Дисертації з теми "Density theorem"
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1
Cazaubon, Verne. "In search of a Lebesgue density theorem for Rinfinity." Thesis, University of Ottawa (Canada), 2008. http://hdl.handle.net/10393/27623.
Анотація:
We look at a measure, linfinity , on the infinite-dimensional space, Rinfinity , for which we attempt to put forth an analogue of the Lebesgue density theorem. Although this measure allows us to find partial results, for example for continuous functions, we prove that it is impossible to give an analogous theorem in full generality. In particular, we proved that the Lebesgue density of probability density functions on Rinfinity is zero almost everywhere.
2
Donzelli, Fabrizio. "Algebraic Density Property of Homogeneous Spaces." Scholarly Repository, 2009. http://scholarlyrepository.miami.edu/oa_dissertations/209.
Анотація:
Let X be an affine algebraic variety with a transitive action of the algebraic automorphism group. Suppose that X is equipped with several fixed point free non-degenerate SL_2-actions satisfying some mild additional assumption. Then we prove that the Lie algebra generated by completely integrable algebraic vector fields on X coincides with the set of all algebraic vector fields. In particular, we show that apart from a few exceptions this fact is true for any homogeneous space of form G/R where G is a linear algebraic group and R is a proper reductive subgroup of G.
3
Haruta, Naoki. "Vibronic Coupling Density as a Chemical Reactivity Index and Other Aspects." 京都大学 (Kyoto University), 2016. http://hdl.handle.net/2433/215567.
4
Xia, Honggang. "On zeros of cubic L-functions." Columbus, Ohio : Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1148497121.
5
MATSUMOTO, Kohji. "An introduction to the value-distribution theory of zeta-functions." Šiauliai University, 2006. http://hdl.handle.net/2237/20445.
6
Nyqvist, Robert. "Algebraic Dynamical Systems, Analytical Results and Numerical Simulations." Doctoral thesis, Växjö : Växjö University Press, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-1142.
7
Poulet, Marina. "Equations de Mahler : groupes de Galois et singularités régulières." Thesis, Lyon, 2021. https://tel.archives-ouvertes.fr/tel-03789627.
Анотація:
Cette thèse est consacrée à l'étude des équations de Mahler et des solutions de ces équations, appelées fonctions de Mahler. Des exemples classiques de fonctions de Mahler sont les séries génératrices des suites automatiques. La première partie de cette thèse porte sur les aspects galoisiens des équations de Mahler. Notre résultat principal est un analogue pour ces équations du théorème de densité de Schlesinger selon lequel la monodromie d'une équation différentielle à points singuliers réguliers est Zariski-dense dans son groupe de Galois différentiel. Pour cela, nous commençons par attacher une paire de matrices de connexion à chaque équation de Mahler singulière régulière. Ces matrices nous permettent de construire un sous-groupe du groupe de Galois de l'équation de Mahler et nous montrons que ce sous-groupe est Zariski-dense dans le groupe de Galois. La seule hypothèse de ce théorème de densité est le caractère singulier régulier de l'équation de Mahler considérée. La deuxième partie de cette thèse est consacrée à la construction d'un algorithme qui permet de reconnaître si une équation de Mahler est singulière régulièreThis thesis is devoted to the study of Mahler equations and the solutions of these equations, called Mahler functions. Classic examples of Mahler functions are the generating series of automatic sequences. The first part of this thesis deals with the Galoisian aspects of Mahler equations. Our main result is an analog for Mahler equations of the Schlesinger’s density theorem according to which the monodromy of a regular singular differential equation is Zariski-dense in its differential Galois group. To this end, we start by attaching a pair of connection matrices to each regular singular Mahler equation. These matrices enable us to construct a subgroup of the Galois group of the Mahler equation and we prove that this subgroup is Zariski-dense in the Galois group. The only assumption of this density theorem is the regular singular condition on the considered Mahler equation. The second part of this thesis is devoted to the construction of an algorithm which recognizes whether or not a Mahler equation is regular singular
8
Fernandez, Luis Eduardo Zambrano. "Densidade local em grafos." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/45/45134/tde-15032019-114236/.
Анотація:
Nós consideramos o seguinte problema. Fixado um grafo H e um número real \\alpha \\in (0,1], determine o menor \\beta = \\beta(\\alpha, H) que satisfaz a seguinte propriedade: se G é um grafo de ordem n no qual cada subconjunto de [\\alpha n] vértices induz mais que \\beta n^2 arestas então G contém H como subgrafo. Este problema foi iniciado e motivado por Erdös ao conjecturar que todo grafo livre de triângulo de ordem n contém um subconjunto de [n/2] vértices que induz no máximo n^2 /50 arestas. Nosso resultado principal mostra que i) todo grafo de ordem n livre de triângulos e pentágonos contém um subconjunto de [n/2] vértices que induz no máximo n^2 /64 arestas, e ii) se G é um grafo regular de ordem n livre de triângulo, com grau excedendo n/3, então G contém um subconjunto de [n/2] vértices que induz no máximo n^2 /50 arestas. Se além disso G não é 3-cromático então G contém um subconjunto de [n/2] vértices que induz menos de n^2 /54 arestas. Como subproduto e confirmando uma conjectura de Erdös assintoticamente, temos que todo grafo regular de ordem n livre de triângulo com grau excedendo n/3 pode ser tornado bipartido pela omissão de no máximo (1/25 + o(1))n^2 arestas. Nós também fornecemos um contraexemplo a uma conjectura de Erdös, Faudree, Rousseau e Schelp.We consider the following problem. Fixed a graph H and a real number \\alpha \\in (0,1], determine the smallest \\beta = \\beta(\\alpha, H) satisfying the following property: if G is a graph of order n such that every subset of [\\alpha n] vertices spans more that \\beta n^2 edges then G contains H as a subgraph. This problem was initiated and motivated by Erdös who conjectured that every triangle-free graph of order n contains a subset of [n/2] vertices that spans at most n^2 /50 edges. Our main result shows that i) every triangle- and pentagon-free graph of order n contains a subset of [n/2] vertices inducing at most n^2 /64 edges and, ii) if G is a triangle-free regular graph of order n with degree exceeding n/3 then G contains a subset of [n/2] vertices inducing at most n^2 /50 edges. Furthermore, if G is not 3-chromatic then G contains a subset of [n/2] vertices inducing less than n^2 /54 edges. As a by-product and confirming a conjecture of Erdös asymptotically, we obtain that every n-vertex triangle-free regular graph with degree exceeding n/3 can be made bipartite by removing at most (1/25 + o(1))n^2 edges. We also provide a counterexample to a conjecture of Erdös, Faudree, Rousseau and Schelp.
