Existence of traveling wave solutions for the Diffusion Poisson Coupled Model: a computer-assisted proof

The Diffusion Poisson Coupled Model describes the evolution of a dense oxide layer appearing at the surface of carbon steel canisters in contact with a claystone formation. This model is a one dimensional free boundary problem involving drift-diffusion equations on the density of species (electrons, ferric cations and oxygen vacancies), coupled with a Poisson equation on the electrostatic potential and with moving boundary equations, which describe the evolution of the position of each unknown interfaces of the spatial domain. Numerical simulations suggest the existence of traveling wave solutions for this model. These solutions are defined by stationary profiles on a fixed size domain with interfaces moving both at the same velocity. In this paper, we present and apply a computer-assisted method in order to prove the existence of these traveling wave solutions. We also establish a precise and certified description of the solutions. p, li { white-space: pre-wrap;

A Photogrammetric Technique for Developing Boundary Equations for Flexible Sheath Waterless Trap Seals as Used in Building Drainage Systems

The water trap seal is still the main method of protecting building inhabitants from the ingress of foul contaminated air and noxious gases from the sewer. This seal can become compromised when water is lost in the trap by processes including evaporation and siphonage from excessive system suction pressures. A recent innovation is the waterless trap seal, which uses flexible sheaths, typically made from silicone rubber to form the seal. The sheath opens in response to a sub-atmospheric air pressure and will shut tightly under a supra-atmospheric pressure in order to form a seal. Full system numerical modelling of building drainage systems has offered insight into system responses to pressure transients and has opened up the evaluation of building wastewater systems to predictive modelling which has assisted in producing improvements to public health. A requirement of any predictive model is a mathematical representation of the physical characteristics of the system. This research develops a technique for developing boundary equations so that predictive modelling is possible. We combine photographic and pressure data analysed by Fourier analysis to develop the model. The technique is applicable to any device were the fluid structure interaction plays a significant role in its operation.

ANALYTICAL MODELLING OF PERFORATED GEOMETRICAL DOMAINS BY THE R-FUNCTIONS

This paper deals with the construction of boundary equations for geometric domains with perforation. Different types of perforated geometric domains are considered. The R-functions method for analytical modelling of perforated geometrical domains is used. For all constructed equations, function plots are obtained.

Natural Frequencies of Pressurized Hot Fluid Conveying Pipes

In this study, the transverse natural frequencies of a pressurized hot fluid conveying pipe is investigated using complex mode function. Employing the dispersive relations and the non-trivial solution of the coefficient matrix obtained from the boundary equations, the eigenvalues and the linear natural frequencies are obtained numerically. The parametric study is conducted to highlight the effects of variation in operating pressure and pressure drop on the first two modes of the natural frequency of the system. The natural frequency was found to increase nonlinearly with the increase in the operating pressure and pressures drop but decreases with flow velocity. Keywords— Fluid-conveying pipe, natural frequency, pressure variation, transverse vibrations