Στην παρούσα Διπλωματική Εργασία μελετώνται εφαρμογές της θεωρίας της Διαστατικής Ανάλυσης στην μαθηματική μοντελοποίηση. Πιο συγκεκριμένα, στο πρώτο κεφάλαιο εισάγουμε την έννοια της διαστατικής ανάλυσης καθώς και την χρησιμότητά της κάνοντας ταυτόχρονα μια σύντομη ιστορική αναδρομή. Στο ίδιο κεφάλαιο ακόμα παραθέτουμε το περίφημο παράδειγμα στο οποίο ο G.I. Taylor υπολόγισε, με την βοήθεια της Διαστατικής Ανάλυσης, την ενέργεια που εκλύθηκε από την πρώτη, δοκιμαστική ατομική βόμβα στο New Mexico τον Ιούλιο του 1945. Στο δεύτερο κεφάλαιο αναπτύσσονται το Θεώρημα Π του Buckingham, το οποίο αποτελεί το θεμελιώδες θεωρητικό υπόβαθρο της Διαστατικής Ανάλυσης, καθώς και δύο εφαρμογές που βασίζονται στο παραπάνω θεώρημα. Η πρώτη εξ' αυτών αναφέρεται στην ταχύτητα εξάπλωσης της πετρελαιοκηλίδάς στον Κόλπο του Μεξικού που προκλήθηκε από την έκρηξη σε υποθαλάσσια πλατφόρμα εξόρυξης πετρελαίου την άνοιξη του 2010. Τέλος, στο τρίτο κεφάλαιο αναλύονται οι εξισώσεις Navier-Stokes και συνέχειας της Ρευστοδυναμικης. Ελέγχουμε ότι οι εξισώσεις αυτές είναι διαστατικά ομογενείς και στη συνέχεια περιγράφουμε τη διαδικασία κανονικοποίησής τους. / In this paper, we study applications of the theory of dimensional analysis in mathematical modeling. More specifically, the first chapter introduces the concept of dimensional analysis and the usefulness of simultaneously making a brief historical overview. In the same chapter is describt the famous example in which the G.I. Taylor estimated with the help of dimensional analysis, the energy emitted by the first atomic bomb test in New Mexico in July 1945. In the second chapter, Theorem Π of Buckingham, which is the fundamental theoretical basis of dimensional analysis, as well as two applications based on the above theorem. The first of them refers at the spead of spreading oil slick in the Gulf of Mexico caused by the boom in offshore oil platform in the spring of 2010. Finally, the third chapter analyzes the equations of Navier-Stokes and continuity of fluid dynamics. We check that these equations are dimensional homogeneous and then we describe the process of how we can to normalize them.

The topic of the thesis is to build physically similar systems to simulate behaviors of real-life heavy-duty vehicles using LEGO Mindstorms as hardware platform and Buckingham π theorem as theoretical basis for the parameter scaling. The thesis work includes software and hardware system design and theoretical research in order to prove a newly proposed concept: Using LEGO to build a scaled model of real-life vehicles with specific similar physical properties. To implement the work described above, scaled models were built with LEGO and a software and hardware system was developed for controlling the scaled model. Tests were performed both on real-life vehicles and scaled models. A generalized mathematical model for the vehicle was derived in order to interpret the behaviors of the vehicle in a scientific way. Then, test results of both real-life vehicles and the corresponding scaled model were compared with the mathematical model in order to investigate if they have similar behaviors. Finally it was concluded that the scaled model built with LEGO Mindstorms combined with Buckingham π theorem could calculate the speed and turning radius of the physically similar real-life vehicle with an average accuracy of 94.68% within low speed, conservatively speaking. For further investigation and research, similar research could be performed with higher speeds to generalize the conclusions and results. / Uppsatsen ämnar till att bygga ett fysiskt likvärdigt system, som simulerar beteendet av verkliga tunga fordon, med LEGO Mindstorms som hårdvaruplattform och med Buckingham П teoremet som teoretisk grund from skalning av parametrar. Arbetet inkluderar mjukvaru- och hårdvarusystemdesign samt teoretisk forskning för att kunna bevisa ett nyligen föreslaget koncept: Att använda LEGO för att bygga en skalad modell av verkliga fordon med specifika likartade fysiska egenskaper. För att implementera det ovan föreslagna arbetet, byggdes skalade modeller i LEGO samt ett kombinerat hård- och mjukvarusystem för att styra den skalade modellen. Tester utfördes på både riktiga lastbilar samt de skalade modellerna. För att kunna identifiera parametrar samt simulera och tyda fordonens beteende så adapterades en generell matematisk modell. Testresultaten för på verkliga samt motsvarande skalade modeller jämfördes med den matematiska modellen för att påvisa om beteendet är likartat. Till sist drogs slutsatsen att den skalade modellen bygg med LEGO Mindstorms och parameterskalad med hjälp av Buckingham П teoremet kunde beräkna skalningsfaktorn av hastighet samt svängradie för det fysiskt likartade fordonet med en tillförlitlighet på 94.68%, konservativt räknat. Detta gäller för låga hastigheter och som fortsatt forskning skulle en liknande studie med starkare och snabbare motorer genomföras för att generalisera slutsatserna och resultaten.

