Jaw mechanics of the pterosaur skull construction and the evolution of toothlessness

In the present study, pterosaur skull constructions were analysed using a combined approach of finite element analysis (FEA), static investigations as well as applying classical beam theory and lever mechanics. The study concentrates on the operating regime „bite“, where loads are distributed via the dentition or a keratinous rhamphotheca into the skull during jaw occlusion. As a first step, pterosaur tooth constructions were analysed. The different morphologies of the tooth construction determine specific operational ranges, in which the teeth perform best (= greatest resistance against failure). The incomplete enamel-covering of the pterosaur tooth constructions thereby leads to a reduction of strain and stress and to a greater lateral elasticity than for a complete enamel cover. This permits the development of high and lateral compressed tooth constructions. Further stress-absorption occurs in the periodontal membrane, although its mechanical properties can not be clarified unambiguously. A three-dimensionally preserved skull of Anhanguera was chosen as a case-study for the investigation of the skull constructions. CT-scans were made to get information about the internal architecture, supplemented by thin-sections of a rostrum of a second Anhanguera specimen. These showed that the rostrum can be approximated as a double-walled triangular tube with a large central vacuity and an average wall-thickness of the bony layers of about 1 mm. On base of the CT-scans, a stereolithography of the skull of Anhanguera was made on which the jaw adductor and abductor muscles were modelled, permitting to determine muscular forces. The values were used for the lever mechanics, cantilever and space frame analysis. These studies and the FEA show, that the jaw reaction forces are critical for the stability of the skull construction. The large jugal area ventral to the orbita and the inclined occipital region act as buttresses against these loads. In contrast to the orbitotemporal region which is subject to varying loading conditions, the pattern in the rostrum is less complex. Here, mainly bending in dorsal direction and torsion occur. The hollow rostrum leads to a reduction of weight of the skull and to a high bending and torsional resistance. Similar to the Anhanguera skull construction, the skulls of those pterosaur taxa were analysed, from which enough skull material is know to permit a reliable reconstruction. Furthermore, FEA were made from five selected taxa. The comparison of the biomechanical behaviour of the different skull constructions results in major transformational processes: elongation of rostra, inclination of the occipital region, variation of tooth morphology, reduction of the dentition and replacement of teeth by a keratinous hook or rhamphotheca, fusion of naris and antorbital fenestra, and the development of bony and soft-tissue crests. These processes are discussed for their biomechanical effects during bite. Certain optional operational ranges for feeding are assigned to the different skull constructions and previous hypotheses (e.g. skimming) are verified. Using the principle of economisation, these processes help to establish irreversible transformations and to define possible evolutionary pathways. The resulting constructional levels and the structural variations within these levels are interpreted in light of a greater feeding efficiency and reduction of bony mass combined with an increased stability against the various loads. The biomechanical conclusive pathways are used for comparison and verification of recent hypothesis of the phylogenetic systematics of pterosaurs.

Finite-element discretization of 3D energy-transport equations for semiconductors

In this thesis a mathematical model was derived that describes the charge and energy transport in semiconductor devices like transistors. Moreover, numerical simulations of these physical processes are performed. In order to accomplish this, methods of theoretical physics, functional analysis, numerical mathematics and computer programming are applied. After an introduction to the status quo of semiconductor device simulation methods and a brief review of historical facts up to now, the attention is shifted to the construction of a model, which serves as the basis of the subsequent derivations in the thesis. Thereby the starting point is an important equation of the theory of dilute gases. From this equation the model equations are derived and specified by means of a series expansion method. This is done in a multi-stage derivation process, which is mainly taken from a scientific paper and which does not constitute the focus of this thesis. In the following phase we specify the mathematical setting and make precise the model assumptions. Thereby we make use of methods of functional analysis. Since the equations we deal with are coupled, we are concerned with a nonstandard problem. In contrary, the theory of scalar elliptic equations is established meanwhile. Subsequently, we are preoccupied with the numerical discretization of the equations. A special finite-element method is used for the discretization. This special approach has to be done in order to make the numerical results appropriate for practical application. By a series of transformations from the discrete model we derive a system of algebraic equations that are eligible for numerical evaluation. Using self-made computer programs we solve the equations to get approximate solutions. These programs are based on new and specialized iteration procedures that are developed and thoroughly tested within the frame of this research work. Due to their importance and their novel status, they are explained and demonstrated in detail. We compare these new iterations with a standard method that is complemented by a feature to fit in the current context. A further innovation is the computation of solutions in three-dimensional domains, which are still rare. Special attention is paid to applicability of the 3D simulation tools. The programs are designed to have justifiable working complexity. The simulation results of some models of contemporary semiconductor devices are shown and detailed comments on the results are given. Eventually, we make a prospect on future development and enhancements of the models and of the algorithms that we used.