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Polyhedra-based analysis of computer simulated amorphous structuresKokotin, Valentin 25 June 2010 (has links) (PDF)
Bulk metallic glasses represent a newly developed class of materials. Some metallic glasses possess combinations of very good or even excellent mechanical, chemical and/or magnetic properties uncovering a broad range of both industrial and vital applications. Besides all advantages metallic glasses have also significant drawbacks, which have to be overcome for commercial application. Apart from low critical thicknesses, brittleness and chemical inhomogeneity one important problem of metallic glasses is the lack of an appropriate theory describing their structure. Therefore, the search for new glass forming compositions as well as the improving of existing ones occurs at present by means of trial-and-error methods and a number of empirical rules.
Empirical rules for good glass-forming ability of bulk metallic glasses have been established in recent years by Inoue and Egami. Two of these rules, (i) Preference of more than 3 elements and (ii) Need of more than 12 % radii difference of base elements, seem to be closely related to topological (geometrical) criteria. From this point of view topological parameters contribute essentially to the glass-forming ability. The third rule (iii) demands a negative mixing enthalpy of base elements and refers to the chemical interaction of the atoms.
The generalized Bernal’s model (hard-sphere approximation) was used for the simulation of monatomic, binary and multi-component structures. Excluding chemical interaction, this method allows the investigation of topological criteria of the glass-forming ability. Bernal’s hard-sphere model was shown to be a good approximation for bulk metallic glasses and metallic liquids and yields good coincidence of experimental and theoretical results.
• The Laguerre (weighted Voronoi) tessellation technique was used as the main tool for the structural analysis. Due to very complex structures it is impossible to determine the structure of bulk metallic glasses by means of standard crystallographic methods.
• Density, radial distribution function, coordination number and Laguerre polyhedra analysis confirm amorphism of the simulated structures and are in a good agreement with available experimental results.
• The ratio of the fractions of non-crystalline to crystalline Laguerre polyhedra faces was introduced as a new parameter . This parameter reflects the total non-crystallinity of a structure and the amount of atomic rearrangements necessary for crystallization. Thus, the parameter is related to the glass-forming ability. It depends strongly on composition and atomic size ratio and indicates a region of enhanced glass-forming ability in binary mixtures at 80 % of small atoms and atomic size ratio of 1.3. All found maxima of parameter for ternary mixtures have compositions and size ratios which are nearly the same as for the binary mixture with the maximum value of .
• A new method of multiple-compression was introduces in order to test the tendency towards densification and/or crystallization of the simulated mixtures. The results of the multiple-compression of monatomic mixtures indicate a limiting value of about 0.6464 for the density of the amorphous state. Further densification is necessarily connected to formation and growth of nano-crystalline regions.
• The results of the multiple-compression for binary mixtures shows a new maximum of the density at the size ratio of 1.3 and 30 % to 90 % of small atoms. This maximum indicates a local island of stability of the amorphous state. The maximal receivable density without crystallization in this region is enhanced compared to neighbouring regions.
• The comparison of the parameter and the density to the distribution of known binary bulk metallic (metal-metal) glasses clearly shows that both parameters play a significant role in the glass-forming ability.
• The polyhedra analysis shows regions with enhanced fraction of the icosahedral short-range order (polyhedron (0, 0, 12)) in the binary systems with the maximum at 80 % of small atoms and size ratio of 1.3. Comparison of the distribution of the (0, 0, 12) polyhedra to the distribution of known binary metallic (metal-metal) glasses and to the parameter shows that icosahedral short-range order is not related to the glass-forming ability and is a consequence of the high non-crystallinity (high values of ) of the mixtures and non vice versa. Results for the ternary mixtures confirm this observation.
• A new approach for the calculation of the mixing enthalpy is proposed. The new method is based on the combination of Miedema’s semi-empirical model and Laguerre tessellation technique. The new method as well as 6 other methods including the original Miedema’s model were tested for more than 1400 ternary and quaternary alloys. The results show a better agreement with experimental values of the mixing enthalpy for the new model compared to all other methods. The new model takes into account the local structure at atom site and can be applied to all metallic alloys without additional extrapolations if the atomic structure of the considered alloy is known from a suitable atomistic structure model.