In this study, we employed density functional theory (DFT) and molecular dynamics (MD) to investigate the mechanical and electronic properties of one-dimensional zinc oxide nanostructure. This study can be arranged into two parts: In part I: We investigated the mechanical and electronic properties of one-dimensional zinc oxide nanostructure under axial mechanical deformations by density functional theory. In this case, we could find both the highest occupied molecular orbital and the lowest unoccupied molecular orbital gap (HOMO-LUMO gap) and value of radial buckling will decrease linearly with the increase of axial strain. The changes of bond lengths and bond angles show the variation of nanostructure dependence to the increase of axial strain. This study also used partial density of state (PDOS), bond order (BO) and deformation density to analyse the differences of the electronic properties between the zinc oxide nanotubes under axial strain. In part II: This study, which employed molecular dynamics combines Buckingham and Core-Shell potentials, shows the different physical parameters, such as yield stress, young¡¦s modulus and slip vector to research the mechanical behavior and variation of structure of nanotube under axial strain.

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The purpose of this work is to describe the system of administration which existed on the estates of a megnatic of the fifteenth century, using mainly the estate records, the accounts, as source materials. To set the period and the estates themselves in context, the first two chapters have been devoted to a consideration of the life and career of the magnate, Humfrey Stafford, Duke of Buckingham, and to a description of the estates, their history and their extent. The various types of accounts themselves as working documents are then described. From them it is possible to build up a picture of the estate administration based on the units of the manor or village and the receivership, and the scope and importance of the Receiver-General and the Auditor. The actual work of the memorial officers, the receivers and the auditors is also dealt with insofar as the running of the estates is concerned. Following from the organization of the administration of extensive estates is the secondary consideration of the men who ran the estates, their origins, their connexions with Stafford, their use to Stafford outwith the purely routine affairs of administration and their expectations of advancement within his service. As far as is possible, a study is made of these men and of the men who were supported from the estates by retaining fees, in order to discover their political importance to Stafford, and whether he used them as a means of increasing his own influence and power in national or local politics. These points are covered in the two final chapters and the conclusion.

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This thesis examines the relationship of George Villiers, First Duke of Buckingham (1592--1628) to the art and aesthetic ideas of his era. As the intimate and all-powerful favourite of two successive kings, James I and Charles 1, Buckingham profoundly influenced the course of English politics, both at home and abroad, and it is as a political force that he is generally viewed. But, as a major patron of many artists and the builder of one of the largest art collections of the time, his influence in the cultural sphere must have been equally significant. Yet no modern study of this aspect of Buckingham's persona exists. / After a review of the general historiographical material on Buckingham as well as his evaluation by art historians over the years, Chapter I presents an analysis of the concept and role of Favourite in social and cultural terms. It goes on to detail Buckingham's personal position within early Stuart court culture, and argues that while this culture formed and defined him, he simultaneously re-formed and redefined it through his choices and actions. / Chapter II examines the dynamics of art patronage and Buckingham's activity as a patron, beginning with his early dealings with the native English painter, William Larkin. The relationship of Buckingham and the young Anthony Van Dyck is discussed, with parlicular attention to the artist's brief visit to England in 1620--21, and it is suggested that Buckingham was instrumental in bringing about this event. The Duke's dealings with the controversial polymath, Balthazar Gerbier, are explored, as are his many-layered connections with the premier painter of the day, Peter Paul Rubens. / In Chapter III the traditions of art collecting, especially in England are discussed, as is Buckingham's reputation as a collector compared to some of his rivals in the field. The extant documentation of his collection is examined, along with the chronology and methodology of its formation. Particular attention is given to gifts of art to Buckingham by King Charles, the Earl of Arundel and others; the art-buying by Buckingham's agents like Balthazar Gerbier; and the incorporation by the Duke into his own inventory of parts of other collections such as that of the Duke of Hamilton and, more importantly, that of Rubens. / Both in the realm of court culture and in the world of art patronage and art collecting, it was Buckingham more than anyone else who supplied the energy and set the fashion. And he continued to do so even after his premature death: the Duke's image remained bright in the memory of King Charles, whose subsequent expanded relationships with Rubens and Van Dyck owe much of their intensity to both artists' previous connections with Buckingham.

The 1632 appointment of Van Dyck as Court Painter by King Charles I changed the course of art in England. But in spite of its importance, the dynamics and mechanics of this event remain imperfectly understood. This paper suggests that one determining factor was the influence of George Villiers, Duke of Buckingham. An early admirer of Van Dyck, Buckingham in turn incarnated the young artist's own aspirations to aristocratic status. For Charles, the Duke was a personal partner and aesthetic alter-ego whose presence in the King's psyche remained strong long after Buckingham's assassination in 1628. The examination of certain of Van Dyck's paintings of the 1620's shows how the interlocking agendas and affinities of the three men combined to affect the evolution of English art.

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No description available.