Sixth-order superstable two-step methods for second-order initial-value problems

AbstractFor the numerical integration of general second-order initial-value problems y″ = f(x, y, y′), y(x0) = y0, y′(x0) = y′0, we report a family of two-step sixth-order methods which are superstable for the test equation y″ + 2αy′ + β2y = 0, α, β ⩾ 0, α + β\s>0, in the sense of Chawla [1]

Stability of stratified compressible shear flows

AbstractFor stratified compressible shear flows, it is shown that the instability region for subsonic disturbances is a semiellipse type region, which depends on the Richardson number, wave number, and depth of the fluid layer. If U(y) is the basic velocity, c = cr + ici is the complex phase velocity, and J0 the minimum of the local Richardson number, then this region reduces to the line ci = 0 when U′min ≠ 0 and J0 → 14− in accord with Miles's theorem. Under an approximation, the role of curvature of the basic velocity profile on the stability of the flow is also studied

Economics and Marketing of Aromatic Rice - A Case Study of Chhattisgarh

In recent years there has been a serious concern among the farmers, scientists, policymakers and environmentalists regarding the continuous erosion of genetic biodiversity of rice cultivars in Chhattisgarh which has traditionally been known as bowl of scented rices in central India. In view of India’s potential competitiveness in aromatic rices in the international market, it is imperative to understand the dynamics of domestic trade in aromatic rice. In this study, marketing and price-spread patterns of aromatic rice in the state of Chhattisgarh have been examined. A few policy interventions have been suggested for promoting aromatic rices in the state.Crop Production/Industries, Marketing,

Analysis of cell flux in the parallel plate flow chamber: implications for cell capture studies

The parallel plate flow chamber provides a controlled environment for determinations of the shear stress at which cells in suspension can bind to endothelial cell monolayers. By decreasing the flow rate of cell-containing media over the monolayer and assessing the number of cells bound at each wall shear stress, the relationship between shear force and binding efficiency can be determined. The rate of binding should depend on the delivery of cells to the surface as well as the intrinsic cell-surface interactions; thus, only if the cell flux to the surface is known can the resulting binding curves be interpreted correctly. We present the development and validation of a mathematical model based on the sedimentation rate and velocity profile in the chamber for the delivery of cells from a flowing suspension to the chamber surface. Our results show that the flux depends on the bulk cell concentration, the distance from the entrance point, and the flow rate of the cell-containing medium. The model was then used in a normalization procedure for experiments in which T cells attach to TNF-alpha-stimulated HUVEC monolayers, showing that a threshold for adhesion occurs at a shear stress of about 3 dyn/cm2

High order difference schemes for the system of two space second order nonlinear hyperbolic equations with variable coefficients

AbstractIn this paper, we develop implicit difference schemes of O(k4 + k2h2 + h4), where k > 0, h > 0 are grid sizes in time and space coordinates, respectively, for solving the system of two space dimensional second order nonlinear hyperbolic partial differential equations with variable coefficients having mixed derivatives subject to appropriate initial and boundary conditions. The proposed difference method for the scalar equation is applied for the solution of wave equation in polar coordinates to obtain three level conditionally stable ADI method of O(k4 + k2h2 + h4). Some physical nonlinear problems are provided to demonstrate the accuracy of the implementation

Comparative Analysis of MIT Rule and Lyapunov Rule in Model Reference Adaptive Control Scheme

Adaptive control involves modifying the control law used by the controller to cope with the fact that the parameters of the system being controlled change drastically due to change in environmental conditions or change in system itself. This technique is based on the fundamental characteristic of adaptation of living organism. The adaptive control process is one that continuously and automatically measures the dynamic behavior of plant, compares it with the desired output and uses the difference to vary adjustable system parameters or to generate an actuating signal in such a way so that optimal performance can be maintained regardless of system changes. This paper deals with application of model reference adaptive control scheme and the system performance is compared with Lyapunov rule and MIT rule. The plant which is taken for the controlling purpose is the first order system for simplicity. The comparison is done for different values of adaptation gain between MIT rule and Lyapunov rule. Simulation is done in MATLAB and simulink and the results are compared for varying adaptation mechanism due to variation in adaptation gain