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Zeros de séries de Dirichlet e de funções na classe de Laguerre-Pólya / Zeros of Dirichlet series and of functions in the Laguerre-Pólya classOliveira, Willian Diego [UNESP] 11 May 2017 (has links)
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Previous issue date: 2017-05-11 / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Estudamos tópicos relacionados a zeros de séries de Dirichlet e de funções inteiras. Boa parte da tese é voltada à localização de zeros de séries de Dirichlet via critérios de densidade. Estabelecemos o critério de Nyman-Beurling para uma ampla classe de séries de Dirichlet e o critério de Báez-Duarte para L-funções de Dirichlet em semi-planos R(s)>1/2, para p ∈ (1,2], bem como para polinômios de Dirichlet em qualquer semi-plano R(s)>r. Um análogo de uma cota inferior de Burnol relativa ao critério de Báez-Duarte foi estabelecido para polinômios de Dirichlet. Uma das ferramentas principais na prova deste último resultado é a solução de um problema extremo natural para polinômios de Dirichlet inspirado no resultado de Báez-Duarte. Provamos que os sinais dos coeficientes de Maclaurin de uma vasta subclasse de funções inteiras da classe de Laguerre-Pólya possuem um comportamento regular. / We study topics related to zeros of Dirichlet series and entire functions. A large part of the thesis is devoted to the location of zeros of Dirichlet series via density criteria. We establish the Nyman-Beruling criterion for a wide class of Dirichlet series and the Báez-Duarte criterion for Dirichlet L-functions in the semi-plane R(s)>1/p, for p ∈ (1,2], as well as for zeros of Dirichlet polynomials in any semi-plane R(s)>r. An analog for the case of Dirichlet polynomials of a result of Burnol which is closely related to Báez-Duarte’s one is also established. A principal tool in the proof of the latter result is the solution of a natural extremal problem for Dirichlet polynomials inspired by Báez-Duarte’s result. We prove that the signs of the Maclaurin coefficients of a wide class of entire functions that belong to the Laguerre-Pólya class posses a regular behavior. / FAPESP: 2013/14881-9
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Polyhedra-based analysis of computer simulated amorphous structuresKokotin, Valentin 15 June 2010 (has links)
Bulk metallic glasses represent a newly developed class of materials. Some metallic glasses possess combinations of very good or even excellent mechanical, chemical and/or magnetic properties uncovering a broad range of both industrial and vital applications. Besides all advantages metallic glasses have also significant drawbacks, which have to be overcome for commercial application. Apart from low critical thicknesses, brittleness and chemical inhomogeneity one important problem of metallic glasses is the lack of an appropriate theory describing their structure. Therefore, the search for new glass forming compositions as well as the improving of existing ones occurs at present by means of trial-and-error methods and a number of empirical rules.
Empirical rules for good glass-forming ability of bulk metallic glasses have been established in recent years by Inoue and Egami. Two of these rules, (i) Preference of more than 3 elements and (ii) Need of more than 12 % radii difference of base elements, seem to be closely related to topological (geometrical) criteria. From this point of view topological parameters contribute essentially to the glass-forming ability. The third rule (iii) demands a negative mixing enthalpy of base elements and refers to the chemical interaction of the atoms.
The generalized Bernal’s model (hard-sphere approximation) was used for the simulation of monatomic, binary and multi-component structures. Excluding chemical interaction, this method allows the investigation of topological criteria of the glass-forming ability. Bernal’s hard-sphere model was shown to be a good approximation for bulk metallic glasses and metallic liquids and yields good coincidence of experimental and theoretical results.
• The Laguerre (weighted Voronoi) tessellation technique was used as the main tool for the structural analysis. Due to very complex structures it is impossible to determine the structure of bulk metallic glasses by means of standard crystallographic methods.
