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We present new numerical results for shape optimization problems of interior Neumann eigenvalues. This field is not well understood from a theoretical standpoint. The existence of shape maximizers is not proven beyond the first two eigenvalues, so we study the problem numerically. We describe a method to compute the eigenvalues for a given shape that combines the boundary element method with an algorithm for nonlinear eigenvalues. As numerical optimization requires many such evaluations, we put a focus on the efficiency of the method and the implemented routine. The method is well suited for parallelization. Using the resulting fast routines and a specialized parametrization of the shapes, we found improved maxima for several eigenvalues.
Interior transmission eigenvalue problems for the Helmholtz equation play an important role in inverse wave scattering. Some distribution properties of those eigenvalues in the complex plane are reviewed. Further, a new scattering model for the interior transmission eigenvalue problem with mixed boundary conditions is described and an efficient algorithm for computing the interior transmission eigenvalues is proposed. Finally, extensive numerical results for a variety of two-dimensional scatterers are presented to show the validity of the proposed scheme.
The term ocular rigidity is widely used in clinical ophthalmology. Generally it is assumed as a resistance of the whole eyeball to mechanical deformation and relates to biomechanical properties of the eye and its tissues. Basic principles and formulas for clinical tonometry, tonography and pulsatile ocular blood flow measurements are based on the concept of ocular rigidity. There is evidence for altered ocular rigidity in aging, in several eye diseases and after eye surgery. Unfortunately, there is no consensual view on ocular rigidity: it used to make a quite different sense for different people but still the same name. Foremost there is no clear consent between biomechanical engineers and ophthalmologists on the concept. Moreover ocular rigidity is occasionally characterized using various parameters with their different physical dimensions. In contrast to engineering approach, clinical approach to ocular rigidity claims to characterize the total mechanical response of the eyeball to its deformation without any detailed considerations on eye morphology or material properties of its tissues. Further to the previous chapter this section aims to describe clinical approach to ocular rigidity from the perspective of an engineer in an attempt to straighten out this concept, to show its advantages, disadvantages and various applications.
Successful bone sawing requires a high level of skill and experience, which could be gained by the use of Virtual Reality-based simulators. A key aspect of these medical simulators is realistic force feedback. The aim of this paper is to model the bone sawing process in order to develop a valid training simulator for the bilateral sagittal split osteotomy, the most often applied corrective surgery in case of a malposition of the mandible. Bone samples from a human cadaveric mandible were tested using a designed experimental system. Image processing and statistical analysis were used for the selection of four models for the bone sawing process. The results revealed a polynomial dependency between the material removal rate and the applied force. Differences between the three segments of the osteotomy line and between the cortical and cancellous bone were highlighted.
Activated carbons are known as excellent adsorbents. Their applications include the adsorptive removal of color, odor, taste, undesirable organic and inorganic pollutants from drinking and waste water; air purification in inhabited spaces; purification of many chemicals, pharmaceutical products and many others. This chapter elucidates the role of normal microflora in the maintenance of human health and presents materials on possible clinical displays of microecological infringements and ways of their correction. It presents new developments concerning new probiotics with immobilized Lactobacillus and Bacillus. The chapter considers the mechanisms of the intestine disbacteriosis correction by sorbed probiotics. It demonstrates the advantages and creation prospects of immobilized probiotics developed on the basis of carbonized rice husk. There are great prospects for the development of medical biotechnology due to use of carbon sorbents with a nanostructured surface. Microbial communities form a biocenosis of the biotope and together with the host organism create permanent or temporary ecosystems.
The recent advances in microbiology have shed light on understanding the role of vitamins beyond the nutritional range. Vitamins are critical in contributing to healthy biodiversity and maintaining the proper function of gut microbiota. The sharing of vitamins among bacterial populations promotes stability in community composition and diversity; however, this balance becomes disturbed in various pathologies. Here, we overview and analyze the ability of different vitamins to selectively and specifically induce changes in the intestinal microbial community. Some schemes and regularities become visible, which may provide new insights and avenues for therapeutic management and functional optimization of the gut microbiota.