Applied Mathematics to Mechanisms and Machines

This book brings together all 16 articles published in the Special Issue "Applied Mathematics to Mechanisms and Machines" of the MDPI Mathematics journal, in the section “Engineering Mathematics”. The subject matter covered by these works is varied, but they all have mechanisms as the object of study and mathematics as the basis of the methodology used. In fact, the synthesis, design and optimization of mechanisms, robotics, automotives, maintenance 4.0, machine vibrations, control, biomechanics and medical devices are among the topics covered in this book. This volume may be of interest to all who work in the field of mechanism and machine science and we hope that it will contribute to the development of both mechanical engineering and applied mathematics

13th Annual Review of Progress in Applied Computational Electromagnetics at the Naval Postgraduate School, Monterey, CA, March 17-21, 1997, Conference Proceedings Volumes I & II

Includes Volumes 1 &

A Bottom-Up Approach to Building an Artificial Cell by Self-Assembly

Synthetic biology is a rapidly growing field in which recent advances now allow the formation of minimal or artificial cells composed of a minimum number of components, capable of performing specific functions. New developments contributing to the complexity of artificial cells or making their design more cell-like increases the number of possible applications. To-date many processes and chemical reactions have been studied in these cells; many more remain to be explored. However, more sophisticated approaches to artificial cell design and preparation will be required to do this. The results presented here provide insights into how artificial cell development can contribute to our understanding of the self-assembly of biomolecules. The formation of lipid based vesicles is an inherent element of artificial cell development, which requires reliable techniques to prepare vesicles of cell size. The most widely applied methods have been evaluated here based on the size, quality and abundance of vesicles formed as well as the ease of encapsulating biological solutes. The effect of various lipid compositions, particularly cholesterol, has also been analysed. This comparison provides reliable information for tailoring the selection of experimental approach when building a model cell. Functionalisation of the artificial cell surface and its interior is required for many applications. For surface modification, there is growing interest in using glycolipids to fulfil a molecular recognition role. A synthetic glycolipid has been incorporated into the phospholipid membrane of giant unilamellar vesicles at biologically relevant concentrations. The synthetic glycolipid shows concentration-dependent phase behaviour in binary mixtures with DOPC and in ternary mixtures with DOPC and cholesterol. At low concentrations, the glycolipid is fully dispersed in the GUV membrane. At concentrations above 10%, the formation of lipid tubules was observed, consistent with the formation of a columnar lipid phase. Lipid tubules are observed in aqueous and oil solvents, suggesting that both hexagonal and inverted hexagonal lipid arrangements can be formed. The self- assembly of proteins in cells is required for normal biological function and unintended self-assembly also can occur following a change in environmental conditions, in some cases leading to disease. To understand these processes more fully, experiments performed in controlled, but closer to physiological conditions are required. Artificial cells provide an idea platform to do this. Bovine Serum Albumin (BSA) was encapsulated in phospholipid based giant unilamellar vesicles of cell size. The formation of aggregates within the GUV was analysed using a fluorescent dye (Thioflavin T) and various modes of microscopy. While protein aggregation was observed inside the vesicles, harsh environmental conditions were required to induce this aggregation (e.g.heat, low pH). An approach to investigate protein condensation upon in-situ expression in physiologically relevant conditions was also explored. In this case, a protein that aggregates at physiological temperature and pH (the P23T mutant of human gamma D crystallin) was expressed in-situ inside a GUV using a cell-free expression system. The formation of P23T specific aggregates was observed after incubation for several hours at 37°C. These aggregates have a fractal dimension lower than those normally observed for amorphous protein aggregate. Furthermore, we have demonstrated that the self-assembly of P23T can also be induced following transfection in mammalian cells, providing deeper insights into the mechanism by which the genetic cataract associated with this mutation occurs

Terrain synthesis: the creation, management, presentation and validation of artificial landscapes