• Density, radial distribution function, coordination number and Laguerre polyhedra analysis confirm amorphism of the simulated structures and are in a good agreement with available experimental results.
• The ratio of the fractions of non-crystalline to crystalline Laguerre polyhedra faces was introduced as a new parameter . This parameter reflects the total non-crystallinity of a structure and the amount of atomic rearrangements necessary for crystallization. Thus, the parameter is related to the glass-forming ability. It depends strongly on composition and atomic size ratio and indicates a region of enhanced glass-forming ability in binary mixtures at 80 % of small atoms and atomic size ratio of 1.3. All found maxima of parameter for ternary mixtures have compositions and size ratios which are nearly the same as for the binary mixture with the maximum value of .
• A new method of multiple-compression was introduces in order to test the tendency towards densification and/or crystallization of the simulated mixtures. The results of the multiple-compression of monatomic mixtures indicate a limiting value of about 0.6464 for the density of the amorphous state. Further densification is necessarily connected to formation and growth of nano-crystalline regions.
• The results of the multiple-compression for binary mixtures shows a new maximum of the density at the size ratio of 1.3 and 30 % to 90 % of small atoms. This maximum indicates a local island of stability of the amorphous state. The maximal receivable density without crystallization in this region is enhanced compared to neighbouring regions.
• The comparison of the parameter and the density to the distribution of known binary bulk metallic (metal-metal) glasses clearly shows that both parameters play a significant role in the glass-forming ability.
• The polyhedra analysis shows regions with enhanced fraction of the icosahedral short-range order (polyhedron (0, 0, 12)) in the binary systems with the maximum at 80 % of small atoms and size ratio of 1.3. Comparison of the distribution of the (0, 0, 12) polyhedra to the distribution of known binary metallic (metal-metal) glasses and to the parameter shows that icosahedral short-range order is not related to the glass-forming ability and is a consequence of the high non-crystallinity (high values of ) of the mixtures and non vice versa. Results for the ternary mixtures confirm this observation.
• A new approach for the calculation of the mixing enthalpy is proposed. The new method is based on the combination of Miedema’s semi-empirical model and Laguerre tessellation technique. The new method as well as 6 other methods including the original Miedema’s model were tested for more than 1400 ternary and quaternary alloys. The results show a better agreement with experimental values of the mixing enthalpy for the new model compared to all other methods. The new model takes into account the local structure at atom site and can be applied to all metallic alloys without additional extrapolations if the atomic structure of the considered alloy is known from a suitable atomistic structure model.
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Génération d'harmoniques d'ordre élevé à deux faisceaux portant du moment angulaire / Generation of high-order harmonics from two beams carrying angular momentumChappuis, Céline 25 January 2019 (has links)
La génération d’harmoniques d’ordre élevé est un processus d’interaction lumière-matière hautement non-linéaire permettant la synthèse d’impulsions sub-femtosecondes, dites attosecondes (1 as = 10⁻¹⁸ s). Mes travaux de thèse portent sur l’étude du transfert de moment angulaire lors de ce processus, afin de contrôler les caractéristiques spatiales et de polarisation du rayonnement émis dans l’extrême ultraviolet. Comme pour la matière, le moment angulaire de la lumière peut être séparé en une composante de spin, associée à l’état de polarisation du faisceau, et une composante orbitale, reliée à la forme du front d’onde. La maitrise complète du moment angulaire des harmoniques nécessite de recourir à des schémas de génération à deux faisceaux non-colinéaires, créant un réseau de diffraction dans le milieu générateur. Nous avons montré que, bien que les règles de transfert obéissent à des lois de conservation du moment angulaire, la description fine du phénomène requiert une analyse précise du champ laser dans le milieu de génération. Ces travaux ouvrent des perspectives de mise en forme avancée des impulsions attosecondes. / High-order harmonic generation is a highly nonlinear laser-matter interaction process which allows the synthesis of sub-femtosecond pulses, also called attosecond (1 as = 10⁻¹⁸ s) pulses. My PhD is centered around the study of angular momentum transfer during this process, in order to control spatial and polarization features of the radiation which is emitted in the extreme ultraviolet. As for matter, the angular momentum of light can be divided into a spin component, associated with the beam’s polarization, and an orbital component, related to the shape of the wavefront. The control of high harmonics’ angular momentum requires generating schemes involving two crossing beams, thus creating a diffraction grating in the generating medium.We have shown that, although the transfer rules obey conservation laws of the angular momentum, the fine description of the phenomenon requires an accurate analysis of the laser field in the generation medium. This work opens the road for advanced shaping of attosecond pulses.
