There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Fractional Differential Equations

Thank you for reading numerical heat transfer and fluid flow. Maybe you have knowledge that, people have search numerous times for their favorite books like this numerical heat transfer and fluid flow, but end up in infectious downloads. Rather than reading a good book with a cup of coffee in the afternoon, instead they cope with some malicious virus inside their computer. numerical heat transfer and fluid flow is available in our digital library an online access to it is set as public so you can get it instantly. Our books collection spans in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the numerical heat transfer and fluid flow is universally compatible with any devices to read.

Numerical Heat Transfer And Fluid Flow

The work is giving estimations of the discrepancy between solutions of the initial and the homogenized problems for a one{dimensional second order elliptic operators with random coeecients satisfying strong or uniform mixing conditions. We obtain several sharp estimates in terms of the corresponding mixing coeecient. Abstract. In the theory of homogenisation it is of particular interest to determine the classes of problems which are stable on taking the homogenisation limits. A notable situation where the limit enlarges the class of original problems is known as memory (nonlocal) eeects. A number of results in that direction has been obtained for linear problems. Tartar (1990) innitiated the study of the eeective equation corresponding to nonlinear equation: @ t u n + a n u 2 n = f: Signiicant progress has been hampered by the complexity of required computations needed in order to obtain the terms in power{series expansion. We propose a method which overcomes that diiculty by introducing graphs representing the domain of integration of the integrals in each term. The graphs are relatively simple, it is easy to calculate with them and they give us a clear image of the form of each term. The method allows us to discuss the form of the eeective equation and the convergence of power{series expansions. The feasibility of our method for other types of nonlinearities will be discussed as well.

Applied Mathematics and Computation

The cardiovascular system is an internal flow loop with multiple branches circulating a complex liquid. The hallmarks of blood flow in arteries are pulsatility and branches, which cause wall stresses to be cyclical and nonuniform. Normal arterial flow is laminar, with secondary flows generated at curves and branches. Arteries can adapt to and modify hemodynamic conditions, and unusual hemodynamic conditions may cause an abnormal biological response. Velocity profile skewing can create pockets in which the wall shear stress is low and oscillates in direction. Atherosclerosis tends to localize to these sites and creates a narrowing of the artery lumen--a stenosis. Plaque rupture or endothelial injury can stimulate thrombosis, which can block blood flow to heart or brain tissues, causing a heart attack or stroke. This small lumen and elevated shear rate in a stenosis create conditions that accelerate platelet accumulation and occlusion. The relationship between thrombosis and fluid mechanics is complex, especially in the post-stenotic flow field. New convection models have been developed to predict clinical from platelet thrombosis in diseased arteries. Future hemodynamic studies should address the complex mechanics of flow-induced, large-scale wall motion and convection of semisolid particles and cells in flowing blood.

Fluid Mechanics of Vascular Systems, Diseases, and Thrombosis

https://www.cell.com/biophysj/pdf/S0006-3495(91)82030-6.pdf

Model of platelet transport in flowing blood with drift and diffusion terms.

In transport phenomena, precise knowledge or estimation of fluids properties is necessary, for mass flow and heat transfer computations. Viscosity is one of the important properties which are affected by pressure and temperature. In the present work, based on statistical techniques for nonlinear regression analysis and correlation tests, we propose a novel equation modeling the relationship between the two parameters of viscosity Arrhenius-type equation, such as the energy () and the preexponential factor (). Then, we introduce a third parameter, the Arrhenius temperature (), to enrich the model and the discussion. Empirical validations using 75 data sets of viscosity of pure solvents studied at different temperature ranges are provided from previous works in the literature and give excellent statistical correlations, thus allowing us to rewrite the Arrhenius equation using a single parameter instead of two. In addition, the suggested model is very beneficial for engineering data since it would permit estimating the missing parameter value, if a well-established estimate of the other parameter is readily available.

https://downloads.hindawi.com/journals/jchem/2015/163262.pdf

A New Equation Relating the Viscosity Arrhenius Temperature and the Activation Energy for Some Newtonian Classical Solvents

We introduce the rudiments of fractional calculus and the consequent applications of the Sumudu transform on fractional derivatives. Once this connection is firmly established in the general setting, we turn to the application of the Sumudu transform method (STM) to some interesting nonhomogeneous fractional ordinary differential equations (FODEs). Finally, we use the solutions to form two-dimensional (2D) graphs, by using the symbolic algebra package Mathematica Program 7.

/pdf/the-analytical-solution-of-some-fractional-ordinary-1vy6rmukjb.pdf

The Analytical Solution of Some Fractional Ordinary Differential Equations by the Sumudu Transform Method

In this work, Sumudu transform applications are extended to fractional integrals and derivatives. A table of a hundred instances of basic and special functions fractional integrals sumudi is provided. Some Sumudu properties are either generalized, or newly established. The Sumudu operator is then shown to help solve wide classes of fractional differential equations. 1 Introduction: Sumudu transform, fractional integrals and derivatives.

Applications of the Sumudu transform to fractional differential equations

Nature of the Natural transform is, it converges to Laplace and Sumudu transform. The theme of this paper is to give detailed study of Natural transform. The Natural transform is derived from the Fourier Integral. We showed it to the theoretical dual of Laplace and Sumudu transforms. This work includes Natural-multiple shift theorems, Bromwich contour integral and Heviside's Expansion formula for Inverse Natural transform.

Fethi Bin Muhammad Belgacem

Papers

Model of platelet transport in flowing blood with drift and diffusion terms.

A New Equation Relating the Viscosity Arrhenius Temperature and the Activation Energy for Some Newtonian Classical Solvents

The Analytical Solution of Some Fractional Ordinary Differential Equations by the Sumudu Transform Method

Applications of the Sumudu transform to fractional differential equations

Theory of Natural Transform