9
Gaertner, Nathaniel Allen. "Special Cases of Density Theorems in Algebraic Number Theory." Thesis, Virginia Tech, 2006. http://hdl.handle.net/10919/33153.
Анотація:
This paper discusses the concepts in algebraic and analytic number theory used in the proofs of Dirichlet's and Cheboterev's density theorems. It presents special cases of results due to the latter theorem for which greatly simplified proofs exist.Master of Science
10
Hurth, Tobias. "Limit theorems for a one-dimensional system with random switchings." Thesis, Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/37201.
Анотація:
We consider a simple one-dimensional random dynamical system with two driving vector fields and random switchings between them. We show that this system satisfies a one force - one solution principle and compute its unique invariant density explicitly. We study the limiting behavior of the invariant density as the switching rate approaches zero and infinity and derive analogues of classical probabilistic results such as the central limit theorem and large deviations principle.
11
Lacombe, Lionel. "On dynamics beyond time-dependent mean-field theories." Thesis, Toulouse 3, 2016. http://www.theses.fr/2016TOU30185/document.
Анотація:
Cette thèse présente différentes approches quantiques pour l'exploration de processus dynamiques dans des systèmes multiélectroniques, en particulier après une forte excitation qui peut aboutir à des effets dissipatifs. Les théories de champ moyen sont un outil utile à cet égard. Malgré l'existence de nombreux travaux réalisés ces deux dernières décennies, ces théories peinent à reproduire complètement la corrélation à deux corps. La thermalisation est un des effets des collisions électron-électron. Après un chapitre introductif, on présentera dans le chapitre 2 le formalisme de plusieurs méthodes étudiées dans cette thèse, ayant pour but la description de ces effets en ajoutant un terme de collision au champ moyen. Ces méthodes sont appelées Stochastic Time-Dependent Hartree Fock (STDHF), Extended TDHF (ETDHF) et Collisional TDHF (CTDHF). Cette dernière méthode représente d'une certaine façon le résultat principal de cette thèse. L'implémentation numérique de chacune de ces méthodes sera aussi examinée en détail. Dans les chapitres 3, 4 et 5, nous appliquerons à différents systèmes les méthodes présentées dans le chapitre 2. Dans le chapitre 3, nous étudions d'abord un canal de réaction rare, ici la probabilité d'un électron de s'attacher à un petit agrégat d'eau. Un bon accord avec les données expérimentales a été observé. Dans le chapitre 4, un modèle fréquemment utilisé en physique nucléaire est résolu exactement et comparé quantitativement à STDHF. L'évolution temporelle des observables à un corps s'accorde entre les deux méthodes, plus particulièrement en ce qui concerne le comportement thermique. Néanmoins, pour permettre une bonne description de la dynamique, il est nécessaire d'avoir une grande statistique, ce qui peut être un frein à l'utilisation de STDHF sur de larges systèmes. Pour surpasser cette difficulté, dans le chapitre 5 nous testons CTDHF, qui a été introduit dans le chapitre 2, sur un modèle à une dimension (et sans émission électronique). Le modèle se compose d'électrons dans un potentiel de type jellium avec une interaction auto-cohérente sous la forme d'une fonctionnelle de la densité. L'avantage de ce modèle à une dimension est que les calculs STDHF sont possibles numériquement, ce qui permet une comparaison directe aux calculs CTDHF. Dans cette étude de validité du concept, CTDHF s'accorde remarquablement bien avec STDHF. Cela pose les jalons pour une description efficace de la dissipation dans des systèmes réalistes en trois dimensions par CTDHFThis thesis presents various quantal approaches for the exploration of dynamical processes in multielectronic systems, especially after an intense excitation which can possibly lead to dissipative effects. Mean field theories constitute useful tools in that respect. Despite the existence of numerous works during the past two decades, they have strong difficulties to capture full 2-body correlations. Thermalization is one of these effects that stems from electron-electron collisions. After an introductory chapter, we present in Chapter 2 the formalism of the various schemes studied in this thesis toward the description of such an effect by including collisional terms on top of a mean field theory. These schemes are called Stochastic Time-Dependent Hartree Fock (STDHF), Extended TDHF (ETDHF) and Collisional TDHF (CTDHF). The latter scheme constitutes in some sense the main achievement of this thesis. The numerical realizations of each scheme are also discussed in detail. In Chapters 3, 4 and 5, we apply the approaches discussed in Chapter 2 but in various systems. In Chapter 3, we first explore a rare reaction channel, that is the probability of an electron to attach on small water clusters. Good agreement with experimental data is achieved. In Chapter 4, a model widely used in nuclear physics is exactly solved and quantitatively compared to STDHF. The time evolution of 1-body observables agrees well in both schemes, especially what concerns thermal behavior. However, to allow a good description of the dynamics, one is bound to use a large statistics, which can constitute a hindrance of the use of STDHF in larger systems. To overcome this problem, in Chapter 5, we go for a testing of CTDHF developed in Chapter 2 in a one-dimensional system (and without electronic emission). This system consists in electrons in a jellium potential with a simplified self-consistent interaction expressed as a functional of the density. The advantage of this 1D model is that STDHF calculations are numerically manageable and therefore allows a direct comparison with CTDHF calculations. In this proof of concept study, CTDHF compares remarkably well with STDHF. This thus paves the road toward an efficient description of dissipation in realistic 3D systems by CTDHF
12
Helbig, Nicole. "Orbital functionals in density-matrix- and current-density-functional theory." [S.l.] : [s.n.], 2006. http://www.diss.fu-berlin.de/2006/442/index.html.
