Adaptive numerical simulation of reaction - diffusion systems

Fluidized beds, granulation, heat and mass transfer, calcium dynamics, stochastic process, finite element methods, Rosenbrock methods, multigrid methods, parallelization

Numerical approximations of population balance equations in particulate systems

Magdeburg, Univ., Fak. für Mathematik, Diss., 2006

Numerical investigation of micro and macro mechanical behaviour of granular media via a discrete element approach

Magdeburg, Univ., Fak. für Mathematik, Diss., 2009

Existence, multiplicity and behaviour of solutions of some elliptic differential equations of higher order

Magdeburg, Univ., Fak. für Mathematik, Diss., 2009

Numerical analysis of finite volume schemes for population balance equations

Magdeburg, Univ., Fak. für Mathematik, Diss., 2011

Numerical prediction of nanoparticle formation in flames

Magdeburg, Univ., Fak. für Verfahrens- und Systemtechnik, Diss., 2012

Experimental and numerical investigation of vehicle soiling processes

Magdeburg, Univ., Fak. für Verfahrens- und Systemtechnik, Diss., 2012

Analysis and numerical investigation of dynamic models for liquid chromatography

Magdeburg, Univ., Fak. für Mathematik, Diss., 2013

Analytical and numerical investigation of the ultra-relativistic Euler equations

Magdeburg, Univ., Fak. für Mathematik, Diss., 2013

Periodic solutions of second-order differential inclusions systems with p-Laplacian

Some existence results are obtained for periodic solutions of nonautonomous second-order differential inclusions systems with p-Laplacian

A study of the endocervical columnar cells II - effects of physiological changes and of oathological lesions of the uterus on the specific numerical composition of the endocervical epithelium

In the second part of this paper we nalysed the correlation between the clinical pathological alterations and the sum of the types of columnar cells of 300 histological sections of cervix. Fifty histological sections of normal cervix of sexually mature women were selected and considered as normal in pattern. The specific counts of the columnar cells which line the endocervical mucosa and those of the glands of 50 normal cervices were compared with other similar counts made in 50 histological sections of cervices of old women and emphasized the differences. Comparisons were made also between 50 normal cervices and 50 sections of cervices with chronic inflammation, 50 cervices with epidermoid metaplasia and 50 cervices with myoma of the corpus. Counts were made from 50 cervices of patients who on the occasion of the surgical operation were in the proliferative phase of the menstrual cycle; these were compared with the counts of 50 cervices of uteri in the luteal phase. Finally, the numerical frequency of the following data encountered in the 300 cervices was recorded: 1. aspects of the ectocervical epithelium; 2. number of Nabothian cysts; 3. number of cervical glands; 5. number of deliveries and 6. aspect of the material within the cervical canal.

Numerical schemes of diffusion asymptotics and moment closures for kinetic equations

We investigate different models that are intended to describe the small mean free path regime of a kinetic equation, a particular attention being paid to the moment closure by entropy minimization. We introduce a specific asymptotic-induced numerical strategy which is able to treat the stiff terms of the asymptotic diffusive regime. We evaluate on numerics the performances of the method and the abilities of the reduced models to capture the main features of the full kinetic equation.

The existence of periodic solutions of a two dimensional Lattice

We consider a two dimensional lattice coupled with nearest neighbor interaction potential of power type. The existence of infinite many periodic solutions is shown by using minimax methods.

Numerical simulation of combined heat transfer phenomena (conduction, convection, and radiation). Application to he optimisation of thermal systems

Thermal systems interchanging heat and mass by conduction, convection, radiation (solar and thermal ) occur in many engineering applications like energy storage by solar collectors, window glazing in buildings, refrigeration of plastic moulds, air handling units etc. Often these thermal systems are composed of various elements for example a building with wall, windows, rooms, etc. It would be of particular interest to have a modular thermal system which is formed by connecting different modules for the elements, flexibility to use and change models for individual elements, add or remove elements without changing the entire code. A numerical approach to handle the heat transfer and fluid flow in such systems helps in saving the full scale experiment time, cost and also aids optimisation of parameters of the system. In subsequent sections are presented a short summary of the work done until now on the orientation of the thesis in the field of numerical methods for heat transfer and fluid flow applications, the work in process and the future work.

Positive solutions of nonlinear problems involving the square root of the Laplacian

We consider nonlinear elliptic problems involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive solutions to problems with power nonlinearities, we establish existence and regularity results, as well as a priori estimates of Gidas-Spruck type. In addition, among other results, we prove a symmetry theorem of Gidas-Ni-Nirenberg type.