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Asymptotic bounds and values for the norm of the Laplace operator and other partial differential operators on spaces of polynomialsRebs, Christian 09 December 2020 (has links)
In der vorliegenden Dissertation werden endlichdimensionale Räume multivariater Polynome in N Variablen mit der Laguerre-, Hermite- bzw. Legendrenorm versehen.
Dabei sei der Höchstgrad der Polynome oder die Summe der Grade der Variablen durch eine natürliche Zahl n nach oben beschränkt. Wir betrachten auf diesen Räumen den Laplaceoperator und zwei weitere partielle Differentialoperatoren
und interessieren uns für das Verhalten der von den Polynomnormen induzierten Operatornormen dieser Operatoren, wenn n gegen unendlich strebt.
Im Fall der Laguerre- und Legendrenorm werden asymptotische obere und untere Schranken der Operatornormen hergeleitet. Im Fall der Hermitenorm kann sogar eine asymptotische Formel gezeigt werden, wenn man voraussetzt, dass der Höchstgrad der Poynome duch n beschränkt ist.
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Performance of alternative option pricing models during spikes in the FTSE 100 volatility index : Empirical evidence from FTSE100 index optionsRehnby, Nicklas January 2017 (has links)
Derivatives have a large and significant role on the financial markets today and the popularity of options has increased. This has also increased the demand of finding a suitable option pricing model, since the ground-breaking model developed by Black & Scholes (1973) have poor pricing performance. Practitioners and academics have over the years developed different models with the assumption of non-constant volatility, without reaching any conclusions regarding which model is more suitable to use. This thesis examines four different models, the first model is the Practitioners Black & Scholes model proposed by Christoffersen & Jacobs (2004b). The second model is the Heston´s (1993) continuous time stochastic volatility model, a modification of the model is also included, which is called the Strike Vector Computation suggested by Kilin (2011). The last model is the Heston & Nandi (2000) Generalized Autoregressive Conditional Heteroscedasticity type discrete model. From a practical point of view the models are evaluated, with the goal of finding the model with the best pricing performance and the most practical usage. The model´s robustness is also tested to see how the models perform in out-of-sample during a high respectively low implied volatility market. All the models are effected in the robustness test, the out-sample ability is negatively affected by a high implied volatility market. The results show that both of the stochastic volatility models have superior performances in the in-sample and out-sample analysis. The Generalized Autoregressive Conditional Heteroscedasticity type discrete model shows surprisingly poor results both in the in-sample and out-sample analysis. The results indicate that option data should be used instead of historical return data to estimate the model’s parameters. This thesis also provides an insight on why overnight-index-swap (OIS) rates should be used instead of LIBOR rates as a proxy for the risk-free rate.
