0000000000352521
AUTHOR
Jānis Cepītis
showing 4 related works from this author
A Certain Mathematical Model of the Glass Fibre Material Production
1997
There is considered the full mathematical model of chemical reactions on the surface of glass fibre material that was imbedded in the flow of acid solution and was pulled longitudionally. Self-similar forms of this model are obtained and their approximations by monotone schemes of differences are proposed. Some special cases which make possible to get the analytic solutions are underlined. The self-similar forms of the differential equations of the substances transport allow to calculate the emission of the alkaline oxide from the glass fibre material under the influence of the acid solution flow. Some conclusions with practical significance for the technological process is made up accordin…
Numerical experiments with single mode gyrotron equations
2012
Gyrotrons are microwave sources whose operation is based on the stimulated cyclotron radiation of electrons oscillating in a static magnetic field. This process is described by the system of two complex differential equations: nonlinear first order ordinary differential equation with parameter (averaged equation of electron motion) and second order partial differential equation for high frequency field (RF field) in resonator (Schrödinger type equation for the wave amplitude). The stationary problem of the single mode gyrotron equation in short time interval with real initial conditions was numerically examined in our earlier work. In this paper we consider the stationary and nonstationary …
Non-Isothermal Mathematical Model of Wood and Paper Drying
2002
A mathematical model of wood or paper drying based on a detailed consideration of both heat and moisture transport phenomena is proposed. By averaging we express the model as a sequence of initial value problems for systems of two first order nonlinear ordinary differential equations. This mathematical model makes it possible to efficiently investigate the drying process of a thin wood plate or paper sheet for varying temperature and humidity conditions in the surroundings. In particular, we have considered the optimization of the heat regime over a series of steam-heated cylinders in a papermaking machine.
Phase Plane Analysis of Web Drying
2004
The mathematical model which describes the web drying in the papermaking machine has been carried out in the collaboration between our institute and joint-stock company “Paper Mill ‘Ligatne’” engineers. The general principles of this develpopment were underlined in the report [zz00]. Under some simplifying assumptions this model can be reduced to the nonlinear moisture — temperature phase plane equation. This equation promotes to obtain significant physical parameters used in the mathematical model, clarifies the causes which allow to optimize the papermaking machine drying cylinders temperature regime. The phase plane equation also explains the parabolic temperature distribution in a serie…