Numerical simulation of two-chamber plasma sources using finite element method

Numerical simulation of plasma sources is very important. Such models allows to vary different plasma parameters with high degree of accuracy. Moreover, they allow to conduct measurements not disturbing system balance.Recently, the scientific and practical interest increased in so-called two-chamber plasma sources. In one of them (small or discharge chamber) an external power source is embedded. In that chamber plasma forms. In another (large or diffusion chamber) plasma exists due to the transport of particles and energy through the boundary between chambers.In this particular work two-chamber plasma sources with argon and oxygen as active mediums were onstructed. This models give interesting results in electric field profiles and, as a consequence, in density profiles of charged particles.

Pyörivän keskiökärjen rakenteen kehittäminen työstövärähtelyjen välttämiseksi sorvauksessa

Tässä diplomityössä käsitellään sorvauksen työstövärähtelyjen ja sorvin keskiökärjen rakenteen yhteyttä. Työ on osa Lappeenrannan teknillisen yliopiston VMAX-projektia, ja sen taustalla on pyrkimys uudenlaisen, sorvin kärkipylkän puristusvoiman ajonaikaiseen säätämiseen perustuvan työstövärähtelyjen välttämismenetelmän kehittämiseen. Tämän menetelmän toiminnan todentaminen oli työn ensimmäinen tavoite. Menetelmän toteuttaminen asettaa kuitenkin käytetyn keskiökärjen rakenteelle tiettyjä vaatimuksia. Työn toisena tavoitteena oli nämä vaatimukset täyttävän keskiökärjen prototyypin kehittäminen. Tutkimus eteni seuraavasti. Ensimmäiseksi ongelma määriteltiin tutustumalla työn teoreettiseen taustaan ja aiheeseen liittyvään tutkimukseen Lappeenrannan teknillisestä yliopistosta ja muualta. Myös keskiökärkiä valmistavien yritysten tuotekatalogeja tarkasteltiin. Seuraavaksi siirryttiin alustavaan suunnitteluvaiheeseen, jossa verifioitiin menetelmän toiminta ja luotiin konsepteja keskiökärjen rakenteen kehittämistä varten. Tämän alustavan vaiheen jälkeen suoritettiin suunnitteluprosessi keskiökärjen prototyypille. Lopuksi, suunnitellun prototyypin rakenteen käyttäytymistä arvioitiin tietokonemallinnuksen avulla. Lisätuloksena tutkimuksen aikana johdettiin yksinkertaistettu elementtimenetelmään perustuva laskentamalli järjestelmän ominaistaajuuksien selvittämiseksi. Laskentamallin tarkkuutta arvoitiin. Suunnitteluprosessin tuloksena saatiin kaikki menetelmän toiminnan sekä normaalin käytön asettamat vaatimukset täyttävä rakenne keskiökärjen prototyypille. Myös johdetun laskentamallin tulokset ovat varsin lähellä 3D-elementtimallinnuksen antamia tuloksia. Tutkimuksen tavoitteiden voidaan siis sanoa toteutuneen. Koska prototyyppiä ja laskentamallia ei kuitenkaan ole vielä kokeellisesti verifioitu, tämä ei ole täysin varmaa.

Finite size effects in superconducting nanocomposites

The present Master’s thesis presents theoretical description of the extraodinary behavior of the confined Indium nanoparticles. Superconducting properties of nanoparticles and nanocomposites are extensively reviewed. Special attention has been paid to phase fluctuation, shell and disordered effects. The experimental data has been obtained and provided by Dmitry Shamshur from Ioffe Physical Technical Institute. The investigated material represents a highly ordered system of silicate spheres filled with indium metal, where the In nanoparticles are interconnected between each other. Bulk indium is a superconductor with crititcal superconducting temperature Tc0 = 3:41 K. But indium nanoparticles exhibit different behavior, the critical temperature rise by approximately 20% up to 4.15 K. As well as transition of the indium particles to type-II superconductivity with high critical magnetic fields. Such diversity is explained by finite size effects which originate from nanosize of the samples.

Multicomponent diffusion during Prato cheese ripening: mathematical modeling using the finite element method

The partial replacement of NaCl by KCl is a promising alternative to produce a cheese with lower sodium content since KCl does not change the final quality of the cheese product. In order to assure proper salt proportions, mathematical models are employed to control the product process and simulate the multicomponent diffusion during the reduced salt cheese ripening period. The generalized Fick's Second Law is widely accepted as the primary mass transfer model within solid foods. The Finite Element Method (FEM) was used to solve the system of differential equations formed. Therefore, a NaCl and KCl multicomponent diffusion was simulated using a 20% (w/w) static brine with 70% NaCl and 30% KCl during Prato cheese (a Brazilian semi-hard cheese) salting and ripening. The theoretical results were compared with experimental data, and indicated that the deviation was 4.43% for NaCl and 4.72% for KCl validating the proposed model for the production of good quality, reduced-sodium cheeses.