'Synthetic Terrain' is the term used for artificially-composed computer-based Digital Terrain Models (DTMs) created by a combination of techniques and heavily influenced by Earth Sciences applications. The synthetic landscape is created to produce 'geographically acceptable', 'realistic' or 'valid' computer-rendered landscapes, maps and 3D images, which are themselves based on synthetic terrain Digital Elevation Models (OEMs). This thesis examines the way in which mainly physical landscapes can be synthesised, and presents the techniques by which terrain data sets can be managed (created, manipulated, displayed and validated), both for academic reasons and to provide a convenient and cost-effective alternative to expensive 'real world' data sets. Indeed, the latter are collected by ground-based or aerial surveying techniques (e.g. photogrammetry), normally at considerable expense, depending on the scale, resolution and type required. The digital information for a real map could take months to collect, process and reproduce, possibly involving demanding Information Technology (IT) resources and sometimes complicated by differing (or contradictory) formats. Such techniques are invalid if the region lies within an 'unfriendly' or inaccessible part of the globe, where (for example), overflying or ground surveys are forbidden. Previous attempts at synthesising terrain have not necessarily aimed at realism. Digital terrain sets have been created by using fractal mathematical models, as 'special effects' for the entertainment industry (e.g. science fiction 'alien' landscapes' for motion pictures and arcade games) or for artistic reasons. There are no known examples of synthesised DTMs being created with such a wide range of requirements and functionality, and with such a regard to validation and realism. This thesis addresses the whole concept of producing' alternative' landscapes in artificial form - nearly 22 years of research aimed at creating' geographically-sensible' synthetic terrain is described with the emphasis on the last 5 years, when this PhD thesis was conceived. These concepts are based on radical, inexpensive and rapid techniques for synthesising terrain, yet value is also placed on the 'validity', realism and 'fitness for purpose' of such models. The philosophy - or the 'thought processes' - necessary to achieve the development of the algorithms leading to synthesised DTMs is one of the primary achievement of the research. This in turn led to the creation of an interactive software package called GEOFORMA, which requires some manual intervention in the form of preliminary terrain classification. The sequence is thus: the user can choose to create terrain or landform assemblages without reference to any real world area. Alternatively, he can select a real world region or a 'typical' terrain type on a 'dial up' basis, which requires a short period of intensive parametric analysis based on research into established terrain classification techniques (such as fractals and other mathematical routines, process-response models etc.) The creates a composite synthesised terrain model of high quality and realism, a factor examined both qualitatively and quantitatively. Although the physical terrain is the primary concern, similar techniques are applied to the human landscape, noting such attributes as the density, type, nature and distribution of settlements, transport systems etc., and although this thread of the research is limited in scope compared with the physical landscape synthesis, some spectacular results are presented. The system also creates place names based on a simple algorithm. Fluvial landscapes, upland regions and coastlines have been selected from the many possible terrain types for 'treatment', and the thesis gives each of these sample landscapes a separate chapter with appropriate illustrations from this original and extensive research. Finally, and inevitably, the work also poses questions in attempting to provide answers, this is perhaps inevitable in a relatively new genre, encompassing so many disciplines, and with relatively sparse literature on the subject

Terrain synthesis: the creation, management, presentation and validation of artificial landscapes

'Synthetic Terrain' is the term used for artificially-composed computer-based Digital Terrain Models (DTMs) created by a combination of techniques and heavily influenced by Earth Sciences applications. The synthetic landscape is created to produce 'geographically acceptable', 'realistic' or 'valid' computer-rendered landscapes, maps and 3D images, which are themselves based on synthetic terrain Digital Elevation Models (OEMs). This thesis examines the way in which mainly physical landscapes can be synthesised, and presents the techniques by which terrain data sets can be managed (created, manipulated, displayed and validated), both for academic reasons and to provide a convenient and cost-effective alternative to expensive 'real world' data sets. Indeed, the latter are collected by ground-based or aerial surveying techniques (e.g. photogrammetry), normally at considerable expense, depending on the scale, resolution and type required. The digital information for a real map could take months to collect, process and reproduce, possibly involving demanding Information Technology (IT) resources and sometimes complicated by differing (or contradictory) formats. Such techniques are invalid if the region lies within an 'unfriendly' or inaccessible part of the globe, where (for example), overflying or ground surveys are forbidden. Previous attempts at synthesising terrain have not necessarily aimed at realism. Digital terrain sets have been created by using fractal mathematical models, as 'special effects' for the entertainment industry (e.g. science fiction 'alien' landscapes' for motion pictures and arcade games) or for artistic reasons. There are no known examples of synthesised DTMs being created with such a wide range of requirements and functionality, and with such a regard to validation and realism. This thesis addresses the whole concept of producing' alternative' landscapes in artificial form - nearly 22 years of research aimed at creating' geographically-sensible' synthetic terrain is described with the emphasis on the last 5 years, when this PhD thesis was conceived. These concepts are based on radical, inexpensive and rapid techniques for synthesising terrain, yet value is also placed on the 'validity', realism and 'fitness for purpose' of such models. The philosophy - or the 'thought processes' - necessary to achieve the development of the algorithms leading to synthesised DTMs is one of the primary achievement of the research. This in turn led to the creation of an interactive software package called GEOFORMA, which requires some manual intervention in the form of preliminary terrain classification. The sequence is thus: the user can choose to create terrain or landform assemblages without reference to any real world area. Alternatively, he can select a real world region or a 'typical' terrain type on a 'dial up' basis, which requires a short period of intensive parametric analysis based on research into established terrain classification techniques (such as fractals and other mathematical routines, process-response models etc.) The creates a composite synthesised terrain model of high quality and realism, a factor examined both qualitatively and quantitatively. Although the physical terrain is the primary concern, similar techniques are applied to the human landscape, noting such attributes as the density, type, nature and distribution of settlements, transport systems etc., and although this thread of the research is limited in scope compared with the physical landscape synthesis, some spectacular results are presented. The system also creates place names based on a simple algorithm. Fluvial landscapes, upland regions and coastlines have been selected from the many possible terrain types for 'treatment', and the thesis gives each of these sample landscapes a separate chapter with appropriate illustrations from this original and extensive research. Finally, and inevitably, the work also poses questions in attempting to provide answers, this is perhaps inevitable in a relatively new genre, encompassing so many disciplines, and with relatively sparse literature on the subject