A Study on Inviscid Flow with a Free Surface over an Undulating Bottom

In this paper, the problem involving inviscid flow with a free surface over an undulating bottom is studied within the framework of linear theory. Applying perturbation analysis in conjunction with the Fourier transform technique, the boundary value problem arising from the flow problem is solved analytically. Behaviour of both interface and free-surface profiles, which are unknown at the outset, are analyzed. It is found that each profile (interface and free-surface) possesses a wave free region at the far upstream, followed by a modulated downstream wave. It also observed, for the first time, that the amplitude of the downstream wave is varying. Further, the effects of various system parameters are analyzed and demonstrated in graphical forms

Water-waves Scattering by Permeable Bottom in Two-layer Fluid in the Presence of Surface Tension

In the present paper, reflection and transmission phenomena of water waves due to undulating permeable bottom in a two-layer fluid system are investigated using two-dimensional linearized theory. The effect of surface tension on the free surface is included in this work. In two-layer fluid system, there exist waves with two different wave numbers (modes). When a wave of a particular wave number encounters the undulating bottom, reflection and transmission phenomena occur in both the layers. The reflection and transmission coefficients in both layers due to incident waves of both modes are analyzed with the aid of perturbation analysis along with Fourier transform technique. It is found that these coefficients are obtained in terms of integrals which depend on the shape function of the undulating bottom. Two different kinds of undulating bottoms are considered to determine these coefficients. For a particular undulating bottom, namely sinusoidal bottom undulation the effect of various physical parameters such as number of ripples, surface tension and porous effect parameters are demonstrated graphically. The study further elaborates the energy balance relations associated with the reflection and transmission coefficients to ascertain the correctness of all the computed results

Insulin Like Growth Factor-1 (IGF-1) Causes Overproduction of IL-8, an Angiogenic Cytokine and Stimulates Neovascularization in Isoproterenol-Induced Myocardial Infarction in Rats

Angiogenesis factors are produced in response to hypoxic or ischemic insult at the site of pathology, which will cause neovascularization. Insulin like growth factor-1 (IGF-1) exerts potent proliferative, angiogenic and anti-apoptotic effects in target tissues. The present study was aimed to evaluate the effects of IGF-1 on circulating level of angiogenic cytokine interleukin-8 (IL-8), in experimentally-induced myocardial ischemia in rats. Male Sprague-Dawley rats were divided into control, IGF-1 treated (2 μg/kg/day subcutaneously, for 5 and 10 days), isoproterenol (ISO) treated (85 mg/kg, subcutaneously for two days) and ISO with IGF-1 treated (for 5 and 10 days). Heart weight, serum IGF-1, IL-8 and cardiac marker enzymes (CK-MB and LDH) were recorded after 5 and 10 days of treatment. Histopathological analyses of the myocardium were also done. There was a significant increase in serum cardiac markers with ISO treatment indicating myocardial infarction in rats. IGF-1 level increased significantly in ISO treated groups and the level of IGF-1 was significantly higher after 10 days of treatment. IL-8 level increased significantly after ISO treatment after 5 and 10 days and IGF-1 concurrent treatment to ISO rats had significantly increased IL-8 levels. Histopathologically, myocyte necrosis and nuclear pyknosis were reduced significantly in IGF-1 treated group and there were numerous areas of capillary sprouting suggestive of neovascularization in the myocardium. Thus, IGF-1 protects the ischemic myocardium with increased production of circulating angiogenic cytokine, IL-8 and increased angiogenesis

Cardioprotective Effects of Glycyrrhizic Acid Against Isoproterenol-Induced Myocardial Ischemia in Rats

The aim of the present study was to look into the possible protective effects of glycyrrhizic acid (GA) against isoproterenol-induced acute myocardial infarction in Sprague-Dawley rats. The effect of three doses of glycyrrhizic acid in response to isoproterenol (ISO)-induced changes in 8-isoprostane, lipid hydroperoxides, super oxide dismutase and total glutathione were evaluated. Male Sprague-Dawley rats were divided into control, ISO-control, glycyrrhizic acid alone (in three doses-5, 10 and 20 mg/kg BW) and ISO with glycyrrhizic acid (in three doses) groups. ISO was administered at 85 mg/kg BW at two consecutive days and glycyrrhizic acid was administered intraperitoneally for 14 days. There was a significant increase in 8-isoprostane (IP) and lipid hydroperoxide (LPO) level in ISO-control group. A significant decrease in total superoxide dismutase (SOD) and total glutathione (GSH) was seen with ISO-induced acute myocardial infarction. Treatment with GA significantly increased SOD and GSH levels and decreased myocardial LPO and IP levels. Histopathologically, severe myocardial necrosis and nuclear pyknosis and hypertrophy were seen in ISO-control group, which was significantly reduced with GA treatment. Gycyrrhizic acid treatment proved to be effective against isoproterenol-induced acute myocardial infarction in rats and GA acts as a powerful antioxidant and reduces the myocardial lipid hydroperoxide and 8-isoprostane level

