Sixth order compact multi-phase block-AGE iteration methods for computing 2D Helmholtz equation.

We discuss sixth order accurate 9-point compact 2- and 3-phase block alternating group explicit (block-AGE) iteration methods for computing 2D Helmholtz equation. We use Dirichlet boundary conditions and no fictitious points are involved outside the solution region for computation. The proposed 2- and 3-phase block-AGE methods require only two and three sweeps for computation and the error analysis of the suggested approximation is analyzed. We have compared the 2- and 3-phase block-AGE iteration methods with the corresponding block successive over relaxation (block-SOR) method in three experiments, in regard to number of iterations required for convergence and cpu time, where the importance of the role performed by optimal relaxation parameters of the proposed block-AGE iteration methods become evident in stipulating the convergence and precision of the calculated results. In all cases we use the tridiagonal solver and obtain the optimal relaxation parameters through computation.

Spline-in-compression approximation of order of accuracy three (four) for second order non-linear IVPs on a graded mesh.

A spline-in-compression method, implicit in nature, for computing numerical solution of second order nonlinear initial-value problems (IVPs) on a mesh not necessarily equidistant is discussed. The proposed estimation has been derived directly from consistency condition which is third-order accurate. For scientific computation, we use monotonically descending step lengths. The suggested method is applicable to a wider range of physical problems including the problems which are singular in nature. This is possible due to off-step discretization employed in the spline technique. We examine the absolute stability and super-stability of the method when applied to a problem of physical significances. We have shown that the method is absolutely stable in the case of graded mesh and super stable in the case of constant mesh. The advantage of our method lies in it being highly cost and time effective, as we employ a three-point compact stencil, thereby reducing the algebraic calculations considerably. The proposed method which is applicable to singular, boundary layer and singularly perturbed problems is a research gap which we overcame by proposing this new compact spline method.

Higher order approximation in exponential form based on half-step grid-points for 2D quasilinear elliptic BVPs on a variant domain.

This paper reports a new fourth order Finite Difference Method (FDM) in exponential form for two-dimensional quasilinear boundary value problem of elliptic type (BVPE) with variant solution domain. Further, this discretization is extended to solve the system of quasilinear BVPEs. Following are the main highlights of the proposed FDM: • An unequal mesh 9-point compact stencil is used to approximate the solution. Half-step points are used to evaluate the known variables of this problem. The convergence theory is studied for unequal mesh to validate the fourth order convergence of the suggested FDM. • It is applicable to BVPE irrespective of coordinate systems. Various benchmark problems, for example, Poisson equation in cylindrical coordinates, Burgers' equation, Navier-Stokes (NS) equations in cylindrical and rectangular coordinates, are solved to depict their fourth order convergence. • Numerical results confirm the accuracy, trustworthiness and acceptability of the suggested numerical algorithm. These results endorse the superiority of the proposed FDM over the previously existing techniques of Mohanty and Kumar (2014), Mohanty and Setia (2014), Priyadarshini and Mohanty (2021).

High precision compact numerical approximation in exponential form for the system of 2D quasilinear elliptic BVPs on a discrete irrational region.

This article presents a new approximation of order four in exponential form for two-dimensional (2D) quasilinear partial differential equation (PDE) of elliptic form with solution domain being irrational. It is further extended for application to a system of quasilinear elliptic PDEs with Dirichlet boundary conditions (DBCs). The main highlights of the method framed in this article are as under:•It uses a 9-point stencil with unequal mesh to approach the solution. The error analysis is discussed to authenticate the order of convergence of the proposed numerical approximation.•Various validating problems, for instance the Burgers' equation, Poisson equation in cylindrical coordinates, Navier-Stokes (NS) equations in rectangular and cylindrical coordinates are solved using the proposed techniques to depict their stability. The proposed approximation produces solution free of oscillations for large values of Reynolds Number in the vicinity of a singularity.•The results of the proposed method are superior in comparison to the existing methods of [49] and [56].

Comparison of energy cost in transtibial amputees using "prosthesis" and "crutches without prosthesis" for walking activities.