13
Schweigert, Igor Vitalyevich. "Ab initio Density Functional Theory." [Gainesville, Fla.] : University of Florida, 2005. http://purl.fcla.edu/fcla/etd/UFE0011614.
14
Laming, Gregory John. "Density functional theory for molecules." Thesis, University of Cambridge, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.336907.
15
Chan, G. K. L. "Aspects of density functional theory." Thesis, University of Cambridge, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.597413.
Анотація:
The first part of our work, we describe investigations into the formal and conceptual aspects of density functional theory. These have been in four main areas. The first, is the theory of the derivative discontinuity, where we extended the theory to density matrix functionals, and carried out calculations of the effects of the discontinuity. Our second investigation concerned a new channel concept, namely, the shape and local chemical potentials. These describe the electron donating or accepting power of a density fragment. We demonstrated in simple model systems, that chemical features such as shell structure, or atoms in molecules, could be characterised as regions of constant shape chemical potential. Our third investigation concerned the homogeneous scaling of the Kohn-Sham kinetic energy. We disproved certain existing relations in the literature; we then went on to derive simple bounds on the kinetic energy, and to numerically calculate the approximate scaling of the kinetic energy in atomic systems. Our fourth investigation concerned an improved Lieb-Oxford bound for the exchange-correlation energy. By improving the numerical optimisation in the last part of the proof, we were able to tighten the bound. The second part of our work focused on the search for new energy functionals, and procedures for developing new functionals. Our efforts have been in two areas. The first was an investigation of the correlation functional of Hartree-Fock-Kohn-Sham theory. We observed the deficiencies of current functionals in the reproduction of the correlation potential, and attempted to correct this by fitting a functional to best reproduce numerical correlation potentials. In doing so, we observed the highly non-local nature of correlation in Hartree-Fock-Kohn-Sham theory, and the important effect of the derivative discontinuity on the energy. The second investigation attempted an exhaustive study of the Generalised Gradient Approximation (GCA), within a well-defined ab initio model. We developed a rigorous fitting methodology, and constructed well-converged fits to conclusively explore the limits of the accuracy of the GCA. A large number of observations were made concerning the choice of functional basis, the importance of additional gradient corrections, and the role of exact exchange. We also applied our fitting methodology to the construction of approximate Kohn-Sham kinetic energy functionals, with some success.
16
Belisle, Jordan. "A Theory of Relational Density." OpenSIUC, 2018. https://opensiuc.lib.siu.edu/dissertations/1556.
Анотація:
Relational Density Theory describes quantifiable higher-order properties governing relational framing of verbal organisms. Consistent with Newtonian classical mechanics, the theory posits that relational networks, and relating itself, will demonstrate the higher-order emergent properties of density, volume, and mass. Thus, networks that contain more relations (volume) that are stronger (density) will be more resistant to change (i.e., contain greater mass; mass = volume * density). Consistent with Newton’s law of gravity, networks that contain greater mass will also demonstrate force, accelerating the acquisition of new relations beyond that accounted for by direct acting contingencies, therefore demonstrating emergent self-organization that is highly susceptible to small changes at initial conditions. The current set of experiments provides initial proof of concept data for foundational principles introduced in the theory. Experiment 1 (N = 6) models the volumetric mass density formula, predicting that networks with greater volume and density will be more resistant to change (i.e., contain greater mass) when counterconditioning is applied to a subset of derived relations contained within experimentally established networks. Results were consistent with theoretical predictions based on density on 10 of 12 occasions, and resistance appeared greater for relations operating at greater volume. Experiment 2 (N = 6) extended directly from Experiment 1, generating a density differential through exposure at initial training conditions, and utilizing response time as a measure of relational density. Results again demonstrated successful prediction of resistance corresponding with the emergent density differential on 10 of 12 occasions, along with overall greater resistance corresponding with and volumetric increases. Experiment 3 (N = 9) demonstrated that relational volume can detract from relational density when accurate responding is near 100%, and that network density is predictive of class mergers when no merged responding is ever reinforced, suggesting that network mass can exert force on relational responding in the absence of any experimental conditioning (i.e., gravity). Taken together, results have radical implications for understanding the self-emergent nature of complex human behavior, with applications in therapy and treatment, as well as in understanding the human condition more broadly.
17
Roberge, André. "Finite density effects in gauge theories." Thesis, University of British Columbia, 1989. http://hdl.handle.net/2429/29272.
Анотація:
Various effects of finite fermionic densities in gauge theories are studied. The phase structure of SU(N) gauge theories with fermions as a function of imaginary chemical potential is related to the confining properties of the theory. This phase structure is controlled by a remnant of the Z[sub N] symmetry which is present in the absence of fermions. At high temperature the theory has a first-order phase transition as a function of imaginary chemical potential. This transition is expected to be absent in the low-temperature phase. It is shown that properties of the theory at nonzero fermion density can be deduced from its behaviour at finite imaginary chemical potential.
Anomalies in gauge theories are introduced using various two-dimensional models. In particular, the chiral Schwinger model is shown to be consistent despite being anomalous. The effects of finite densities in anomalous gauge theories is investigated. It is found that, contrary to some recent claims, an effective Harniltonian (obtained by integrating out the fermions) cannot be obtained by the simple inclusion of a Chern-Simons term multiplying the fermionic chemical potential. The importance of dynamical effects is stressed and a mechanism for producing primordial magnetic field is suggested.Science, Faculty of
Physics and Astronomy, Department of
Graduate
18
Deltuvienė, Dovilė. "Asimptotiniai skleidiniai didžiųjų nuokrypių zonose." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2005. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2004~D_20050111_161823-34609.
Анотація:
The novelty and originality of the work consists in the fact that in order to obtain asymptotic expansions with optimal values of the remainder terms in the zone of large deviations, along with the cumulant method the classical method of characteristic functions has to be used. In addition, when solving the problems stated in the work, other than the well known results in the problems of limit theorems of the probability theory and mathematical statistics, we have to estimate constants. Technically it is frequently rather a complicated task. The results obtained in the work have good opportunities to be applied in probability theory, mathematical statistics, econometric, etc. That is illustrated in the last section of the work in which theorems of large deviations are proved in the summation of weighted random variables with weights as well as discounted limit theorems.
