectiveness and efficiency of the method various celebrated Sturm–Liouville problems are analyzed for their eigenvalues and solutions. Also, eigensystems are investigated for their asymptotic and oscillatory behavior. The proposed scheme, unlike the conventional numerical schemes, such as Rayleigh quotient and Rayleigh–Ritz approximation, gives eigenpairs simultaneously and provides upper and lower estimates of the smallest eigenvalue, and it is found to have quadratic convergence with increase in resolution.     

Analysis of modified Reynolds equation using the wavelet‐multigrid scheme

The combined study of effects of surface roughness and poroelasticity on the squeeze film behavior of bearings in general and that of synovial joints in particular are presented. The modified form of Reynolds equation, which incorporates the randomized roughness structure as well as elastic nature of articular cartilage, is derived. Christensen stochastic theory describing roughness structure of cartilage surfaces is used by assuming the roughness asperity heights to be small compared to the film thickness. A recently developed wavelet‐multigrid method is used for the solution of Reynolds equation. The method has the greatest advantage of minimizing the errors using wavelet transforms in obtaining accurate solution, as grid size tends to zero. Based on the results obtained, the influence of roughness and elasticity on bearing characteristics are discussed in some detail. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007     

Wavelet-multigrid analysis of squeeze film characteristics of poroelastic bearings

The combined study of effects of poroelasticity and couple stresses on the performance of lubrication aspects of porelastic bearings in general and that of synovial joints in particular are analyzed. The modified form of Reynolds equation which incorporates the elastic nature of cartilage and Stokes couple-stress fluid as lubricant is derived and solved using a recently developed wavelet multigrid method. This method has greatest advantage of minimizing the errors using wavelet transforms in obtaining accurate solution as grid size tends to zero. It is found that, 6–7 cycles are required to obtain a reasonably accurate solution in the multigrid scheme, whereas, only one cycle is required to obtain the solution in the wavelet-multigrid method. Also, matrix of discrete wavelet-transform acts as a natural preconditioner producing rapid convergence. It is observed that, the poroelastic bearings with couple-stress fluid as lubricant provide enhancement in pressure and ensure the increased load carrying capacity compared with viscous fluids. This may be one of the reasons in the efficient lubrication and proper functioning of synovial joints.     

A comparative study of SELBOX-JLT and SOI-JLT

Analysis of thermal and electrical characteristics of the proposed device, selective buried oxide junctionless transistor (SELBOX-JLT) along with its analog performance, is compared with silicon on insulator junctionless transistor (SOI-JLT). The proposed device shows better thermal efficiency. The maximum device temperature of SELBOX-JLT is 311 K, much less than that of SOI-JLT (445 K). The proposed device has almost no effect of self-heating on output characteristics. SELBOX-JLT exhibits better I _ON/I _OFF ratio, subthreshold slope, and drain-induced barrier lowering as compared to SOI-JLT for the same channel length. The analog performance parameters as transconductance (G _m ), transconductance/drain current ratio (G _m /I _D), drain conductance (G _D), output resistance (R ₀), intrinsic gain (G _m R ₀), and unity-gain frequency (f _T ) of the proposed device are found to be better than SOI-JLT.     

Numerical solution of stiff systems from nonlinear dynamics using single-term Haar wavelet series

The paper presents single-term Haar wavelet series (STHWS) approach to the solution of nonlinear stiff differential equations arising in nonlinear dynamics. The properties of STHWS are given. The method of implementation is discussed. Numerical solutions of some model equations are investigated for their stiffness and stability and solutions are obtained to demonstrate the suitability and applicability of the method. The results in the form of block-pulse and discrete solutions are given for typical nonlinear stiff systems. As compared with the TR BDF2 method of Shampine and Gill’s method, the STHWS turns out to be more effective in its ability to solve systems ranging from mildly to highly stiff equations and is free from stability constraints.     

An application of single-term Haar wavelet series in the solution of nonlinear oscillator equations

In this paper, a novel single-term Haar wavelet series (STHWS) method is implemented for the solution of the Duffing equation and Painleve’s transcendents (PI and PII). The results, in the form of a block pulse and a discrete solution, are presented. Unlike classical numerical schemes, the STHWS method has no restrictions on the coefficients of the Duffing equation as regards its solution. PI and PII are analysed as regards their solutions, up to nearest singularities (poles), using the STHWS. Also, an efficient computational implementation shows the remarkable features of wavelet based techniques.     

Effect of electric field and magnetic field on spin transport in bilayer graphene armchair nanoribbons: A Monte Carlo simulation study

In this article we study the effect of external magnetic field and electric field on spin transport in bilayer armchair graphene nanoribbons (GNR) by employing semiclassical Monte Carlo approach. We include D'yakonov-Perel' (DP) relaxation due to structural inversion asymmetry (Rashba spin-orbit coupling) and Elliott-Yafet (EY) relaxation to model spin dephasing. In the model we neglect the effect of local magnetic moments due to adatoms and vacancies. We have considered injection polarization along z-direction perpendicular to the plane of graphene and the magnitude of ensemble averaged spin variation is studied along the x-direction which is the transport direction. To the best of our knowledge there has been no theoretical investigation of the effects of external magnetic field on spin transport in graphene nanoribbons. This theoretical investigation is important in order to identify the factors responsible for experimentally observed spin relaxation length in graphene GNRs.     

Buffalo Colostrum β-lactoglobulin Inhibits VEGF-Induced Angiogenesis by Interacting with G protein-Coupled Receptor Kinase

β-lactoglobulin (β-lg), a major whey protein was purified and characterised from buffalo colostrum. The in silico analysis of the tryptic peptides based on LC-CID-MS/MS facilitated the identification of protein as β-lg. The sequences IIVTQ f[1–5] and LSFNPTQLEEQCHV f(149–162) of m/z 933⁺ and 851²⁺ were found to match N- and C-extreme of β-lg while IDALNENK f(84–91) and TPEVDDEALEKFDK f(125–138) sequences deduced for m/z 916⁺ and 818²⁺ were in compliance to buffalo milk β-lg. Considering the sequence similarity of β-lg to glycodelin, a proven angiogenic protein, similar role for β-lg from buffalo colostrum (BLG-col) was examined. Interestingly, BLG-col exhibited anti-angiogenic activity by potently inhibiting cell proliferation, micro-vessel sprouting, cell migration and tube formation of human umbilical vein endothelial cells (HUVECs) in a dose-dependent manner but having varied effect on Ehrlich ascites tumor cells, MCF-7, MDA-MB 435 and MDA-MB 231 cell lines. The anti-angiogenic potential of BLG-col was found to be vascular endothelial growth factor mediated. The immunolocalisation of BLG-col on the cell surface of HUVECs evidenced using FITC-labelled β-lg antibody indicated its extra-cellular binding. Furthermore, BLG-col interacting HUVEC membrane protein (64 kDa) was detected by immunoblot and its identity was established by matrix-assisted laser desorption/ionisation time-of-flight mass spectrometry analysis, which showed peptide sequence homology to G protein-coupled receptor kinase 4.