Doubly Transitive Automorphism Groups of Combinatorial Surfaces

   Abstract. The combinatorial surfaces with doubly transitive automorphism groups are classified. This is established by classifying the automorphism groups of combinatorial surfaces which act doubly transitively on the vertices of the surface. The doubly transitive automorphism groups of combinatorial surfaces are the symmetric group S ₄ , the alternating group A ₅ and the Frobenius group C ₇ · C ₆ . In each case the combinatorial surface is uniquely determined. The symmetric group S ₄ acts doubly transitively on the tetrahedron surface, the alternating group A ₅ on the triangulation of the projective plane with six vertices and the Frobenius group C ₇ · C ₆ on the Moebius torus with seven vertices.     

Dynamic Equilibrium of a Coupled ODE-PDE Problem for Surface Nanobubbles

We consider a mathematical model for surface nanobubbles arising from hydrogen electrolysis in polymer electrolyte membrane (PEM) electrolyzers. Experimental advances in recent years indicated longer lifetimes of surface nanobubbles than may be explained by classical theories. Contrary to [5], we state a full model of an evolving single surface nanobubble yielding a coupled system consisting of a partial differential equation (PDE) for the hydrogen concentration in water and an ordinary differential equation (ODE) for the radius evolution. In the special case of dynamic equilibrium conditions, we prove the well-posedness of this steady state problem by a fixed-point strategy, assuming an acute-angled contact angle, and that the corresponding algorithm allows for its numerical simulation. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling,simulation and optimization of an elastic structure under moving loads

We consider an elastic structure that is subject to moving loads representing e.g. heavy trucks on a bridge or a trolley on a crane beam. A model for the quasi-static mechanical behaviour of the structure is derived, yielding a coupled problem involving partial differential equations (PDE) and ordinary differential equations (ODE). The problem is simulated numerically and validated by comparison with a standard formula used in engineering. We derive an optimal policy for passing over potentially fragile bridges. In general, our problem class leads to optimal control problems subject to coupled ODE and PDE. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermodynamic characterisation of adsorptive gas/adsorbent systems using the ALIc-model

The ALI^c-Model is a thermodynamically consistent pore filling model which allows microporous and mesoporous adsorptive gas/adsorbent systems to be described and compared directly. Examples of this will be shown on 20 systems. To this end, the standard-molar-free-enthalpy of adsorption is divided into a material-specific concentrate term and a geometric mixing term. At standard pressure and boiling temperature, all the curves of the standard-molar-free-enthalpy of adsorption as a function of the degree of pore filling end at the point of free-enthalpy of adsorption = 0 and at the degree of pore filling = 1. From these characteristic curves, finite molar values for free-enthalpy, enthalpy and entropy of adsorption can be calculated for the adsorbate-concentrate at a negligible degree of pore filling. Alkanes on activated carbons and CO₂ on Zeolite 5A are used as demonstrating examples. These values and curves obtained from measurement of adsorption-isotherm-fields enable the interaction of the adsorbate with the adsorbent to be characterized, thus providing additional information for adsorption processes and for the development of adsorbents.     

Effects of radially dependent parameters on proton transport in polymer electrolyte membrane nanopores

A three-dimensional continuum model is explored to investigate the effects of radially dependent system parameters, such as relative permittivity and viscosity, on the transport of proton and water in nanoscale cylindrical pores of a fully hydrated polymer electrolyte membrane (PEM). The model employs Poisson, Nernst-Planck, and Stokes equations. Based on evidence from the literature for the presence of a stagnant water layer near the pore surface, we assume that a no-slip surface is located inside the pore, a few Angstroms from the pore wall. To solve the system numerically, the steady-state solution for the transport of protons and water is considered to be a perturbation around the equilibrium solution. Our results indicate that a radial variation of relative permittivity has the greatest influence on pore conductivity, reducing it by about 50% when compared to that of constant permittivity. On the other hand, viscosity plays the dominant role when the effective water drag within such pores is considered. We conclude that a continuum approach, including constant viscosity, is applicable in nanoscale models provided that the location of the no-slip surface is properly specified and the radial variation of the relative permittivity is taken into consideration.     

Heavily doped Si:P emitters of crystalline Si solar cells: recombination due to phosphorus precipitation

The measured saturation current density J_0e of heavily phosphorus‐doped emitters of crystalline Si solar cells is analysed by means of sophisticated numerical device modelling. It is concluded that Shockley–Read–Hall (SRH) recombination exceeds Auger recombination significantly; it is caused by inactive phosphorus. This explains the large discrepancies between measured and simulated J_0e values, observed persist‐ently over the last two decades in industrially fabricated Si solar cells. As a consequence, the heavily phosphorus‐diffused emitters still bear a significant potential to contribute to higher Si solar cell efficiency levels, if the amount of inactive phosphorus can be reduced. (© 2014 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Optimal Control of an Elastic Tyre-Damper System with Road Contact

We study an elastic tyre with a wheel rim that is suspended at the chassis of a car by means of a spring-damper element. This quarter car model may be controlled by varying the damping constant of the electrorheological damper. Our mathematical model yields a coupled ODE-PDE problem with a free boundary at the tyre-road contact. In this study we approximate the tyre by the Hertz contact stress formula. The resulting optimal control problem with control constraints is solved numerically. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

NON-ISOMORPHIC GROUPS WITH ISOMORPHICSPECTRAL TABLES AND BURNSIDE MATRICES

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On Principal Blocks of p-Constrained Groups

A theorem of K. W. Roggenkamp and L. L. Scott shows that fora finite group G with a normal p-subgroup containing its owncentralizer, any two group bases of the integral group ringZG are conjugate in the units of Z_pG. Though the theorem presentsitself in the work of others and appears to be needed, thereis no published account. There seems to be a flaw in the proof,because a ‘theorem’ appearing in the survey [K.W. Roggenkamp, ‘The isomorphism problem for integral grouprings of finite groups’, Progress in Mathematics 95 (Birkhäuser,Basel, 1991), pp. 193--220], where the main ingredients of aproof are given, is false. In this paper, it is shown how toclose this gap, at least if one is only interested in the conclusionmentioned above. Therefore, some consequences of the resultsof A. Weiss on permutation modules are stated. The basic stepsof which any proof should consist are discussed in some detail.In doing so, a complete, yet short, proof of the theorem isgiven in the case that G has a normal Sylow p-subgroup. 2000Mathematical Subject Classification: primary 16U60; secondary20C05.