Towards understanding the critical heat flux for industrial applications

Understanding CHF is of an upmost importance in many industries, especially in the design and operation of boilers, nuclear power plants, cryogenic systems, etc. Due to safety issues related to the nuclear power plants, and the adaptation of CHF as the limiting criterion of power generation, it is important to understand the mechanisms of CHF relevant to nuclear systems operation. Moreover, CHF is expected to occur during transients than steady-state conditions. Therefore, knowledge of transient CHF is of great importance for the safety evaluation of nuclear reactors under transient condition. In this paper, the existing CHF experimental and modeling studies are discussed in order to understand the phenomena leading to CHF. Also, the effect of transient conditions on CHF for nuclear fuels has been evaluated.     

When is a partial Latin square uniquely completable, but not its completable product?

Let P and Q be uniquely completable partial Latin squares. It is an open problem to determine necessary and sufficient conditions so that the completable product P⊗Q is also uniquely completable. So far, only a few specific examples of P have been given such that the completable product of P with itself (P⊗P) does not have a unique completion. In this paper, we find a whole class of such partial Latin squares.     

Existence and Concentration of Ground States of Coupled Nonlinear Schr(o)dinger Equations with Bounded Potentials

A 2-coupled nonlinear Schr(o)dinger equations with bounded varying potentials and strongly attractive interactions is considered.When the attractive interaction is strong enough,the existence of a ground state for sufficiently small Planck constant is proved.As the Planck constant approaches zero,it is proved that one of the components concentrates at a minimum point of the ground state energy function which is defined in Section 4.     

Investigation of critical influential speed for moving mass problems on beams

A traveling mass due to its mass inertia has significant effects on the dynamic response of the structures. According to recent developments in structural materials and constructional technologies, the structures are likely to be affected by sudden changes of masses and substructure elements, in which the inertia effect of a moving mass is not negligible. The transverse inertia effects have been a topic of interest in bridge dynamics, design of railway tracks, guide way systems and other engineering applications such as modern high-speed precision machinery process. In this study an analytical–numerical method is presented which can be used to determine the dynamic response of beams carrying a moving mass, with various boundary conditions. It has been shown that the Coriolis acceleration, associated with the moving mass as it traverses along the vibrating beam shall be considered as well. Influences regarding the speed of the moving mass on the dynamic response of beams with various boundary conditions were also investigated. Results illustrated that the speed of a moving mass has direct influence on the entire structural dynamic response, depending on its boundary conditions. Critical influential speeds in the moving mass problems were introduced and obtained in numerical examples for various BC’s.     

Resonance problems for the p-Laplacian systems

Two existence theorems of the solutions are obtained for the p-Laplacian systems at resonance under a Landesman-Lazer-type condition by critical point theory.     

Wetting, adsorption and surface critical phenomena

Our understanding of interfacial phenomena at the surfaces of critical systems, and in particular at the surfaces of critical binary liquid mixtures, has improved significantly in the past decade. There is now substantial agreement between theory and experiment. In this paper we review recent experimental progress, provide a conceptual framework within which the majority of these experiments can now be understood, and discuss critically any remaining unresolved discrepancies between experiments or with theory.     

Positive solutions for Schrödinger–Poisson equations with a critical exponent

In this paper we establish the existence of a positive solution of the Schrödinger–Poisson equations with a critical Sobolev exponent. The methods used here are based on the concentration–compactness principle of P. L. Lions and methods of Brezis and Nirenberg.     

Critical exponents for nonlinear diffusion equations with nonlinear boundary sources

This paper is concerned with the large time behavior of solutions to two types of nonlinear diffusion equations with nonlinear boundary sources on the exterior domain of the unit ball. We are interested in the critical global exponent q₀ and the critical Fujita exponent qc for the problems considered, and show that q₀=qc for the multi-dimensional porous medium equation and non-Newtonian filtration equation with nonlinear boundary sources. This is quite different from the known results that q₀<qc for the one-dimensional case.     

Finite-size effects in the self-organized critical forest-fire model

We study finite-size effects in the self-organized critical forest-fire model by numerically evaluating the tree density and the fire size distribution. The results show that this model does not display the finite-size scaling seen in conventional critical systems. Rather, the system is composed of relatively homogeneous patches of different tree densities, leading to two qualitatively different types of fires: those that span an entire patch and those that do not. As the system size becomes smaller, the system contains less patches, and finally becomes homogeneous, with large density fluctuations in time. Received 24 April 1999 and Received in final form 26 October 1999