19
Esplugas, Ricardo Oliveira. "Density functional theory and time-dependent density functional theory studies of copper and silver cation complexes." Thesis, University of Sussex, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.496931.
Анотація:
A particular emphasis of this thesis has been to provide insight into the underlying stability of these complexes and hence interpret experimental data, and to establish the development of solvation shell structure and its effect on reactivity and excited states. Energy decomposition analysis, fragment analysis and charge analysis has been used throughout to provide deeper insight into the nature of the bonding in these complexes. This has also been used successfully to explain observed preferential stability and dissociative loss products.
20
Dianzinga, Mamy Rivo. "N-representable density matrix perturbation theory." Thesis, Bordeaux, 2016. http://www.theses.fr/2016BORD0285/document.
Анотація:
Alors que les approches standards de résolution de la structure électronique présentent un coût de calcul à la puissance 3 par rapport à la complexité du problème, des solutions permettant d’atteindre un régime asymptotique linéaire,O(N), sont maintenant bien connues pour le calcul de l'état fondamental. Ces solutions sont basées sur la "myopie" de la matrice densité et le développement d'un cadre théorique permettant de contourner le problème aux valeurs propres. La théorie des purifications de la matrice densité constitue une branche de ce cadre théorique. Comme pour les approches de type O(N) appliquées à l'état fondamental,la théorie des perturbations nécessaire aux calculs des fonctions de réponse électronique doit être révisée pour contourner l'utilisation des routines coûteuses.L'objectif est de développer une méthode robuste basée uniquement sur la recherche de la matrice densité perturbée, pour laquelle seulement des multiplications de matrices creuses sont nécessaires. Dans une première partie,nous dérivons une méthode de purification canonique qui respecte les conditions de N-representabilité de la matrice densité à une particule. Nous montrons que le polynôme de purification obtenu est auto-cohérent et converge systématiquement vers la bonne solution. Dans une seconde partie, en utilisant une approche de type Hartree-Fock, nous appliquons cette méthode aux calculs des tenseurs de réponses statiques non-linéaires pouvant être déterminés par spectroscopie optique. Au delà des calculs à croissance linéaire réalisés, nous démontrons que les conditions N-representabilité constituent un prérequis pour garantir la fiabilité des résultatsWhereas standard approaches for solving the electronic structures present acomputer effort scaling with the cube of the number of atoms, solutions to overcomethis cubic wall are now well established for the ground state properties, and allow toreach the asymptotic linear-scaling, O(N). These solutions are based on thenearsightedness of the density matrix and the development of a theoreticalframework allowing bypassing the standard eigenvalue problem to directly solve thedensity matrix. The density matrix purification theory constitutes a branch of such atheoretical framework. Similarly to earlier developments of O(N) methodology appliedto the ground state, the perturbation theory necessary for the calculation of responsefunctions must be revised to circumvent the use of expensive routines, such asmatrix diagonalization and sum-over-states. The key point is to develop a robustmethod based only on the search of the perturbed density matrix, for which, ideally,only sparse matrix multiplications are required. In the first part of this work, we derivea canonical purification, which respects the N-representability conditions of the oneparticledensity matrix for both unperturbed and perturbed electronic structurecalculations. We show that this purification polynomial is self-consistent andconverges systematically to the right solution. As a second part of this work, we applythe method to the computation of static non-linear response tensors as measured inoptical spectroscopy. Beyond the possibility of achieving linear-scaling calculations,we demonstrate that the N-representability conditions are a prerequisite to ensurereliability of the results
21
Taga, Adrian. "Materials Engineering Using Density Functional Theory." Doctoral thesis, KTH, Materials Science and Engineering, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3809.
Анотація:
This doctoral thesis presents density functionalcalculations applied in several domains of interest in solidstate physics and materials science. Non-collinear magnetismhas been studied both in an artificial multi-layer structure,which could have technological relevance as a magnetic sensordevice, and as excitations in 3d ferromagnets. The intricatebulk crystal structure of γ-alumina has been investigated.An improved embedded cluster method is developed and applied tostudy the geometric and electronic structures and opticalabsorption energies of neutral and positively charged oxygenvacancies in α-quartz. Ab initio total energycalculations, based on the EMTO theory, have been used todetermine the elastic properties of Al1-xLixrandom alloys in the face-centered cubiccrystallographic phase. The obtained overall good agreementwith experiment demonstrates the applicability of the quantummechanics formulated within the framework of the DensityFunctional Theory for mapping the structural and mechanicalproperties of random alloys against chemical composition.
22
Scholz, Timothy Theodore. "Density matrix theory of diatomic molecules." Title page, contents and summary only, 1989. http://web4.library.adelaide.edu.au/theses/09SM/09sms368.pdf.
23
Reed, Mark Wilbert. "The "virtual density" theory of neutronics." Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/87497.
Анотація:
Thesis: Sc. D., Massachusetts Institute of Technology, Department of Nuclear Science and Engineering, 2014.Cataloged from PDF version of thesis. Vita.
Includes bibliographical references (pages 461-478).
