Analiza kinematičke funkcionalnosti modela otisnutog 3D tiskačem i usporedba s istovjetnim tvornički proizvedenim modelom

Računala su takoreći budućnost gotovo svake grane, sa zadatkom da ih se funkcijski što opširnije i raznovrsnije iskoristi. Pojavom 3D printera stvorila se nova razina praktičnosti gdje se pomoću digitalne datoteke, rađene u nekom od programa s mogućnošću 3D modeliranja i animiranja, može izraditi trodimenzionalni oblik. Cilj rada je izrada i animacija modela kugličnog ležaja, prema tvorničkom modelu FAG, u programu 'Blender', koristeći pritom teksture radi preglednosti gibanja pojedinih dijelova i zatim izrada otiska 3D printerom. Nakon izrade modela printanjem, analizirati kinematičke funkcionalnosti ležaja te usporediti sa istovjetnim, originalnim tvorničku proizvedenim modelom. 3D model laserskim graviranjem izraditi i u staklu kako bi se vidjela sama preglednost modela sa tom tehnikom otiskivanja. U slučaju nedostataka postignute kinematike, predložiti načine za poboljšanje

Singularity structure of Feynman integrals with applications to six-particle scattering processes

Scattering amplitudes serve as a bridge between theoretical predictions and experimental data in Quantum Field Theories (QFTs). They are computed in perturbation theory as a series in the coupling constants. Beyond the leading order, computing the contributing Feynman integrals is one of the most critical and often complex steps required to draw predictions from the theory. A well--known method for addressing this involves deriving a system of ordinary differential equations in the canonical form that the Feynman integrals satisfy, where solutions in terms of known functions can be readily obtained. An important aspect of this method lies in understanding the singularity structure of Feynman integrals. We first introduce several representations of Feynman integrals used in different parts of this thesis. In particular, we introduce two parametric representations suitable for analyzing the singularities of Feynman integrals. Next, we address the question of determining the location of possible kinematic singularities of Feynman integrals. To this end, we first review the Landau equations and a modern approach for finding their solutions based on methods from nonlinear algebra. Next, we use the connection between the singularities of Feynman integrals and symbol alphabets to find the alphabets without ever solving the integrals. Furthermore, we review a method for the analytic computation of Feynman integrals based on differential equations. We argue that knowing the singularity structure and a good basis of Feynman integrals makes the computation more efficient and simplifies finding a solution. The main contribution of the thesis is an efficient algorithm for finding algebraic letters from the knowledge of the kinematic singularities of Feynman integrals. The algorithm is based on an observed factorization property of algebraic letters. In order to make the algorithm more efficient and ready to use in cutting--edge applications, we introduce a criterion that significantly reduces the size of the problem at hand, allowing us to handle large alphabets appearing in the high--multiplicity problems. Finally, we use the methods discussed in this thesis in a state--of--the--art computation of Feynman integrals that could not be computed without having insight into their singularity structure

Escílax de Carianda, Pseudo-Escílax e el Periplo de Paris: reconsiderando la tradición antigua de un texto geográfico

O Périplo, preservado no manuscrito Parisinus suppl. gr. 443 e erroneamente atribuído a Cílax de Carianda (sexto século a. C.), é o mais antigo espécime da periplografia grega antiga. Ele pertence ao quarto século antes de Cristo. No presente artigo, todos os testemunhos da tradição antiga tanto de Cílax quanto do Périplo de Paris são cuidadosamente avaliadas. O objetivo é determinar quando e por que o Périplo de Paris foi equivocadamente atribuído a Cílax e dissipar qualquer dúvida da suposta autoria deste trabalho geográfico antigo. A confusão, ou a falsificação deliberada, é evidente em Estrabão: ele sabia que a viagem de Cílax para o Oriente e, ao mesmo tempo estava familiarizado com o texto do Périplo de Paris, que ele atribui ao antigo navegador. Autores gregos e latinos da Época Imperial Romana conheciam o Périplo de Paris, mas muitos seguiam cegamente a atribuição equivocada a Cílax de Carianda. Quando Marciano de Heracleia no período Bizantino Antigo coletou seu corpus de geógrafos gregos antigos, ele também atribuiu o Périplo de Paris a Cílax, assim transmitindo o erro aos copistas do Paris. suppl. gr. 443.The Periplus preserved in the manuscript Parisinus suppl. gr. 443, and erroneously ascribed to Scylax of Caryanda (sixth century BC), is the oldest extant specimen of ancient Greek periplography: it belongs to the second half of the fourth century. In the present article, all the testimonies on the ancient tradition of both Scylax and the Paris Periplus are carefully evaluated. The aim is to determine when and why the Paris Periplus was mistakenly ascribed to Scylax and to clear any doubts on the alleged authorship of this ancient geographic work. The confusion, or the wilful falsification, is evident in Strabo: he knew of Scylax’s voyage in the East and at the same time was acquainted with the text of the Paris Periplus, which he ascribed to this famous ancient seafarer. Greek and Latin authors of the Roman Imperial age knew the Paris Periplus, but many followed slavishly the erroneous ascription to Scylax of Caryanda. When Marcianus of Heraclea in the early Byzantine age collected his corpus of ancient Greek geographers he also ascribed the Paris Periplus to Scylax, thus handing down the error to the copyist of the Paris. suppl. gr. 44

Kinetics of dolomite grinding in a laboratory ball mill

Grinding is one of the most widely used methods of obtaining solid particles of controled/ desired distribution systems in all branches of industry. Enlargement of this process is often based on experience and on trial and error methods that requires a large number of experiments. The development of mathematical models enabled the transfer of results to a larger scale in similar systems. The proposed researches were conducted in a laboratory scale. The modeling of the grinding process by the population balance included a description of the kinetics of dolomite grinding by kinetic parameters and the development of models that enabled the estimation of kinetic parameters on the basis of the particle size, the geometric characteristics of the mill and the process parameters. Rajamani and Herbst model is suggested for the development of selection function in a ball mill under given conditions process. The selection function was determined based on the change in the proportion of unbroken material over time for eight size intervals in four mills of different volumes, using one-size interval method. Change of unbroken material content with time is linear.The specified dependence suggests first-order breakage kinetics. The selection function was then described by the Rajamani Herbst model. Laboratory-level researches and the development of mathematical models for transferring results to a larger scale is a potential way of reducing energy consumption

Another Look at Kastril on the Premantura Cape of Kamenjak (Medulin)

Položaj Kastrila na premanturskom rtu Kamenjak, najjužnijem rtu Istre, lijep je primjer zanimljivog položaja zbog nadzora nad širokim okolnim područjem. Nikakva arheološka istraživanja na tom lokalitetu nisu dosad poduzimana, a može se očekivati svojevrsni kontinuitet korištenja te točke, od gradinskog naselja, preko antičke i kasnoantičke osmatračnice, te možda do ranobizantskog kastruma, utvrde za nadzor plovidbe kakvih je duž istočne jadranske obale poznato mnogo. U literaturi se spominje od kraja 19. stoljeća, no dosad nije privukao veću pažnju aktivnih istraživača.The position of Kastril on the Premantura Cape of Kamenjak, the southernmost cape of Istria, is a nice example of an interesting position due to its control over a large surrounding territory. No archaeological excavations of any kind have been carried out on the site, but we may expect a certain continuity of use of that point, from a hillfort settlement, through an observation post from classical and late antiquity, perhaps to an early Byzantine castrum, a fortification for purposes of controlling navigation, similar to the many known along the eastern Adriatic coast. It is mentioned in the literature since the end of the 19th century, but it failed to attract any greater attention of active researchers