Assessment of Homotopy Analysis Method and Modified Homotopy Perturbation Method for Strongly Nonlinear Oscillator

Abstract: Some recently developed analytical methods namely; homotopy analysis method, homotopy perturbation method and modified homotopy perturbation method are applied successfully for solving strongly nonlinear oscillators. The analytical results obtained by using HAM are compared with those of HPM, mH-PM as well as with numerical results. In this study, different examples with strong nonlinearity are assessed in detail to illustrate the effectiveness and convenience of the methods. Comparing the three methods, the attention is focused on the accuracy of the results and applicability of the methods. It has been observed that the solution using HAM which is valid in a small region is more accurate than the solutions obtained using other two methods. Whereas mHPM works very well for a wide range and it is computationally more efficient

Two-period decision strategies in a dual-channel supply chain considering reference price and online reviews

The rapid development of e-commerce and Internet technology impacts the consumer purchasing practices and the decision-making of the supply chain. In this regard, dealing with online reviews and reference price together for a competitive interaction in a two-period dual-channel scenario is one of the main challenges. To address this interaction, in the present research, we consider a dual-channel supply chain with a two-period. The selling price and the reference price impact on the retailer’s demand in both channels. Whereas, the online reviews influence the demands of the direct channels only. The manufacturer, who announces wholesale prices and direct channel selling prices, is Stackelberg game’s leader and the retailer is the follower. Two different decision-making strategies (I, II) are made by both players: (I) The manufacturer and the retailer both make all their decisions at the beginning of the selling season. (II) Here all decisions are made at the beginning of each selling period. In order to compare these strategies, we create a centralized policy as a benchmark scenario. The optimal solutions of the supply chain and each player are determined and analyzed. The numerical and sensitivity analysis suggests that the responsive pricing can bring additional benefits to both the players

THREE-LAYER FLUID FLOW OVER A SMALL OBSTRUCTION ON THE BOTTOM OF A CHANNEL

Many boundary value problems occur in a natural way while studying fluid flow problems in a channel. The solutions of two such boundary value problems are obtained and analysed in the context of flow problems involving three layers of fluids of different constant densities in a channel, associated with an impermeable bottom that has a small undulation. The top surface of the channel is either bounded by a rigid lid or free to the atmosphere. The fluid in each layer is assumed to be inviscid and incompressible, and the flow is irrotational and two-dimensional. Only waves that are stationary with respect to the bottom profile are considered in this paper. The effect of surface tension is neglected. In the process of obtaining solutions for both the problems, regular perturbation analysis along with a Fourier transform technique is employed to derive the first-order corrections of some important physical quantities. Two types of bottom topography, such as concave and convex, are considered to derive the profiles of the interfaces. We observe that the profiles are oscillatory in nature, representing waves of variable amplitude with distinct wave numbers propagating downstream and with no wave upstream. The observations are presented in tabular and graphical forms

Three-layer fluid flow over a small obstruction on the bottom of a channel

Many boundary value problems occur in a natural way while studying fluid flow problems in a channel. The solutions of two such boundary value problems are obtained and analysed in the context of flow problems involving three layers of fluids of different constant densities in a channel, associated with an impermeable bottom that has a small undulation. The top surface of the channel is either bounded by a rigid lid or free to the atmosphere. The fluid in each layer is assumed to be inviscid and incompressible, and the flow is irrotational and two-dimensional. Only waves that are stationary with respect to the bottom profile are considered in this paper. The effect of surface tension is neglected. In the process of obtaining solutions for both the problems, regular perturbation analysis along with a Fourier transform technique is employed to derive the first-order corrections of some important physical quantities. Two types of bottom topography, such as concave and convex, are considered to derive the profiles of the interfaces. We observe that the profiles are oscillatory in nature, representing waves of variable amplitude with distinct wave numbers propagating downstream and with no wave upstream. The observations are presented in tabular and graphical forms. doi:10.1017/S144618111400048

An alternative approach to study nonlinear inviscid flow over arbitrary bottom topography

This paper deals with a new approach to study the nonlinear inviscid flow over arbitrary bottom topography. The problem is formulated as a nonlinear boundary value problem which is reduced to a Dirichlet problem using certain transformations. The Dirichlet problem is solved by applying Plemelj-Sokhotski formulae and it is noticed that the solution of the Dirichlet problem depends on the solution of a coupled Fredholm integral equation of the second kind. These integral equations are solved numerically by using a modified method. The free-surface profile which is unknown at the outset is determined. Different kinds of bottom topographies are considered here to study the influence of bottom topography on the free-surface profile. The effects of the Froude number and the arbitrary bottom topography on the free-surface profile are demonstrated in graphical forms for the subcritical flow. Further, the nonlinear results are validated with the results available in the literature and compared with the results obtained by using linear theory. (C) 2015 Elsevier Inc. All rights reserved