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Tailoring quantum entanglement of orbital angular momentumMcLaren, Melanie 12 1900 (has links)
Thesis (PhD)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: High-dimensional quantum entanglement offers an increase in information capacity per
photon; a highly desirable property for quantum information processes such as quantum
communication, computation and teleportation. As the orbital angular momentum (OAM)
modes of light span an infinite-dimensional Hilbert space, they have become frontrunners
in achieving entanglement in higher dimensions. In light of this, we investigate the potential
of OAM entanglement of photons by controlling the parameters in both the generation
and measurement systems. We show the experimental procedures and apparatus involved
in generating and measuring entangled photons in two-dimensions. We verify important
quantum tests such as the Einstein, Podolsky and Rosen (EPR) paradox using OAM and angle
correlations, as well as a violation of a Bell-type inequality. By performing a full state
tomography, we characterise our quantum state and show we have a pure, highly entangled
quantum state. We demonstrate that this method can be extended to higher dimensions. The
experimental techniques used to generate and measure OAM entanglement place an upper
bound on the number of accessible OAM modes. As such, we investigate new methods in
which to increase the spiral bandwidth of our generated quantum state. We alter the shape
of the pump beam in spontaneous parametric down-conversion and demonstrate an effect on both OAM and angle correlations. We also made changes to the measurement scheme
by projecting the photon pairs into the Bessel-Gaussian (BG) basis and demonstrate entanglement
in this basis. We show that this method allows the measured spiral bandwidth
to be optimised by simply varying the continuous radial parameter of the BG modes. We
demonstrate that BG modes can be entangled in higher dimensions compared with the commonly
used helical modes by calculating and comparing the linear entropy and fidelity for
both modes. We also show that quantum entanglement can be accurately simulated using
classical light using back-projection, which allows the study of projective measurements
and predicts the strength of the coincidence correlations in an entanglement experiment.
Finally, we make use of each of the techniques to demonstrate the effect of a perturbation
on OAM entanglement measured in the BG basis. We investigate the self-healing property
of BG beams and show that the classical property is translated to the quantum regime. By
calculating the concurrence, we see that measured entanglement recovers after encountering
an obstruction. / AFRIKAANSE OPSOMMING: Hoë-dimensionele kwantumverstrengeldheid bied ’n toename in inligtingskapasiteit per foton.
Hierdie is ’n hoogs wenslike eienskap vir kwantum inligting prosesse soos kwantum
kommunikasie, berekening en teleportasie. Omdat die orbitale hoekmomentum (OAM) modusse
van lig ’n oneindig dimensionele Hilbertruimte beslaan, het dit voorlopers geword in
die verkryging van verstrengeling in hoër dimensies. In die lig hiervan, ondersoek ons die
potensiaal van OAM verstrengeling van fotone deur die parameters in beide die generering
en meting stelsels te beheer. Ons toon die eksperimentele prosedures en apparaat wat betrokke
is by die generering en die meet van verstrengelde fotone in twee dimensies. Ons
verifieer kwantumtoetse, soos die Einstein, Podolsky en Rosen (EPR) paradoks vir OAM en
die hoekkorrelasies, sowel as ’n skending van ’n Bell-tipe ongelykheid. Deur middel van ’n
volledige toestand tomografie, karakteriseer ons die kwantum toestand en wys ons dat dit ’n
suiwer, hoogs verstrengel kwantum toestand is. Ons toon ook dat hierdie metode uitgebrei
kan word na hoër dimensies. Die eksperimentele tegnieke wat tydens die generasie en meet
van OAM verstrengeling gebruik is, plaas ’n bogrens op die aantal toeganklik OAM modusse.
Dus ondersoek ons nuwe metodes om die spiraal bandwydte van ons gegenereerde kwantum toestand te verhoog. Ons verander die vorm van die pomp bundel in spontane
parametriese af-omskakeling en demonstreer die uitwerking daarvan op beide OAM en die
hoekkorrelasies. Ons het ook veranderinge aan die meting skema gemaak deur die foton
pare op die Bessel-Gauss (BG) basis te projekteer. Ons wys dat hierdie metode die gemeetde
spiraal bandwydte kan optimeer deur eenvoudig die kontinue radiale parameter van
die BG modes te verander. Ons demonstreer dat BG modusse verstrengel kan word in hoër
dimensies as die heliese modusse, wat algemeen gebruik word, deur berekeninge te maak
en te vergelyk met lineêre entropie en vir beide modusse. Ons wys ook dat kwantumverstrengling
akkuraat nageboots kan word, met behulp van die klassieke lig terug-projeksie,
wat die studie van projeksie metings toelaat en voorspel die krag van die saamval korrelasies
in ’n verstrengeling eksperiment. Ten slotte, gebruik ons elk van die tegnieke om die effek
van ’n storing op OAM verstrengling wat in die BG basis gemeet is, te demonstreer. Ons
ondersoek die self-genesingseienskap van BG bundels en wys dat die klassieke eienskap
vertaal na die kwantum-gebied. Deur die berekening van die konkurrensie (concurrence),
sien ons dat die gemeetde verstrengeling herstel word nadat ’n obstruksie ondervind is.