Sustainable nuclear energy will likely require fast reactors to complement the current light water reactor paradigm. In particular, breed-and-burn sodium fast reactors (SFRs) offer a unique combination of fuel cycle and power density features. Unfortunately, large breed-and-burn SFRs are plagued by positive sodium void worth. In order to mitigate this drawback, one must quantify various sources of negative reactivty feedback, among which geometry distortions (bowing and flowering of fuel assemblies) are often dominant. These distortions arise mainly from three distinct physical phenomena: irradiation swelling, thermal swelling, and seismic events. Distortions are notoriously difficult to model, because they break symmetry and periodicity. Currently, no efficient and fully generic method exists for computing neutronic effects of distortions. Computing them directly via diffusion would require construction of exotic hyperfine meshes with continuous re-meshing. Many deterministic transport methods are geometrically flexible but would require tedious, intricate re-meshing or re-tracking to capture distortion effects. Monte Carlo offers the only high-fidelity approach to arbitrary geometry, but resolving minute reactivities and flux shift tallies within large heterogeneous cores requires CPU years per case and is thus prohibitively expensive. Currently, the most widely-used methods consist of various approximations involving weighting the uniform radial swelling reactivity coefficient by the power distribution. These approximations agree fairly well with experimental data for flowering in some cores, but they are not fully generic and cannot be trusted for arbitrary distortions. Boundary perturbation theory, developed in the 1980s, is fully general and mathematically rigorous, but it is inaccurate for coarse mesh diffusion and has apparently never been applied in industry. Our solution is the "virtual density" theory of neutronics, which alters material density (isotropically or anisotropically) instead of explicitly changing geometry. While geometry is discretized, material densities occupy a continuous domain; this allows density changes to obviate the greatest computational challenges of geometry changes. Although primitive forms of this theory exist in Soviet literature, they are only applicable to cases in which entire cores swell uniformly. Thus, we conceive a much more general and pragmatic form of "virtual density" theory to model non-uniform and localized geometry distortions via perturbation theory. In order to efficiently validate "virtual density" perturbation theory, we conceive the "virtual mesh" method for diffusion theory. This new method involves constructing a slightly perturbed "fake" mesh that produces correct first-order reactivity and flux shifts due to anisotropic swelling or expansion of individual mesh cells. First order reactivities computed on a "virtual mesh" agree with continuous energy Monte Carlo to within 1- uncertainty. We validate "virtual density" theory via the "virtual mesh" method in 3-D coarse mesh models of the Fast Flux Test Facility (FFTF) and Jōyō benchmarks using the MATLAB-PETSc-SLEPc (MaPS) multigroup finite difference diffusion code, which we developed for this purpose. We model a panoply of non-uniform anisotropic swelling scenarios, including axial swelling of individual assemblies, axial swelling of each mesh cell in proportion to its fission power, and radial core flowering with arbitrary axial dependence. In 3-D coarse mesh Cartesian cores with explicit coolant gaps, we model individual assembly motion, assembly row motion with arbitrary axial dependence, and assembly row "s-shape" bowing. In all cases, we find that "virtual density" perturbation theory predicts reactivity coefficients that agree with "virtual mesh" reference cases to within 0.01%. These reactivity coefficients are two to four orders of magnitude more accurate than those computed via boundary perturbation theory. We also develop the Pseudo-Seismic (PseuSei) Animator within MaPS to explore point-kinetic effects of arbitrary assembly motion for 3-D coarse mesh Cartesian cases. In general, this "virtual density" perturbation method can precisely predict reactivity coefficients due to anisotropic swelling or expansion of any core region in any direction. Furthermore, we compute flux and power shift distributions due to geometry distortions. We find that our "virtual density" formalism couples seamlessly with existing modal expansion perturbation theory (MEPT) formalism, and we use the resulting new hybrid method to compute flux and power shifts due to arbitrary anisotropic swelling of arbitrary core regions. We test this new method for a large, highly-heterogeneous Cartesian core, and we find that predicted (global and local) flux and power shift distributions typically agree with "virtual mesh" reference cases to within a few percent. Development of the "Virtual Density" Theory (VirDenT) industry code constitutes the culmination of this work. This parallelized Python code computes "virtual density" reactivity coefficients given a DIF3D flux solution as input. VirDenT contains a flux reconstruction module that computes individual pin powers from a homogenized nodal diffusion solution. It also contains PyPinPlot, a high-resolution visualization tool for pin-level powers, fluxes, and current vector fields. Most importantly, VirDenT computes reactivity coefficients due to local anisotropic swelling of assembly zones (which direct diffusion theory cannot compute) in CPU seconds, while Monte Carlo (currently the only high-fidelity approach) requires CPU years to do the same.
by Mark Wilbert Reed.
Sc. D.
24
Kaduk, Benjamin James. "Constrained Density-Functional Theory--Configuration Interaction." Thesis, Massachusetts Institute of Technology, 2012. http://hdl.handle.net/1721.1/73175.
Анотація:
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemistry, 2012.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (p. 117-136).
In this thesis, I implemented a method for performing electronic structure calculations, "Constrained Density Functional Theory-- Configuration Interaction" (CDFT-CI), which builds upon the computational strengths of Density Functional Theory and improves upon it by including higher level treatments of electronic correlation which are not readily available in Density-Functional Theory but are a keystone of wavefunction-based electronic structure methods. The method involves using CDFT to construct a small basis of hand-picked states which suffice to reasonably describe the static correlation present in a particular system, and efficiently computing electronic coupling elements between them. Analytical gradients were also implemented, involving computational effort roughly equivalent to the evaluation of an analytical Hessian for an ordinary DFT calculation. The routines were implemented within Q-Chem in a fashion accessible to end users; calculations were performed to assess how CDFT-CI improves reaction transition state energies, and to assess its ability to produce conical intersections, as compared to ordinary DFT. The analytical gradients enabled optimization of reaction transition-state structures, as well as geometry optimization on electronic excited states, with good results.
by Benjamin James Kaduk.
Ph.D.
25
Watson, Mark Adrian. "Density-functional theory and molecular properties." Thesis, University of Cambridge, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.615929.
26
Schenk, Stefan. "Density functional theory on a lattice." kostenfrei, 2009. http://d-nb.info/998385956/34.
27
Landreau, Bernard. "Majorations de fonctions arithmétiques en moyenne sur des ensembles de faible densité." Bordeaux 1, 1987. http://www.theses.fr/1987BOR10629.
