high weissenberg boundary layer flow of viscoelastic fluids on a stretching surface has been studied. the flow is considered to be steady and two dimensional. flows of viscoelastic liquids at high weissenberg number exhibit stress boundary layers near walls. these boundary layers are caused by the memory of the fluid. upon proper scaling and by means of an exact similarity transformation, the n...

Carrier phase ambiguity resolution is the key to precise positioning with a global navigation satellite system GNSS ; therefore, quite a few ambiguity resolution methods have been developed in the past two decades. In this paper, a new ambiguity searching algorithm by treating part of normal equations as constraints is developed. The process starts with the truncation of the terms with respect ...

We give conditions under which a general class of delay differential equations has a point of Bogdanov-Takens or a triple zero bifurcation. We show how a centre manifold projection of the delay equations reduces the dynamics to a two or three dimensional systems of ordinary differential equations. We put these equations in normal form and determine how the coefficients of the normal forms depen...

We introduce and investigate a new type of reductions between counting problems, which we call subtractive reductions. We show that the main counting complexity classes #P, #NP, as well as all higher counting complexity classes # · kP, k 2, are closed under subtractive reductions. We then pursue problems that are complete for these classes via subtractive reductions. We focus on the class #NP (...

We suggest a linear non-conforming triangular element for Maxwell’s equations and test it in the context of the vector Helmholtz equation for the electric field. The element uses discontinuous normal fields and tangential fields with continuity at the midpoint of the element sides, an approximation related to the Crouzeix-Raviart element for Stokes. The element is stabilized using the jump of t...

A dynamic α model for the isotropic incompressible LANS-α equations is proposed in this investigation. To derive this model, the incompressible Navier-Stokes equations are Helmholtz-filtered at the grid and test filter levels. A Germano type identity is derived by comparing the filtered subgrid scale stress terms with those given in LANS-α equations. Considering a constant value of α and averag...

This paper investigates the pseudospectra and the numerical range of the OrrSommerfeld operator for plane Poiseuille flow. A number z E C is in the E-pseudospectrum of a matrix or operator A if Il(zI A)-'II 2 E-l, or, equivalently, if z is in the spectrum of A + E for some perturbation E satisfying IlEll 5 E. The numerical range of A is the set of numbers of the form (Au, u), where (., .) is th...

A dynamic procedure for the Lagrangian Averaged Navier-Stokes-α (LANS-α) equations is developed where the variation in the parameter α in the direction of anisotropy is determined in a self-consistent way from data contained in the simulation itself. In order to derive this model, the incompressible Navier-Stokes equations are Helmholtz-filtered at the grid and a test filter levels. A Germano t...

Results are reported from a three-dimensional computational stability analysis of flow over a backward-facing step with an expansion ratio (outlet to inlet height) of 2 at Reynolds numbers between 450 and 1050. The analysis shows that the first absolute linear instability of the steady two-dimensional flow is a steady three-dimensional bifurcation at a critical Reynolds number of 748. The criti...

Turbulent viscosity in cold accretion disks is likely to be hydrodynamic in origin. We investigate the growth of hydrodynamic perturbations in a small region of a disk, which we model as a linear shear flow with Coriolis force, between two parallel walls. Although there are no exponentially growing eigenmodes in this system, because of the non-normal nature of the modes, it is possible to have ...