A convective weakly viscoelastic rotating flow with pressure Neumann condition

The objective of this work is to investigate through the numeric simulation, the effects of the weakly viscoelastic flow within a rotating rectangular duct subject to a buoyancy force due to the heating of one of the walls of the duct. A direct velocity–pressure algorithm in primitive variables with a Neumann condition for the pressure is employed. The spatial discretization is made with finite central differences on a staggered grid. The pressure field is directly updated without any iteration. Numerical simulations were done for several Weissemberg numbers (We) and Grashof numbers (Gr) . The numerical results show that for high Weissemberg numbers (We>7.4 × 10^?5) and for ducts with aspect ratio 2:1 and 8:1, the secondary flow is restabilized with a stretched double vortex configuration. It is also observed that when the Grashof number is increased (Gr>17 × 10^?4) , the buoyancy force neutralizes the effects of the Coriolis force for ducts with aspect ratio 8:1. Copyright © 2008 John Wiley & Sons, Ltd.     

Anisotropy of electron structure at InAs(1 1 1) surfaces by laser pump-and-probe photoemission spectroscopy

The electronic structure and the electron dynamics of the clean InAs(1 1 1)A 2 × 2 and the InAs(1 1 1)B 1 × 1 surfaces have been studied by laser pump-and-probe photoemission spectroscopy. Normally unpopulated electron states above the valence band maximum (VBM) are filled on the InAs(1 1 1)A surface due to the conduction band pinning above the Fermi level (E_F). Accompanied by the downward band banding alignment, a charge accumulation layer is confined to the surface region creating a two dimensional electron gas (2DEG). The decay of the photoexcited carriers above the conduction band minimum (CBM) is originated by bulk states affected by the presence of the surface. No occupied states were found on the InAs(1 1 1)B 1 × 1 surface. This fact is suggested to be due to the surface stabilisation by the charge removal from the surface into the bulk. The weak photoemission intensity above the VBM on the (1 1 1)B surface is attributed to electron states trapped by surface defects. The fast decay of the photoexcited electron states on the (1 1 1)A and the (1 1 1)B surfaces was found to be τ_1 1 1 A ? 5 ps and τ_1 1 1 B ?  4 ps, respectively. We suggest the diffusion of the hot electrons into the bulk is the decay mechanism.     

Fixed-bed drying simulation of agricultural products using a new backward finite difference scheme

This work is concerned with the numerical simulation of fixed-bed corn drying using MSU (Michigan State University) drying model. The classical numerical procedure for MSU model relies on an explicit method of finite differences which requires certain stability conditions between the step sizes of the time and space variables. The objective of the present paper is to establish a stable implicit method based on backward finite differences, in both time and space variables, which takes into account some specific empirical aspects of the problem. Computational results illustrate the efficiency and the flexibility of method.     

Computational methods in lattice-subspaces of with applications in portfolio insurance

In this article, we develop a computational method for an algorithmic process first posed by Polyrakis in 1996 in order to check whether a finite collection of linearly independent positive functions in C[a,b] forms a lattice-subspace. Lattice-subspaces are closely related to a cost minimization problem in the theory of finance that ensures the minimum-cost insured portfolio and this connection is further investigated here. Finally, we propose a computational method in order to solve the minimization problem and to calculate the minimum-cost insured portfolio. All of the numerical work is performed using the Matlab high-level language.     

Asymptotic behaviour of the three-dimensional α-Navier-Stokes model with delays

We prove the existence and exponential stability of the stationary solutions for a three-dimensional α-Navier-Stokes model with delays. Instead of working directly with the model, we establish the results for a general abstract delay model, and then we apply them to our particular situation. We use two techniques in the stability analysis: the Lyapunov and Razumikhin approaches.     

Lattice-Boltzmann type relaxation systems and high order relaxation schemes for the incompressible Navier-Stokes equations

A relaxation system based on a Lattice-Boltzmann type discrete velocity model is considered in the low Mach number limit. A third order relaxation scheme is developed working uniformly for all ranges of the mean free path and Mach number. In the incompressible Navier-Stokes limit the scheme reduces to an explicit high order finite difference scheme for the incompressible Navier-Stokes equations based on nonoscillatory upwind discretization. Numerical results and comparisons with other approaches are presented for several test cases in one and two space dimensions.

     

Topology optimization of microfluidic mixers

This paper demonstrates the application of the topology optimization method as a general and systematic approach for microfluidic mixer design. The mixing process is modeled as convection dominated transport in low Reynolds number incompressible flow. The mixer performance is maximized by altering the layout of flow/non‐flow regions subject to a constraint on the pressure drop between inlet and outlet. For a square cross‐sectioned pipe the mixing is increased by 70% compared with a straight pipe at the cost of a 2.5 fold increase in pressure drop. Another example where only the bottom profile of the channel is a design domain results in intricate herring bone patterns that confirm findings from the literature. Copyright © 2008 John Wiley & Sons, Ltd.     

New Reductive Transformations of Unsaturated Cyclic Hydrocarbons [New Synthetic Methods (66)]

The successive reduction of fully conjugated cyclic hydrocarbons leads to singly and multiply charged ions with unusual bonding. The charge distribution in these ions can be determined spectroscopically, and the information so obtained is then used in kinetically controlled trapping reactions for the regioselective introduction of electrophilic groups. When non-benzenoid substrates are used, syntheses become possible which can either not be carried out or can only be carried out with great difficulty in other ways. Examples of new preparative applications are cycloannelation and bridging reactions as well as polymerization reactions. The ion pair structure of the intermediate and the type of electrophile used are of paramount importance in controlling the mechanism of these reductive transformations.     

Explicit Volume-Preserving Splitting Methods for Linear and Quadratic Divergence-Free Vector Fields

We present new explicit volume-preserving methods based on splitting for polynomial divergence-free vector fields. The methods can be divided in two classes: methods that distinguish between the diagonal part and the off-diagonal part and methods that do not. For the methods in the first class it is possible to combine different treatments of the diagonal and off-diagonal parts, giving rise to a number of possible combinations. This paper is dedicated to Arieh Iserles on the occasion of his 60th anniversary.     

A random Euler scheme for Carathéodory differential equations

We study a random Euler scheme for the approximation of Carathéodory differential equations and give a precise error analysis. In particular, we show that under weak assumptions, this approximation scheme obtains the same rate of convergence as the classical Monte–Carlo method for integration problems.