This paper investigates the axial unsteady flow of a generalized Burgers’ fluid with fractional constitutive equation in a circular micro-tube, in presence of a time-dependent pressure gradient and an electric field parallel to flow direction and a magnetic field perpendicular on the flow direction. The mathematical model used in this work is based on a time-nonlocal constitutive equation for s...

We consider exponential functionals of a multi-dimensional Brownian motion with drift, defined via a collection of linear functionals. We give a characterisation of the Laplace transform of their joint law as the unique bounded solution, up to a constant factor, to a Schrödinger-type partial differential equation. We derive a similar equation for the probability density. We then characterise al...

In this article, we construct robust (i.e. lower and upper semicontinuous) exponential attractors for singularly perturbed phase-field type equations. Moreover, we obtain estimates for the symmetric distance between these exponential attractors and that of the limit Cahn-Hilliard equation in terms of the perturbation parameter. We can note that the continuity is obtained without time shifts as ...

In this paper‎, ‎the static bending‎, ‎free vibration‎, ‎and dynamic response of functionally graded‎ ‎piezoelectric beams have been carried out by finite element method‎‎under different sets of mechanical‎, ‎thermal‎, ‎and electrical‎ ‎loadings‎. ‎The beam with functionally graded piezoelectric material‎ ‎(FGPM) is assumed to be graded across the thickness with a simple‎ ‎power law distributio...

We try to answer the following set of questions: ``Is it possible to design step edge detection filters given the desired response to an input step edge signal?''; ``The method extends easily to two dimensions?'' and ``Do we improve edge detection using this method?''. Answers to these questions are given by formulating the step edge detection problem in terms of a linear first kind Fredholm in...

the aim of this paper is to present a new numerical method for solving the bagley-torvik equation. this equation has an important role in fractional calculus. the fractional derivatives are described based on the caputo sense. some properties of the sinc functions required for our subsequentdevelopment are given and are utilized to reduce the computation of solution of the bagley-torvik equatio...

in this paper, changes of casson non-newtonian fluid velocity profile, for different distribution of porosity, have been investigated. for distribution of porosity, fixed, radial and exponential variations has been considered. for all three states, brinkman model has been used as momentum equation. since the casson fluid is a good model for blood, this analysis can be used in studying about cho...

introduction: nano-indentation has recently been employed as a powerful tool for determining the mechanical properties of biological tissues on nano and micro scales. a majority of soft biological tissues such as ligaments and tendons exhibit viscoelastic or time-dependent behaviors. the constitutive characterization of soft tissues is among very important subjects in clinical medicine and espe...

Classical Constitutive equations like the Navier-Stokes model for fluids and the linearized elastic model for solids are explicit models in that they provide explicit expressions for the stress in terms of kinematical quantities. Similarly, the constitutive equation for a Simple Material is also an explicit equation for the stress in terms of the histories of the deformation gradient and the de...