Ideals contracted from a Noetherian extension ring

Let R be a commutative ring with identity such that for each ideal A of R, there exists a Noetherian unitary extension ring T(A) of R such that A is contracted from T(A). We investigate the structure of R. The context in which this topic has usually been considered is where R is an integal domain and T(A) is an overring of R. Under these hypotheses we show that R is Neotherian if R is one-dimensional. In the general case, R is strongly Laskerian, has Noetherian spectrum, and satisfies certain chain conditions for quotient ideals, but R need not be Noetherian.     

First-passage Monte Carlo algorithm: diffusion without all the hops

We present a novel Monte Carlo algorithm for N diffusing finite particles that react on collisions. Using the theory of first-passage processes and time dependent Green's functions, we break the difficult N-body problem into independent single- and two-body propagations circumventing numerous diffusion hops used in standard Monte Carlo simulations. The new algorithm is exact, extremely efficient, and applicable to many important physical situations in arbitrary integer dimensions.     

Applications of molecular dynamics methods to low energy ion beams and film deposition processes

Abstract

Molecular dynamics methods are used to model the impingement of low energy ions onto crystalline targets, and the effects of these beams on thin film deposition. Simulations of the deposition of silicon films show that the structure of deposits can often be improved by the use of low energy ion beams instead of the conventional thermal beam. We examine the influence of beam energy on the formation of amorphous or crystalline deposits. The influence of ion beams on surface diffusion rates and the interdiffusion between atomic layers near the surface are also considered. Cluster deposition is treated, and the results suggest that cluster beams would be effective for depositing smooth films of materials that do not wet the substrate. We discuss the use of special purpose computers and signal processing boards to extend the time scales of molecular dynamics simulations. Rapid advances in computer hardware, algorithms, and the development of accurate interatomic potentials are dramatically increasing the power of these simulations.     

Lattice Boltzmann simulation of natural convection in nanofluid-filled 2D long enclosures at presence of magnetic field

In this paper, the effects of a magnetic field on natural convection flow in filled long enclosures with Cu/water nanofluid have been analyzed by lattice Boltzmann method. This study has been carried out for the pertinent parameters in the following ranges: the Rayleigh number of base fluid, Ra = 10³–10⁵, the volumetric fraction of nanoparticles between 0 and 6 %, the aspect ratio of the enclosure between A = 0.5 and 2. The Hartmann number has been varied from Ha = 0 to 90 with interval 30 while the magnetic field is considered at inclination angles of θ = 0°, 30°, 60° and 90°. Results show that the heat transfer decreases by the increment of Hartmann number for various Rayleigh numbers and the aspect ratios. Heat transfer decreases with the growth of the aspect ratio but this growth causes the effect of the nanoparticles to increase. The magnetic field augments the effect of the nanoparticles at high Rayleigh numbers (Ra = 10⁵). The effect of the nanoparticles rises for high Hartmann numbers when the aspect ratio increases. The rise in the magnetic field inclination improves heat transfer at aspect ratio of A = 0.5.     

On the Homflypt skein module of $S^1 \times S^2$

Let k be a subring of the field of rational functions in x, v,s which contains . If M is an oriented 3-manifold, let denote the Homflypt skein module of M over k. This is the free k-module generated by isotopy classes of framed oriented links in M quotiented by the Homflypt skein relations: (1) ; (2) L with a positiv e twist ; (3) where O is the unknot. We give two bases for the relative Homflypt skein module of the solid torus with 2 points in the boundary. The first basis is related to the basis of given by J. Hoste and M. Kidwell and also V. Turaev; the second basis is related to a Young idempotent basis for based on the work of A. Aiston, H. Morton and C. Blanchet. We prove that if the elements , for n a nonzero integer, and the elements , for any integer m, are invertible ink, then -torsion module . Here the free part is generated by the empty link . In addition, if the elements , for m an integer, are invertible in k, then has no torsion. We also obtain some results for more general k. Received January 7, 2000; in final form September 20, 2000 / Published online April 12, 2001     

Synthesis,characterization, and mechanical properties of PMMA/poly(aromatic/aliphatic siloxane) semi-interpenetrating polymer networks

Semi-interpenetrating polymer networks (IPNs) composed of poly(methyl methacrylate) (PMMA) and aromatic/aliphatic siloxanes have been made via sequential and simultaneous polymerizations. As the percentage of aliphatic siloxane increases, flexibility and, in general, toughness of the IPNs increases and clarity is reduced. This loss in clarity is due to the mismatch of refractive indices (1.49 form PMMA vs. 1.43 for aliphatic siloxane). PMMA is quite transparent. On the other hand, in making aromatic siloxane/PMMA IPNs clarity is retained as aromatic siloxane is increased due to better matching refractive index (1.49 for PMMA and −1.49 for poly(diphenyl siloxane)). Gel permeation chromatography (GPC) indicates slightly crosslinked IPNs with the THF soluble portions having number-average molecular weight, M¯_n, of 10⁵–10⁶. NMRs of IPNs essentially show peaks for the components, PMMA and the siloxane, which make up the respective IPNs. ²⁹Si-NMRs indicate cross-linking and grafting. Mechanical properties show increased toughness of IPNs versus PMMA as percentage of siloxane and crosslinker increases, but with a corresponding loss in tensile strength. © 1996 John Wiley & Sons, Inc.