1,720,959 research outputs found
Phase field modeling and numerical simulation of crystal growth
Get PDFKrystalizace je formou fázového přechodu z kapalného do pevného skupenství, při které se atomy uspořádají do krystalové mřížky. Stefanova úloha zkoumá časový vývoj rozhraní mezi kapalnou a pevnou fází při předpokladu ostrého rozhraní. Dochází zde ke skokové nespojitosti termodynamických veličin. Tato práce se zabývá především modelem fázového pole vycházejícího z myšlenky pozvolného přechodu jedné fáze v druhou na tenké vrstvě. Analytické řešení modelu fázového pole neexistuje, proto je použito numerické řešení metodou konečných diferencí. Praktická část je věnována výpočetní studii pomocí programu implementovaného v jazyce C/C++. Cílem numerických simulací je porozumět vlivu jednotlivých parametrů na chování modelu.Crystallization is a phase transition from liquid to solid state, in which the atoms are organized into a regular crystal structure. Stefan problem deals with the time evolution of the interface between the liquid and solid phases under the assumption of a sharp interface, i.e., with a step discontinuity of thermodynamic quantities. This work deals with the phase field model based on the idea of a gradual transition from one phase to another on a thin layer. There is no analytical solution of the phase eld model, therefore the finite difference method is used. The practical part is dedicated to a computational study using a program implemented in C / C ++. Numerical simulations are performed in order to understand the influence of individual parameters on the model behavior
Mathematical modelling of phase interface using lattice Boltzmann method
Get PDFTato práce je úvodem do metody fázového pole a mřížkové Boltzmannovy metody pro simulaci vývoje rozhraní mezi dvěma fázemi. Hlavním cílem této práce je představit zmíněné metody a použít je pro modelování vývoje rozhraní mezi dvěma fázemi. Dalším cílem této práce je paralelní implementace algoritmu mřížkové Boltzmannovy metody pro simulaci vývoje rozhraní mezi dvěma fázemi v jazyce C++ a CUDA, úprava výpočtu normálového vektoru a aplikace algoritmu na dvourozměrný případ. Na základě získaných výsledků mřížková Boltzmannova metoda konverguje rychlostí druhého řádu v případě diagonální translace. V případě Zalesakova disku metoda konverguje rychlostí druhého řádu pouze pro některé použité způsoby výpočtu chyb. Pro ostatní způsoby výpočtu chyb konverguje nižší rychlostí nebo diverguje. Při složitějších rychlostních polí mřížková Boltzmannova metoda buď konverguje nižší rychlostí než druhého řádu nebo diverguje.This work is an introduction to the phase-field method and the lattice Boltzmann method for the simulation of the interface evolution between two phases. The main goal is to introduce these methods and use them to simulate the interface evolution between two phases. The additional aim of this work is the parallel implementation of the LBM algorithm in C++ and CUDA, the modification of normal vector computation, and the application in the two-dimensional case. Based on the obtained results, the lattice Boltzmann method converges in the case of diagonal translation with speed of second order. In the case of Zalesak's Disk, the method converges with speed of second order only for some used methods of the error computation. For other methods of error computation the method converges with lesser speed or diverges. For more complicated velocity fields, the lattice Boltzmann method either converges with lesser speed than that of second order or diverges
Numerical methods for modelling of parametric surfaces in computer graphics
Get PDFV této práci se zabýváme diskretizací Laplaceova-Beltramiho operátoru na neuspořádaných sítích. Je popsán úvod do diferenciální geometrie potřebný pro zadefinování Laplaceova-Beltramiho operátoru. Následně je vysvětlena nutná část diskrétní diferenciální geometrie. S pomocí ní je odvozen vzorec pro diskretizovaný Laplaceův-Beltramiho operátor. Za použití tohoto vzorce je odvozeno numerické schéma pro úlohu povrchové difuze. Nakonec je provedena výpočetní studie, ve které toto schéma aplikujeme na konkrétní plochy. Je popsán účinek úlohy povrchové difuze na různé tvary ploch. Program implementující úlohu je napsán v C++ za použití knihovny TNL.In this paper, we study the discretization of the Laplace-Beltrami operator on unordered meshes. An introduction to differential geometry needed to define the Laplace-Beltrami operator is described. Then the necessary part of discrete differential geometry is explained. With its help, a formula for the discretized Laplace-Beltrami operator is derived. Using this formula, a numerical scheme for the surface diffusion problem is derived. Finally, a computational study is performed in which we apply this scheme to specific surfaces. The effect of the surface diffusion problem on different surface shapes is described. The program implementing the problem is written in C++ using the TNL library
Controlling Processes Governed by Partial Differential Equations using Optimization Methods
Get PDFTato práce se zabývá problematikou minimalizačních úloh s nekonečně dimenzionální vazbou danou parciálními diferenciálními rovnicemi. Nejprve jsou studovány Banachovy a Hilbertovy prostory, na kterých je následně formulována typová minimalizační úloha. Jsou diskutovány možnosti jejího řešení pomocí citlivostní a adjungované metody a nalezeny nutné podmínky optimálního řešení této úlohy. Následně je adjungovaná metoda použita při optimalizaci Dirichletovy okrajové podmínky v počáteční a okrajové úloze pro rovnici vedení tepla a je představen numerický algoritmus založený na metodě gradientního sestupu řešící tuto úlohu.This Bachelor project deals with PDE constrained optimization problems. Firstly, the minimization problem with infinite dimensional constrain is defined. The necessary condition for this problem is formulated and the possibilities of its solving using the sensitivity and the adjoint approach are discussed. Further, the adjoint approach is applied to controlling process governed by heat equation and the numerical method solving this task is introduced
On Taylor-like Estimates for Polynomial Approximations
Get PDFPolynomial series approximations are a central theme in approximation theory.
Two types of series, which are featured most prominently in pure and applied
mathematics, are Taylor series expansions and expansions derived based on
families of orthogonal polynomials on bounded intervals. The identity
theorem implies that all such series agree on in the limit. This
motivates an effort to derive properties, which relate the original function to
a truncated series based on orthogonal polynomial approximation which
hold on unbounded intervals. In particular, the Chebyshev series expansion of
is studied and an algebraic criterion which can be used to confirm
bounds analogous to the Taylor series upper and lower bound estimates for
is provided. In addition to this, the generalizations to other settings
involving different functions and alternative families of -orthogonal
polynomials are discussed.Comment: 10 pages, 0 figure
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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