We establish an analog of the Beale–Kato–Majda criterion for singularities of smooth solutions of the system of PDE arising in the Oldroyd model for ideal viscoelastic flow. It is well known that smooth solutions of the initial value problem associated with Euler’s equations { ∂tu+ (u · ∇)u = −∇p ∇ · u = 0 , (x, t) ∈ R 3 × (0, T ) (1.1) exist for some finite time T > 0. Here u = u(x, t) ∈ R and...

Abstract A so-called semi-ideal model has been derived for a pulse-operated MEMS thermal flow sensor by reciprocal numerical mapping of the ideal an instantaneous line heat source to experimental data sensor. The novel not only applies as precise potential working equation but also provides insight into complete signal transmission chain from heater thermometers It gives answers prominent pecul...

A jet is a stream of one fluid entering another at high speed. In the simplest classical model of jet flow, the geometry is two-dimensional, gravity and viscosity are ignored, the moving fluid is a liquid, and the stationary fluid is a gas whose influence is assumed negligible. The description of this idealized flow can be reduced to a problem of complex analysis, but, except for very simple no...

This lecture discusses the mathematical relationship between network structure and network utilization of transportation network. Network structure means the graph itself. Network utilization represent the aggregation of trajectories of agents in using the network graph. I show the similarity and relationship between the structural pattern of the network and network utilization.

An ideal coronary vasodilator for studying coronary flow reserve in humans would rapidly produce maximal coronary vasodilation, be short acting to permit repeated measurements, and not alter systemic hemodynamics. The two commonly used vasodilators (dipyridamole and meglumine diatrizoate) do not satisfy these criteria; meglumine diatrizoate does not produce maximal hyperemia and dipyridamole ha...

a numerical framework has been proposed to model the interacting effects of mixture non-ideality and mass transfer on hydrodynamics of a multiphase system using cfd methods.mass transfer during condensation and vaporization is modeled by chemical potential at the liquid-vapor interface. species mass transfers are related to the diffusion at the interface which in turn is related to the concentr...