Cohen–Macaulay Multi–Rees Algebras

Let A be a local ring, and let I ₁,...,I _r A be ideals of positive height. In this article we compare the Cohen–Macaulay property of the multi–Rees algebra R _A (I ₁,...,I _r ) to that of the usual Rees algebra R _A (I ₁ ··· I _r ) of the product I ₁ ··· I _r . In particular, when the analytic spread of I ₁ ··· I _r is small, this leads to necessary and sufficient conditions for the Cohen–Macaulayness of R _A (I ₁,...,I _r ). We apply our results to the theory of joint reductions and mixed multiplicities.     

Rheological effect on thermocapillary flow of a liquid film jet painted on a moving boundary

In the present paper, a liquid (or melt) film of relatively high temperature ejected from a vessel and painted on the moving solid film is analyzed by using the second-order fluid model of the non-Newtonian fluid. The thermocapillary flow driven by the temperature gradient on the free surface of a Newtonian liquid film was discussed before. The effect of rheological fluid on thermocapillary flow is considered in the present paper. The analysis is based on the approximations of lubrication theory and perturbation theory. The equation of liquid height and the process of thermal hydrodynamics of the non-Newtonian liquid film are obtained, and the case of weak effect of the rheological fluid is solved in detail.     

Topological mixing in -spaces

If is a proper -space and a non-elementary discrete group of isometries acting properly discontinuously on it is shown that the geodesic flow on the quotient space is topologically mixing, provided that the generalized Busemann function has zeros on the boundary and the non-wandering set of the flow equals the whole quotient space of geodesics (the latter being redundant when is compact). Applications include the proof of topological mixing for (A) compact negatively curved polyhedra, (B) compact quotients of proper geodesically complete -spaces by a one-ended group of isometries and (C) finite -dimensional ideal polyhedra.

     

Temperature Evolution During Radiative Gravitational Collapse

We investigate the evolution of the temperature profile of a Friedmann-like collapsing sphere undergoing dissipative gravitational collapse in the form of a radial heat flux. We further consider the behavior of the star close to quasi-static equilibrium (weak heat flux approximation) and show that relaxational effects cannot be ignored. It is explicitly shown that extended irreversible thermodynamics predict a higher temperature at all interior points of the stellar configuration compared to the Eckart theory. These results carry over to the weak heat flux approximation with the magnitude of the temperature being lower than the full radiating model. The stability of the model after its departure from equilibrium is studied by considering the behavior of the control parameter throughout the stellar interior.     

取样管型流分相式气液两相流体流量计

提出了用取样管来组成一种分流分相式气液两相流体流量计,通过取样管从被测两相流中成比例地分流出一部分气液混合物,然后应用-小型分离器将其分离成单相气体和液体,并用单相流量计分别测量它们的流量,最后根据测量值计算被测两相流体的各相总流量.文中给出了这种两相流体流量计的组成原理,分流系数特性及实验结果.研究结果表明,取样管的端口形状对分流系数的特性影响较大,其中S型端口的效果较理想,能够在较宽的测量范围内保持分流系数的稳定.     

Simulation on the Effect of Brownian Motion on Nanoparticle Trajectories in a Pulsed Microplasma Cluster Source

We describe a simulation of the nanoparticle trajectories in a pulsed cluster beam source. Clusters, formed by condensation of atomic vapor in a helium bath, and considered here as rigid spheres having a diameter of 1.5nm, were tracked during their travel inside the source cavity, an aerodynamic lens, and a cylindrical nozzle. Steady state supersonic laminar flow of helium is considered in an axi-symmetric geometry aiming to simulate, within some limitations, the conditions under which cluster formation takes place in a pulsed microplasma cluster source. In spite of the unsteady nature of the pulsed source, the time scale characterizing particle motion in the flow field is significantly smaller than the characteristic time constant for the evolution of gas pressure in the source. For this reason, a steady simulation can shed some light on the understanding of processes governing nanoparticle motion in a pulsed vaporization source. The extent to which the Brownian diffusion can affect the particle extraction from the source is investigated. Simulations have shown that the Brownian motion perturbs the clusters from the trajectories dictated by the carrier gas and increases the rate of cluster deposition on the source internal walls. However, it does not hinder the aerodynamic focalization produced by the lens even in nano-size cluster regime. This result is qualitatively confirmed by experiment.     

对可压缩流体若干问题的讨论

根据气体幼力学中一维定常等熵等流的基本方程组,得出的一维定常等熵管流的速度变化与管截面变化关系式,定性一讨论了一维定常等熵管流的截面变化对气流速度的影响。     

The Osher scheme for non-equilibrium reacting flows

An extension of the Osher upwind scheme to non-equilibrium reacting flows is presented, Owing to the presence of source terms, the Riemann problem is no longer self-similar and therefore its approximate solution becomes tedious. With simplicity in mind, a linearized approach which avoids an iterative solution is used to define the intermediate states and sonic points. The source terms are treated explicitly. Numerical computations are presented to demonstrate the feasibility, efficiency and accuracy of the proposed method. The test problems include a ZND (Zeldovich-Neumann-Doring) detonation problem for which spurious numerical solutions which propagate at mesh speed have been observed on coarse grids. With the present method, a change of limiter causes the solution to change from the physically correct CJ detonation solution to the spurious weak detonation solution.     

Bulk and microscopic properties of copolymer networks in mixed aqueous solvents

Amphiphilic films and hydrogels have been prepared from ethanol/water solutions containing a hydrocarbon-grafted water-soluble cellulose ether. These materials are characterized by dispersed hydrophobic microdomains which form spontaneously in the solvent due to the inherent incompatibility of the side chains with water. At low applied shear stress, the microdomains behave as temporary linkages of finite lifetimes, imparting viscoelastic properties to the networks. The molecular weight between microdomains was found to be independent of the volume fraction of polymer in the gel, and the number of linkages per backbone ranges from 22.8 ± 1.3 to 26.2 ± 1.5 over the frequency range 30–50 rad/s. The behavior of the solutions and gels was characterized using fluorescence and dynamic rheological measurements. It was demonstrated that the microdomains are capable of sequestering water-insoluble solutes. © 1992 John Wiley & Sons, Inc.