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Wed, 28 May 2008 10:22:37 +0200Wed, 28 May 2008 10:22:37 +0200Numerical evidance for the non-existing of solutions of the equations desribing rotational fiber spinning
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1961
Abstract. The stationary, isothermal rotational spinning process of fibers is considered. The investigations are concerned with the case of large Reynolds (± = 3/Re ¿ 1) and small Rossby numbers (\\\" ¿ 1). Modelling the fibers as a Newtonian fluid and applying slender body approximations, the process is described by a two–point boundary value problem of ODEs. The involved quantities are the coordinates of the fiber’s centerline, the fluid velocity and viscous stress. The inviscid case ± = 0 is discussed as a reference case. For the viscous case ± > 0 numerical simulations are carried out. Transfering some properties of the inviscid limit to the viscous case, analytical bounds for the initial viscous stress of the fiber are obtained. A good agreement with the numerical results is found. These bounds give strong evidence, that for ± > 3\\\"2 no physical relevant solution can exist. A possible interpretation of the above coupling of ± and \\\" related to the die–swell phenomenon is given.Th. Götz; A. Klar; A. Unterreiter; R. Wegenerreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1961Wed, 28 May 2008 10:22:37 +0200A Hybrid Simulation Method for Radivative Transfer Equations
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1274
We consider heat transfer processes where radiation in a large number of frequency bands plays a dominant role.Michael Junk; A. Unterreiter; F. Zingsheimpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1274Mon, 10 Dec 2001 00:00:00 +0100A Residual Based Error Formula for a Class of Transport Equations
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1275
We present an exact residual based error formula in natural norms for a class of transport equations.M. Junk; A. Unterreiter; F. Zingsheimpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1275Mon, 10 Dec 2001 00:00:00 +0100On singular limits of mean-field equations
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1054
Mean field equations arise as steady state versions of convection-diffusion systems where the convective field is determined as solution of a Poisson equation whose right hand side is affine in the solutions of the convection-diffusion equations. In this paper we consider the repulsive coupling case for a system of 2 convection-diffusion equations. For general diffusivities we prove the existence of a unique solution of the mean field equation by a variational technique. Also we analyse the small-Debye-length limit and prove convergence to either the so-called charge-neutral case or to a double obstacle problem for the limiting potential depending on the data.Jean Dolbeault; Peter A. Markowich; Andreas Unterreiterpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1054Wed, 21 Jun 2000 00:00:00 +0200The Stationary Current-Voltage Characteristics of the Quantum Drift Diffusion Model
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/650
This paper is concerned with numerical algorithms for the bipolar quantum drift diffusion model. For the thermal equilibrium case a quasi-gradient method minimizing the energy functional is introduced and strong convergence is proven. The computation of current - voltage characteristics is performed by means of an extended emph{Gummel - iteration}. It is shown that the involved fixed point mapping is a contraction for small applied voltages. In this case the model equations are uniquely solvable and convergence of the proposed iteration scheme follows. Numerical simulations of a one dimensional resonant tunneling diode are presented. The computed current - voltage characteristics are in good qualitative agreement with experimental measurements. The appearance of negative differential resistances is verified for the first time in a Quantum Drift Diffusion model.R. Pinnau; A. Unterreiterpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/650Mon, 03 Apr 2000 00:00:00 +0200