Анотація:
Le but de cette these est d'etablir des majorations de valeurs de fonctions arithmetiques f, en moyenne sur des ensembles d'entiers a de faible densite exponentielle. En suivant des idees d'erdoes et nicolas, on commence par traiter le cas ou les ensembles a n'ont aucune structure particuliere. Il est alors possible de majorer la valeur moyenne de f sur a par une puissance du maximum de f sur a, avec un exposant inferieur a 1, d'autant plus proche de zero que l'ensemble a est riche. La partie principale du travail consiste a obtenir des majorations de la valeur f(n) par une somme de valeurs f(d) etendue aux petits diviseurs d de n et a en deduire des majorations de f en moyenne sur des ensembles a bien repartis dans les progressions arithmetiques de petite raison (par exemple, les suites polynomiales en une ou plusieurs variables). On determine en outre les fonctions f optimales. Ces methodes conduisent notamment a une nouvelle demonstration simple et particulierement rapide d'un resultat classique de van der corput
28
Yam, Chi-yung, and 任志勇. "Linear-scaling time-dependent density functional theory." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2003. http://hub.hku.hk/bib/B31246199.
29
Osorio, Guillén Jorge Mario. "Density Functional Theory in Computational Materials Science." Doctoral thesis, Uppsala University, Department of Physics, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-4496.
Анотація:
The present thesis is concerned to the application of first-principles self-consistent total-energy calculations within the density functional theory on different topics in materials science.
Crystallographic phase-transitions under high-pressure has been study for TiO2, FeI2, Fe3O4, Ti, the heavy alkali metals Cs and Rb, and C3N4. A new high-pressure polymorph of TiO2 has been discovered, this new polymorph has an orthorhombic OI (Pbca) crystal structure, which is predicted theoretically for the pressure range 50 to 100 GPa. Also, the crystal structures of Cs and Rb metals have been studied under high compressions. Our results confirm the recent high-pressure experimental observations of new complex crystal structures for the Cs-III and Rb-III phases. Thus, it is now certain that the famous isostructural phase transition in Cs is rather a new crystallographic phase transition.
The elastic properties of the new superconductor MgB2 and Al-doped MgB2 have been investigated. Values of all independent elastic constants (c11, c12, c13, c33, and c55) as well as bulk moduli in the a and c directions (Ba and Bc respectively) are predicted. Our analysis suggests that the high anisotropy of the calculated elastic moduli is a strong indication that MgB2 should be rather brittle. Al doping decreases the elastic anisotropy of MgB2 in the a and c directions, but, it will not change the brittle behaviour of the material considerably.
The three most relevant battery properties, namely average voltage, energy density and specific energy, as well as the electronic structure of the Li/LixMPO4 systems, where M is either Fe, Mn, or Co have been calculated. The mixing between Fe and Mn in these materials is also examined. Our calculated values for these properties are in good agreement with recent experimental values. Further insight is gained from the electronic density of states of these materials, through which conclusions about the physical properties of the various phases are made.
The electronic and magnetic properties of the dilute magnetic semiconductor Mn-doped ZnO has been calculated. We have found that for an Mn concentration of 5.6%, the ferromagnetic configuration is energetically stable in comparison to the antiferromgnetic one. A half-metallic electronic structure is calculated by the GGA approximation, where Mn ions are in a divalent state leading to a total magnetic moment of 5 μB per Mn atom.
30
Sargolzaei, Mahdi. "Orbital Polarization in Relativistic Density Functional Theory." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2007. http://nbn-resolving.de/urn:nbn:de:swb:14-1167841057730-69007.
Анотація:
The description of the magnetic properties of interacting many-particle systems has been one of the most important goals of physics. The problem is to derive the magnetic properties of such systems from quantum mechanical principles. It is well understood that the magnetization in an atom described by quantum numbers, spin (S), orbital (L), and total angular momentum (J) of its electrons. A set of guidelines, known as Hund's rules, discovered by Friedrich Hermann Hunds help us to determine the quantum numbers for the ground states of free atoms. The question ``to which extent are Hund's rules applicable on different systems such as molecules and solids?'' is still on the agenda. The main problem is that of finding the ground state of the considered system. Density functional theory (DFT) methods apparently are the most widely spread self-consistent methods to investigate the ground state properties. This is due to their high computational efficiency and very good accuracy. In the framework of DFT, usually the total energy is decomposed into kinetic energy, Coulomb energy, and a term called the exchange-correlation energy. Taking into account the relativistic kinetic energy leads to direct and indirect relativistic effects on the electronic structure of a solid. The most pronounced direct effect (although not the biggest in magnitude) is the spin-orbit splitting of band states. A well-known indirect relativistic effect is the change of screening of valence electrons from the nuclear charge by inner-shell electrons. One can ask that how relativistic effects come into play in ordinary density functional theory. Of course ordinary density functional theory does not include those effect. Four-current density functional theory (CDFT), the quantum electrodynamic version of the Hohenberg-Kohn theory is a powerful tool to treat relativistic effects. Although it is principally designed for systems in strong magnetic fields, CDFT can also be applied in situations where currents are present without external magnetic fields. As already pointed out by Rajagopal and Callaway (1973), the most natural way to incorporate magnetism into DFT is the generalization to CDFT. These authors, however, treated its most simple approximation, the spin density functional theory (SDFT), which keeps the spin current only and neglects completely correlation effects of orbital currents. By using the Kohn-Sham-Dirac (KSD) equation, spin-orbit coupling is introduced kinematically. The part of the orbital magnetism that is a consequence of Hund's second rule coupling is absent in this theory and there is not any more a one-to-one mapping of spin densities onto external fields. In solids, in particular in metals, the importance of Hund's second rule coupling (orbital polarization) and Hund's third rule (spin-orbit coupling) is usually interchanged in comparison to atoms. Thus, in applications of the relativistic CDFT to solids, the usual way has been to keep the spin-orbit coupling in the KSD equation (an extension to ordinary Kohn-Sham (KS) equation) and to neglect the orbital contribution to the total current density and approximate exchange-correlation energy functional with spin density only. This scheme includes a spontaneous exchange and correlation spin polarization. Orbital polarization, on the other hand, comes into play not as a correlation effect but also as an effect due to the interplay of spin polarization and spin-orbit coupling: In the presence of both couplings, time reversal symmetry is broken