BACKGROUND: In a survey of 100 transtibial amputees (TTA) in the study place, it was noticed that nearly 30% of total activities performed by crutches. It was recorded nearly 52% of the amputees were totally independent, 39% had to use a crutch or cane and only 9% need not used any devices simply because they are unaware of current technology or availability. Out of 39 TTA, nine used crutches only for performing daily activities while 30 used both prosthesis and crutch. Walking is a major activity in lower limb amputees and therefore it is imperative to know the energy cost in both the mobility devices (prosthesis and crutches without prosthesis) for walking activities. OBJECTIVES: The purpose of this study was to quantify and compare the difference in energy cost between the two most commonly used assistive devices (prosthesis and axillary crutches) in adults with Transtibial amputation by indirect calorimetric method at the self-selected speed in plane surface walking. METHODS: Thirty adults who had a unilateral transtibial amputation participated in this study. Oxygen consumption was measured with a Cosmed K4 b(2) oxygen analysis telemetry unit (Rome, Italy) as the participants walked over level ground for 30 meters at a self-selected speed. The variables that were analyzed were VO(2) rate (mL/min), VO(2) cost (mL/kg/m), heart rate (bpm), self-selected walking velocity (m/min) and energy expenditure per minute (Kcal/min). RESULTS: It was observed that VO(2) uptake rate and EE comparisons were highly significant for both prosthesis and crutches without prosthesis walking in adults with transtibial amputation (P<0.025). There was significant difference between prosthesis walking and crutches without prosthesis walking in terms of VO(2) uptake rate (P<0.005) and EE/min (P<0.00001). It was noticed the adults with transtibial amputation using prosthesis walked with 21% more efficient in terms of VO(2) uptake rate and 92% more efficient in terms of EE/min as compared to crutches without prosthesis. CONCLUSIONS: The data on energy cost indicates that all below knee amputee groups walk with less effort by using prosthesis. It may be concluded that crutches without prosthesis may not be used as a permanent rehabilitative measure in transtibial amputations.

Ancient skeletal evidence for leprosy in India (2000 B.C.).

BACKGROUND: Leprosy is a chronic infectious disease caused by Mycobacterium leprae that affects almost 250,000 people worldwide. The timing of first infection, geographic origin, and pattern of transmission of the disease are still under investigation. Comparative genomics research has suggested M. leprae evolved either in East Africa or South Asia during the Late Pleistocene before spreading to Europe and the rest of the World. The earliest widely accepted evidence for leprosy is in Asian texts dated to 600 B.C. METHODOLOGY/PRINCIPAL FINDINGS: We report an analysis of pathological conditions in skeletal remains from the second millennium B.C. in India. A middle aged adult male skeleton demonstrates pathological changes in the rhinomaxillary region, degenerative joint disease, infectious involvement of the tibia (periostitis), and injury to the peripheral skeleton. The presence and patterning of lesions was subject to a process of differential diagnosis for leprosy including treponemal disease, leishmaniasis, tuberculosis, osteomyelitis, and non-specific infection. CONCLUSIONS/SIGNIFICANCE: Results indicate that lepromatous leprosy was present in India by 2000 B.C. This evidence represents the oldest documented skeletal evidence for the disease. Our results indicate that Vedic burial traditions in cases of leprosy were present in northwest India prior to the first millennium B.C. Our results also support translations of early Vedic scriptures as the first textual reference to leprosy. The presence of leprosy in skeletal material dated to the post-urban phase of the Indus Age suggests that if M. leprae evolved in Africa, the disease migrated to India before the Late Holocene, possibly during the third millennium B.C. at a time when there was substantial interaction among the Indus Civilization, Mesopotamia, and Egypt. This evidence should be impetus to look for additional skeletal and molecular evidence of leprosy in India and Africa to confirm the African origin of the disease.

Atypical presentations of falciparum malaria.

To identify the uncommon presentations of falciparum malaria in an endemic area and to assess the outcome of treatment, a study was carried out on 35 proved cases whose clinical presentations were either dominated by features other than fever or the history of fever was totally absent. Both urban and rural patients were included. Seventeen cases (48.3%) presented with features of cerebral malaria. Acute abdomen, urticaria, and unexplained shock were the other atypical presentations. Five cases (14.3%) of cerebral malaria died. We conclude that awareness of atypical presentations is important to detect cases of falciparum malaria in an endemic area. Intravenous quinine may need to be given promptly even when cerebral malaria is diagnosed empirically.

Contouring by speckle interferometry.

An optical method of generating high-constrast contours by using speckle interferometry has been proposed. To demonstrate the use of this technique the conventional dual-index immersion method has been adopted.

Speckle interferometric methods of measuring small out-of-plane displacements.

We present two new methods for measuring small out-of-plane displacement. These methods are descendents of Leendertz's method in speckle interferometry but provide fringes of good contrast.