Simulation and material calibration of ultra high strength steel (UHSS) S960 welded joint under static tensile test utilizing finite element method (FEM)

The aim of this work was to calibrate the material properties including strength and strain values for different material zones of ultra-high strength steel (UHSS) welded joints under monotonic static loading. The UHSS is heat sensitive and softens by heat due to welding, the affected zone is heat affected zone (HAZ). In this regard, cylindrical specimens were cut out from welded joints of Strenx® 960 MC and Strenx® Tube 960 MH, were examined by tensile test. The hardness values of specimens’ cross section were measured. Using correlations between hardness and strength, initial material properties were obtained. The same size specimen with different zones of material same as real specimen were created and defined in finite element method (FEM) software with commercial brand Abaqus 6.14-1. The loading and boundary conditions were defined considering tensile test values. Using initial material properties made of hardness-strength correlations (true stress-strain values) as Abaqus main input, FEM is utilized to simulate the tensile test process. By comparing FEM Abaqus results with measured results of tensile test, initial material properties will be revised and reused as software input to be fully calibrated in such a way that FEM results and tensile test results deviate minimum. Two type of different S960 were used including 960 MC plates, and structural hollow section 960 MH X-joint. The joint is welded by BöhlerTM X96 filler material. In welded joints, typically the following zones appear: Weld (WEL), Heat affected zone (HAZ) coarse grained (HCG) and fine grained (HFG), annealed zone, and base material (BaM). Results showed that: The HAZ zone is softened due to heat input while welding. For all the specimens, the softened zone’s strength is decreased and makes it a weakest zone where fracture happens while loading. Stress concentration of a notched specimen can represent the properties of notched zone. The load-displacement diagram from FEM modeling matches with the experiments by the calibrated material properties by compromising two correlations of hardness and strength.

Publication Statistics Sets of slides, transparents and microfiche 1991-

Vapaakappalekartuntaan perustuva tilasto Suomessa julkaistuista dia-, kalvo- ja filmikorttisarjoista vuodesta 1991 lähtien

The finite bandwidth model for spin fluctuations in Pd

The frequency dependence of the electron-spin fluctuation spectrum, P(Q), is calculated in the finite bandwidth model. We find that for Pd, which has a nearly full d-band, the magnitude, the range, and the peak frequency of P(Q) are greatly reduced from those in the standard spin fluctuation theory. The electron self-energy due to spin fluctuations is calculated within the finite bandwidth model. Vertex corrections are examined, and we find that Migdal's theorem is valid for spin fluctuations in the nearly full band. The conductance of a normal metal-insulator-normal metal tunnel junction is examined when spin fluctuations are present in one electrode. We find that for the nearly full band, the momentum independent self-energy due to spin fluctuations enters the expression for the tunneling conductance with approximately the same weight as the self-energy due to phonons. The effect of spin fluctuations on the tunneling conductance is slight within the finite bandwidth model for Pd. The effect of spin fluctuations on the tunneling conductance of a metal with a less full d-band than Pd may be more pronounced. However, in this case the tunneling conductance is not simply proportional to the self-energy.

Zero-sum problems in finite cyclic groups

The purpose of this thesis is to investigate some open problems in the area of combinatorial number theory referred to as zero-sum theory. A zero-sequence in a finite cyclic group G is said to have the basic property if it is equivalent under group automorphism to one which has sum precisely IGI when this sum is viewed as an integer. This thesis investigates two major problems, the first of which is referred to as the basic pair problem. This problem seeks to determine conditions for which every zero-sequence of a given length in a finite abelian group has the basic property. We resolve an open problem regarding basic pairs in cyclic groups by demonstrating that every sequence of length four in Zp has the basic property, and we conjecture on the complete solution of this problem. The second problem is a 1988 conjecture of Kleitman and Lemke, part of which claims that every sequence of length n in Zn has a subsequence with the basic property. If one considers the special case where n is an odd integer we believe this conjecture to hold true. We verify this is the case for all prime integers less than 40, and all odd integers less than 26. In addition, we resolve the Kleitman-Lemke conjecture for general n in the negative. That is, we demonstrate a sequence in any finite abelian group isomorphic to Z2p (for p ~ 11 a prime) containing no subsequence with the basic property. These results, as well as the results found along the way, contribute to many other problems in zero-sum theory.

ReAlM - a system to manipulate relations

Given a heterogeneous relation algebra R, it is well known that the algebra of matrices with coefficient from R is relation algebra with relational sums that is not necessarily finite. When a relational product exists or the point axiom is given, we can represent the relation algebra by concrete binary relations between sets, which means the algebra may be seen as an algebra of Boolean matrices. However, it is not possible to represent every relation algebra. It is well known that the smallest relation algebra that is not representable has only 16 elements. Such an algebra can not be put in a Boolean matrix form.[15] In [15, 16] it was shown that every relation algebra R with relational sums and sub-objects is equivalent to an algebra of matrices over a suitable basis. This basis is given by the integral objects of R, and is, compared to R, much smaller. Aim of my thesis is to develop a system called ReAlM - Relation Algebra Manipulator - that is capable of visualizing computations in arbitrary relation algebras using the matrix approach.

