Role of Prehistories in the Initial Value Problems of Fractional Viscoelastic Equations

The fractional viscoelastic equation (FVE), which is a second-order differential equation with fractional derivatives describing the dynamical behavior of a single-degree-of-freedom viscoelastic oscillator, is considered. Some viscoelastic damped mechanical systems may be described by FVEs. However, FVEs with conventional nonzero initial values cannot generally be solved. In this paper, the prehistories of the unknown functions before the initial times, referred to as the initial functions, are taken into account to solve FVEs. Mathematically, appropriate initial functions are essential for unique solutions of FVEs. Physically, the initial functions reflect the processes of giving the initial values. FVEs are solved for some initial functions both by analytical and numerical methods. The initial functions affect the solutions of FVEs. It is discussed how the solutions depend on the initial functions. Implication of the solutions to viscoelastic materials will be discussed.     

A boundary element formulation for natural convection problems

This paper presents a boundary element formulation employing a penalty function technique for two-dimensional steady thermal convection problems. By regarding the convective and buoyancy force terms in Navier-Stokes equations as body forces, the standard elastostatics analysis can be extended to solve the Navier-Stokes equations. In a similar manner, the standard potential analysis is extended to solve the energy transport equation. Finally, some numerical results are included, for typical natural convection problems, in order to demonstrate the efficiency of the present method.     

Immobilization of 1-nitroso-2-naphthol on surfactant-coated alumina for the collection of traces of cobalt(II) ions

Positively charged alumina surfaces were coated with sodium dodecyl sulfate, into which 1-nitroso-2-naphthol was immobilized. The alumina particles were effectively used for the collection of nanogram amounts of cobalt(II) from aqueous solutions of pH 1–2.5. The method has been applied to the electrothermal AAS determination of cobalt in high-purity zinc metal.     

One-pot assembly of tricyclo[6.2.1.0(1,6)]undecan-4-one and related polycyclic compounds by tandem electroreductive cyclization

[reaction: see text] Electroreductive tandem cyclization of 4-allyl-4-(2-bromoprop-2-en-1-yl)cyclohex-2-en-1-one to tricyclo[6.2.1.0(1,6)]undecan-4-one has been demonstrated. This protocol represents an attractive alternative to conventional tandem radical cyclization.     

Transport coefficients and orientational distributions of rodlike particles with magnetic moment normal to the particle axis under circumstances of a simple shear flow

We have investigated the influences of the magnetic field strength, shear rate, and random forces on transport coefficients such as viscosity and diffusion coefficient, and also on the orientational distributions of rodlike particles of a dilute colloidal dispersion. This dispersion is composed of ferromagnetic spheroidal particles with a magnetic moment normal to the particle axis. In the present analysis, these spheroidal particles are assumed to conduct the rotational Brownian motion in a simple shear flow as well as an external magnetic field. The basic equation of the orientational distribution function has been derived from the balance of the torques and solved numerically. The results obtained here are summarized as follows. For a very strong magnetic field, the rodlike particle is significantly restricted in the field direction, so that the particle points to a direction normal to the flow direction (and also to the magnetic field direction). However, the present particle does not exhibit a strong directional characteristic, which is one of the typical properties for the previous particle with a magnetic moment parallel to the particle axis. That is, the particle can rotate around the axis of the magnetic moment, although the magnetic moment nearly points to the field direction. The viscosity significantly increases with the field strength, as in the previous particle model. The particle of a larger aspect ratio leads to the larger increase in the viscosity, since such elongated particles induce larger resistance in a flow field. The diffusion coefficient under circumstances of an applied magnetic field is in reasonable agreement between theoretical and experimental results.     

Polymer electrolyte based on lithium oxalate

Ionics - Polymer electrolytes composed of poly(ethylene oxide) (PEO), lithium oxalate (LiOX), and borontrifluoride diethyl ether (BF3·OEt2) were prepared, and their ionic conductivities,...