and a non-zero orbital current density may occur. Application of this scheme to 3d and 4f magnets yields orbital moments that are smaller than related experimental values by typically a factor of two. Orbital magnetism in a solid is strongly influenced by the ligand field, originating from the structural environment and geometry of the solid. The orbital moments in a solid with cubic symmetry are expected to be quenched if spin-orbit coupling is neglected. However, spin-orbit coupling induces orbital moments, accordingly. The relativistic nature of the spin-orbit coupling requires orbital magnetism to be treated within QED, and the treatment of QED in solids is possible in the frame of current density functional theory. The kinematic spin-orbit coupling is accounted for in many DFT calculations of magnetic systems within the LSDA. However, a strong deviation of the LSDA orbital moments from experiment is found in such approaches. To avoid such deviations, orbital polarization corrections would be desirable. In this Thesis, those corrections have been investigated in the framework of CDFT. After a short review for CDFT in Chapter 2, in Chapter 3, an "ad hoc" OP correction term (OPB) suggested by Brooks and Eriksson is given. This correction in some cases gives quite reasonable corrections to orbital moments of magnetic materials. Another OP correction (OPE), which has been introduced recently, was derived from the CDFT in the non-relativistic limit. Unfortunately, the program can only incompletely be carried through, as there are reasonable but uncontrolled approximations to be made in two steps of the derivation. Nevertheless, the result is quite close to the "ad hoc"ansatz. The calculated OPE energies for 3d and 4f free ions are in qualitative agreement with OPB energies. In Chapter 4, both corrections are implemented in the FPLO scheme to calculate orbital moments in solids. We found that both OPB and OPE corrections implemented in FPLO method, yield reasonably well the orbital magnetic moments of bcc Fe, hcp Co and fcc Ni compared with experiment. In Chapter 5, the effect of spin-orbit coupling and orbital polarization corrections on the spin and orbital magnetism of full-Heusler alloys is investigated by means of local spin density calculations. It is demonstrated, that OP corrections are needed to explain the experimental orbital moments. Model calculations employing one ligand field parameter yield the correct order of magnitude of the orbital moments, but do not account for its quantitative composition dependence. The spin-orbit coupling reduces the degree of spin polarization of the density of states at Fermi level by a few percent. We have shown that the orbital polarization corrections do not change significantly the spin polarization degree at the Fermi level. We also provide arguments that Co2FeSi might not be a half-metal as suggested by recent experiments. In Chapter 6, to understand recent XMCD data for Co impurities in gold, the electronic structure of Co impurities inside gold has been calculated in the framework of local spin density approximation. The orbital and spin magnetic moment have been evaluated. In agreement with experimental findings, the orbital moment is enhanced with respect to Co metal. On the other hand, internal relaxations are found to reduce the orbital moment considerably, whereas the spin moment is less affected. Both OPB and OPE yield a large orbital moment for Co impurities. However, those calculated orbital moments are almost by a factor of two larger than the experimental values. We also found that the orbital magnetic moment of Co may strongly depend on pressure.
31
Akyar, Ozge. "Density Functional Theory For Trapped Ultracold Fermions." Master's thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/12610948/index.pdf.
Анотація:
Recently a new outlook on dealing with dipolar ultracold fermions based on density
functional methods has received attention. A Thomas-Fermi treatment coupled with
a variational approach has been developed for a collection of fermions trapped in a
harmonic potential interacting via dipole-dipole forces. In this thesis, firstly our alternative
formalism for Thomas-Fermi method by performing some calculations based
on the Kohn-Sham formalism which is one of the main idea of density functional theory
is investigated. Furthermore, density distributions are obtained dependent to the
parametersrescaled interaction strength, dipole-dipole energy and the trap parameter which determine the trap geometry based on this theory. The thesis starts with a brief outline of the density functional theory and theory of our system, continues with calculations based on this theory, which are free of any variational assumptions for the density profile. Moreover, results of density graphics for harmonic trap will be followed by discussion of comparison and contrast with Thomas-Fermi method based on the paper of Goral et al.. These discussions are mainly about the shape of the density distribution, variation of the cloud parameters and energy behaviours according to the rescaled interaction strength. The thesis concludes with an analysis of contribution of density functional theory to this fermionic system.
32
Pawluk, Tiffany. "Iridium nanoparticles : a density functional theory study /." Available to subscribers only, 2005. http://proquest.umi.com/pqdweb?did=1075692711&sid=20&Fmt=2&clientId=1509&RQT=309&VName=PQD.
33
Osorio, Guillén Jorge Mario. "Density functional theory in computational materials science /." Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-4496.
34
Choudhury, Rathin. "Application and development of density functional theory." Thesis, University College London (University of London), 2006. http://discovery.ucl.ac.uk/1444572/.
Анотація:
This thesis concerns developments and applications using the density functional theory (DFT) ab initio electronic structure method. Implementation of a pseudo atomic orbital (PAO) basis set in the linear scaling DFT program CONQUEST is reported and used to test aspects of the linear scaling algorithm. Also a separate study using plane-wave DFT (VASP code) to model the strained growth of Indium Arsenide (InAs) on the (110) surface of Gallium Arsenide (GaAs), in particular the formation of a strain relieving dislocation network, has been performed. Pseudo atomic orbitals are the eigenstates of a pseudo-atom confined to a spherical potential, as used in the SIESTA linear scaling DFT program, and consist of a radial function multiplied by a spherical harmonic. Code to evaluate overlap and kinetic energy matrix elements between PAOs has been written, and tested using Gaussian PAOs, whose overlap integrals can be computed analytically. The PAO code has been integrated into the CON QUEST program and used to perform tests of the linear scaling algorithms on Silicon. Conventional plane wave DFT has been applied to calculate the energetics of a dislocation network in InAs grown on GaAs(110). Both InAs and GaAs have the zinc-blende crystal structure but the lattice constant of InAs is seven percent greater than that of GaAs. Experiments show that during deposition of the InAs by molecular beam epitaxy (MBE) compressive strain leads to formation of a strain relieving dislocation network after a critical amount of InAs coverage. In this thesis DFT is applied to calculate the energetically favoured location for the dislocation core and the resulting structure. In addition the critical InAs coverage necessary for dislocation formation is also calculated and compared to that measured by experiment.