Generating finite integral relation algebras

Relation algebras and categories of relations in particular have proven to be extremely useful as a fundamental tool in mathematics and computer science. Since relation algebras are Boolean algebras with some well-behaved operations, every such algebra provides an atom structure, i.e., a relational structure on its set of atoms. In the case of complete and atomic structure (e.g. finite algebras), the original algebra can be recovered from its atom structure by using the complex algebra construction. This gives a representation of relation algebras as the complex algebra of a certain relational structure. This property is of particular interest because storing the atom structure requires less space than the entire algebra. In this thesis I want to introduce and implement three structures representing atom structures of integral heterogeneous relation algebras, i.e., categorical versions of relation algebras. The first structure will simply embed a homogeneous atom structure of a relation algebra into the heterogeneous context. The second structure is obtained by splitting all symmetric idempotent relations. This new algebra is in almost all cases an heterogeneous structure having more objects than the original one. Finally, I will define two different union operations to combine two algebras into a single one.

Generalization of the BTK Theory to the Case of Finite Quasiparticle Lifetimes

A generalization to the BTK theory is developed based on the fact that the quasiparticle lifetime is finite as a result of the damping caused by the interactions. For this purpose, appropriate self-energy expressions and wave functions are inserted into the strong coupling version of the Bogoliubov equations and subsequently, the coherence factors are computed. By applying the suitable boundary conditions to the case of a normal-superconducting interface, the probability current densities for the Andreev reflection, the normal reflection, the transmission without branch crossing and the transmission with branch crossing are determined. Accordingly the electric current and the differential conductance curves are calculated numerically for Nb, Pb, and Pb0.9Bi0.1 alloy. The generalization of the BTK theory by including the phenomenological damping parameter is critically examined. The observed differences between our approach and the phenomenological approach are investigated by the numerical analysis.

Improving the Scalability of Reduct Determination in Rough Sets

Rough Set Data Analysis (RSDA) is a non-invasive data analysis approach that solely relies on the data to find patterns and decision rules. Despite its noninvasive approach and ability to generate human readable rules, classical RSDA has not been successfully used in commercial data mining and rule generating engines. The reason is its scalability. Classical RSDA slows down a great deal with the larger data sets and takes much longer times to generate the rules. This research is aimed to address the issue of scalability in rough sets by improving the performance of the attribute reduction step of the classical RSDA - which is the root cause of its slow performance. We propose to move the entire attribute reduction process into the database. We defined a new schema to store the initial data set. We then defined SOL queries on this new schema to find the attribute reducts correctly and faster than the traditional RSDA approach. We tested our technique on two typical data sets and compared our results with the traditional RSDA approach for attribute reduction. In the end we also highlighted some of the issues with our proposed approach which could lead to future research.

Simulation-Based Finite and Large Sample Tests in Multivariate Regressions.

In the context of multivariate linear regression (MLR) models, it is well known that commonly employed asymptotic test criteria are seriously biased towards overrejection. In this paper, we propose a general method for constructing exact tests of possibly nonlinear hypotheses on the coefficients of MLR systems. For the case of uniform linear hypotheses, we present exact distributional invariance results concerning several standard test criteria. These include Wilks' likelihood ratio (LR) criterion as well as trace and maximum root criteria. The normality assumption is not necessary for most of the results to hold. Implications for inference are two-fold. First, invariance to nuisance parameters entails that the technique of Monte Carlo tests can be applied on all these statistics to obtain exact tests of uniform linear hypotheses. Second, the invariance property of the latter statistic is exploited to derive general nuisance-parameter-free bounds on the distribution of the LR statistic for arbitrary hypotheses. Even though it may be difficult to compute these bounds analytically, they can easily be simulated, hence yielding exact bounds Monte Carlo tests. Illustrative simulation experiments show that the bounds are sufficiently tight to provide conclusive results with a high probability. Our findings illustrate the value of the bounds as a tool to be used in conjunction with more traditional simulation-based test methods (e.g., the parametric bootstrap) which may be applied when the bounds are not conclusive.

Ranking Sets of Objects

We provide a survey of the literature on ranking sets of objects. The interpretations of those set rankings include those employed in the theory of choice under complete uncertainty, rankings of opportunity sets, set rankings that appear in matching theory, and the structure of assembly preferences. The survey is prepared for the Handbook of Utility Theory, vol. 2, edited by Salvador Barberà, Peter Hammond, and Christian Seidl, to be published by Kluwer Academic Publishers. The chapter number is provisional.