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A characterization of weight function for construction of minimally-supported D-optimal designs for polynomial regression via differential equationChang, Hsiu-ching 13 July 2006 (has links)
In this paper we investigate (d + 1)-point D-optimal designs for d-th degree polynomial
regression with weight function w(x) > 0 on the interval [a, b]. Suppose that w'(x)/w(x) is a rational function and the information of whether the optimal support
contains the boundary points a and b is available. Then the problem of constructing
(d + 1)-point D-optimal designs can be transformed into a differential equation
problem leading us to a certain matrix with k auxiliary unknown constants. We characterize the weight functions corresponding to the cases when k= 0 and k= 1.
Then, we can solve (d + 1)-point D-optimal designs directly from differential equation
(k = 0) or via eigenvalue problems (k = 1). The numerical results show us an interesting relationship between optimal designs and ordered eigenvalues.
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EM simulation using the Laguerre-FDTD scheme for multiscale 3-D interconnectionsHa, Myunghyun 07 November 2011 (has links)
As the current electronic trend is toward integrating multiple functions in a single electronic device, there is a clear need for increasing integration density which is becoming more emphasized than in the past. To meet the industrial need and realize the new system-integration law [1], three-dimensional (3-D) integration is becoming necessary. 3-D integration of multiple functional IC chip/package modules requires co-simulation of the chip and the package to evaluate the performance of the system accurately. Due to large scale differences in the physical dimensions of chip-package structures, the chip-package co-simulation in time-domain using the conventional FDTD scheme is challenging because of Courant-Friedrich-Levy (CFL) condition that limits the time step. Laguerre-FDTD has been proposed to overcome the limitations on the time step. To enhance performance and applicability, SLeEC methodology [2] has been proposed based on the Laguerre-FDTD method. However, the SLeEC method still has limitations to solve practical 3-D integration problems.
This dissertation proposes further improvements of the Laguerre-FDTD and SLeEC method to address practical problems in 3-D interconnects and 3-D integration. A method that increases the accuracy in the conversion of the solutions from Laguerre-domain to time-domain is demonstrated. A methodology that enables the Laguerre-FDTD simulation for any length of time, which was challenging in prior work, is proposed. Therefore, the analysis of the low-frequency response can be performed from the time-domain simulation for a long time period. An efficient method to analyze frequency-domain response using time-domain simulations is introduced. Finally, to model practical structures, it is crucial to model dispersive materials. A Laguerre-FDTD formulation for frequency-dependent dispersive materials is derived in this dissertation and has been implemented.
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Inégalités de Landau-Kolmogorov dans des espaces de SobolevAbbas, Lamia 18 February 2012 (has links) (PDF)
Ce travail est dédié à l'étude des inégalités de type Landau-Kolmogorov en normes L2. Les mesures utilisées sont celles d'Hermite, de Laguerre-Sonin et de Jacobi. Ces inégalités sont obtenues en utilisant une méthode variationnelle. Elles font intervenir la norme d'un polynômes p et celles de ces dérivées. Dans un premier temps, on s'intéresse aux inégalités en une variable réelle qui font intervenir un nombre quelconque de normes. Les constantes correspondantes sont prises dans le domaine où une certaine forme bilinéaire est définie positive. Ensuite, on généralise ces résultats aux polynômes à plusieurs variables réelles en utilisant le produit tensoriel dans L2 et en faisant intervenir au plus les dérivées partielles secondes. Pour les mesures d'Hermite et de Laguerre-Sonin, ces inégalités sont étendues à toutes les fonctions d'un espace de Sobolev. Pour la mesure de Jacobi on donne des inégalités uniquement pour les polynômes d'un degré fixé par rapport à chaque variable.
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