The evolution of dispersed short-fatigue-cracks is analysed based on the equilibrium of crack-number-density (CND). By separating the mean value and the stochastic ̄uctuation of local CND, the equilibrium equation of overall CND is derived. Comparing with the mean-®eld equilibrium equation, the equilibrium equation of overall CND has di€erent forms in the expression of crack-nucleation-rate or ...

Some rigorous results on discrete velocity models are briefly reviewed and their ramifications for the lattice Boltzmann equation (LBE) are discussed. In particular, issues related to thermodynamics andH -theorem of the lattice Boltzmann equation are addressed. It is argued that for the lattice Boltzmann equation satisfying the correct hydrodynamic equations, there cannot exist an H -theorem. N...

Some rigorous results on discrete velocity models are briefly reviewed and their ramifications for the lattice Boltzmann equation (LBE) are discussed. In particular, issues related to thermodynamics and H-theorem of the lattice Boltzmann equation are addressed. It is argued that for the lattice Boltzmann equation satisfying the correct hydrodynamic equations, there cannot exist an H-theorem. Ne...

For some of the EOS models the dimension of equilibrium problem can be reduced. Stability and difficulties in implementation are among the problems of flash calculation. In this work, a new reduction technique is presented to prepare a reduced number of equilibrium equations. Afterwards, a number of appropriate solution variables are selected for the prepared equation system to solve the equati...

and Applied Analysis 3 Equation (3) has a unique positive equilibrium given by y = 1 + p − z + √(1 + p − z) 2 + 4r (q + 1) 2 (q + 1) . (19) The linearized equation associated with (3) about the equilibrium is given by

Accurate vapor-liquid equilibrium data have been obtained for ethyl acetate + 2-propanol and ethyl acetate + ethanol mixtures at 84.8 kPa, and the results are discussed thermodynamically. The vapor-liquid equilibrium data are correlated with redlich-Kister, Margules, Van-Laar and Ortega, equations the parameters and standard deviation of which are calculated and reported. The best correlati...

A link between the semiclassical Einstein equation and a maximal vacuum entanglement hypothesis is established. The hypothesis asserts that entanglement entropy in small geodesic balls is maximized at fixed volume in a locally maximally symmetric vacuum state of geometry and quantum fields. A qualitative argument suggests that the Einstein equation implies the validity of the hypothesis. A more...

this paper presents a simplified approach to estimate the resultant force, which should be provided by a retention system, for the equilibrium of unstable slopes. the results were obtained with a developed algorithm, based on limit equilibrium analyses, that assumes a two-part wedge failure mechanism. design charts to obtain equivalent earth pressure coefficients are presented. based on the res...