This paper is a tutorial on how to model and prove complex properties of complex hybrid systems in KeYmaera, an automatic and interactive formal verification tool for hybrid systems implementing differential dynamic logic. Hybrid systems can model highly nontrivial controllers of physical plants, whose behaviors are often safety critical such as trains, cars, airplanes, or medical devices. Form...

The superhydrophobicity of a microchannel is determined by not only the wettability of channel wall but also the surface topography. Recent experiments have found that superhrydrophobic surfaces can be achieved by pattering roughness on hydrophobic surfaces. In this paper, the dynamics of two-phase flow in microchannel with different wettability and topography is studied numerically by the latt...

This work is devoted to the numerical approximation of the solutions to the system of conservation laws which arises in the modeling of two-phase flows in pipelines. The PDEs are closed by two highly nonlinear algebraic relations, namely, a pressure law and a hydrodynamic law. We have previously proposed an explicit relaxation scheme which allows us to cope with these nonlinearities. But the sy...

In this paper we propose a modified multiscale finite element method for two-phase flow simulations in heterogeneous porous media. The main idea of the method is to use the global fine-scale solution at initial time to determine the boundary conditions of the basis functions. This method provides a significant improvement in two-phase flow simulations in porous media where the long-range effect...

A free energy (FE) model, the Shan–Chen (S–C) model, and the Rothman and Keller (R–K) model are studied numerically to evaluate their performance inmodeling two-dimensional (2D) immiscible two-phase flow in porous media on the pore scale. The FEmodel is proved to satisfy the Galilean invariance through a numerical test and the mass conservation of each component in the simulations is exact. Two...

purpose: to compare the results of two different methods of frontalis suspension using fascia lata in congenital ptosis. methods: in a randomized clinical trial, double triangle sling was compared with single triangle sling using fascia lata. eight patients with unilateral and 11 patients with bilateral congenital ptosis were randomly assigned for each procedure. results: there was no statistic...

with the growth of technology, supervising systems are increasingly replacing humans in military, transportation, medical, spatial, and other industries. among these systems are machine vision systems which are based on image processing and analysis. one of the important tasks of image processing is classification of images into desirable categories for the identification of objects or their sp...