The consequences of magnetohydrodynamic flow inside the boundary layer a Jeffery fluid in porous material across shrinking/stretching sheet are discussed this paper. Runge–Kutta fourth-order technique is used to turn partial differential equations into nonlinear ordinary and solve them using similarity transformation. On velocity temperature profiles, effects key factors such as “thermal strati...

The forces acting on two fixed spheres in a second-order uniform flow are investigated. When 1+ 2=0, where 1 and 2 are fluid parameters related to the first and second normal stress coefficients, the velocity field for a second-order fluid is the same as the one predicted by the Stokes equations while the pressure is modified. The Stokes solutions given by Stimson and Jeffery Proc. R. Soc. Lond...

A Hamel basis is a set a, ô, c, • • • of real numbers such that if x is any real number whatsoever then x may be expressed uniquely in the form aa+(3b+yc + • • • where a, j8, 7, • • • are rational numbers of which only a finite number are different from zero. Since each of these sums is formed from a finite number of nonzero terms and the coefficients a, /3, 7, • • • are rational and therefore ...

Abstract The Boltzmann–Hamel (BH) equations are central in the dynamics and control of nonholonomic systems described terms quasi-velocities. rigid body is a classical example such systems, it well-known that BH-equations Newton–Euler (NE) when twists as It further known NE-equations Euler–Poincaré, respectively, reduced Euler–Lagrange on SE (3) using body-fixed or spatial representation twists...

We show that an infinite-dimensional complete linear space X has: • a dense hereditarily Baire Hamel basis if |X| ≤ c; • a dense non-meager Hamel basis if |X| = κ = 2 for some cardinal κ. According to Corollary 3.4 of [BDHMP] each infinite-dimensional separable Banach space X has a non-meager Hamel basis. This is a special case of Theorem3.3 of [BDHMP], asserting that an infinite-dimensional Ba...

Using high-speed digital holographic microscopy and microfluidics, we discover that, when encountering fluid flow shear above a threshold, unicellular green alga Dunaliella primolecta migrates unambiguously in the cross-stream direction that is normal to the plane of shear and coincides with the local fluid flow vorticity. The flow shear drives motile microalgae to collectively migrate in a thi...

In this article we consider linear isomorphisms over the field of rational numbers between linear spaces R and R. We prove that if f is such an isomorphism, then the image by f of the unit disk is a strictly non-measurable subset of the real line, which is strongly non-similar to any classical nonmeasurable subset of reals. We also show the consistency and independence of the proposition that a...

I f you make the mistake, as some do, of calling Jeff Dangl a botanist, his embarrassment is palpable. Trained as a mouse immunologist, he admits to a “certain lack” of botanical knowledge. The John N. Couch distinguished professor of biology and adjunct professor of microbiology and immunology at the University of North Carolina, Chapel Hill, will, however, give you an earful about the lack of...