35
Stauffert, Oliver [Verfasser], and Michael [Akademischer Betreuer] Walter. "Electron-phonon coupling with density functional theory." Freiburg : Universität, 2019. http://d-nb.info/1191689328/34.
36
Conroy, Michael W. "Density Functional Theory Studies of Energetic Materials." Scholar Commons, 2009. http://scholarcommons.usf.edu/etd/3691.
Анотація:
First-principles calculations employing density functional theory (DFT) were
performed on the energetic materials PETN, HMX, RDX, nitromethane, and a recently
discovered material, nitrate ester 1 (NEST-1). The aims of the study were to accurately
predict the isothermal equation of state for each material, improve the description of these
molecular crystals in DFT by introducing a correction for dispersion interactions, and
perform uniaxial compressions to investigate physical properties that might contribute to
anisotropic sensitivity.
For each system, hydrostatic-compression simulations were performed. Important
properties calculated from the simulations such as the equilibrium structure, isothermal
equation of state, and bulk moduli were compared with available experimental data to
assess the agreement of the calculation method. The largest contribution to the error was
believed to be caused by a poor description of van der Waals (vdW) interactions within
the DFT formalism.
An empirical van der Waals correction to DFT was added to VASP to increase
agreement with experiment. The average agreement of the calculated unit-cell volumes
for six energetic crystals improved from approximately 9% to 2%, and the isothermal
EOS showed improvement for PETN, HMX, RDX, and nitromethane. A comparison was
made between DFT results with and without the vdW correction to identify possible
advantages and limitations.
Uniaxial compressions perpendicular to seven low-index crystallographic planes
were performed on PETN, HMX, RDX, nitromethane, and NEST-1. The principal
stresses, shear stresses, and band gaps for each direction were compared with available
experimental information on shock-induced sensitivity to determine possible correlations
between physical properties and sensitivity. The results for PETN, the only system for
which the anisotropic sensitivity has been thoroughly investigated by experiment,
indicated a possible correlation between maximum shear stress and sensitivity. The
uniaxial compressions that corresponded to the greatest maximum shear stresses in HMX,
RDX, solid nitromethane, and NEST-1 were identified and predicted as directions with
possibly greater sensitivity. Experimental data is anticipated for comparison with the
predictions.
37
Nair, Nikhil. "New directions in hybrid density functional theory." Thesis, University of Cambridge, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.620224.
38
Hollins, Thomas William. "Local exchange potentials in density functional theory." Thesis, Durham University, 2014. http://etheses.dur.ac.uk/10932/.
Анотація:
DFT is a method that deals eciently with the ground state any-electron problem. It replaces the solution of the many-electron Schrodinger's equation with an equation to determine the electronic density alone. In the Kohn-Sham (KS) scheme, this density is obtained as the ground state density of a ctitious system of non-interacting electrons. The aim is to determine the local potential for these electrons so that their density equals the interacting density of the physical system. This potential is the sum of the electron-nuclear attraction, the Hartree repulsion from the density and nally the exchange and correlation potential. The central approximation in DFT is the functional form of the exchange-correlation potential. The most basic approximate functionals are explicit functions of the electron density. More sophisticated approximations are orbital dependent functionals or hybrids of density and orbital dependent functionals. In this work we present the implementation of some accurate local exchange potentials, the exact exchange (EXX) potential, the local Fock exchange (LFX) potential and an approximation to EXX, the common energy denominator approximation (CEDA) potential. The EXX potential minimises the Hartree-Fock (HF) total energy and is calculated using perturbation theory and the Hylleraas variational method, improving upon previous implementations. Optimising a local potential that adopts the HF density as its own ground state density, gives the LFX potential, which is simple to calculate and physically equivalent to the EXX potential. Both the EXX and LFX methods are extended to be applicable to metallic systems. The implemented potentials are used to calculate the electronic band structures for semiconductors, insulators, antiferromagnetic insulators and metals. For the semiconducting, insulating and metallic systems studied, the LFX method gives very similar results to EXX. In the systems characterised by stronger correlations, we observe a small disparity between the two exchange methods. When compared to experiment, the results are surprisingly accurate, given the complete neglect of correlation in these calculations. This is remarkable for the strongly correlated systems and also for the simple metals, given the well-known qualitative failure of Hartree-Fock for metals. The fundamental gap of a system is the sum of the KS eigenvalue gap and a correction known as the derivative discontinuity. The exact derivative discontinuity for a system is derived from ensemble density functional theory, thus allowing the full calculation of fundamental band gaps. Approximate forms of the discontinuity for the local density approximation (LDA), generalised gradient approximations (GGA), EXX and LFX are also derived and implemented. Contrary to the accepted wisdom, that the derivative discontinuity for local approximations (LDA/GGA) vanishes, calculated LDA and GGA fundamental band gaps give a much improved result over the corresponding Kohn-Sham band gaps, with accuracy comparable to EXX and LFX KS band gaps. Finally the derivative discontinuity using exact exchange and an orbital dependent correlation functional was also derived but not implemented.
39
Johnson, Erin R. "A density-functional theory including dispersion interactions." Thesis, Kingston, Ont. : [s.n.], 2007. http://hdl.handle.net/1974/926.
40
Aarons, Jolyon. "Density functional theory applied to metallic nanoparticles." Thesis, University of Southampton, 2018. https://eprints.soton.ac.uk/418013/.
Анотація:
This thesis will focus on DFT for calculations of large metallic nanoparticles. It will show new algorithms that were developed for reduced scaling DFT methods for metals; the testing, verification and design of new descriptors for predicting the catalytic activity of metallic nanoparticles; application of large-scale DFT calculations to model nanoparticle sequences to show size and oxygen adsorption coverage trends, and finally the application of these techniques and knowledge to perform a study of oxygen adsorption on real-world, experimentally determined platinum nanoparticles in collaboration with the Nellist group at Oxford materials. We explore the binding of atomic oxygen to cuboctahedral platinum nanoparticles of up to 1000 atoms using DFT calculations in ONETEP. We demonstrate convergence to the infinite slab limit for single oxygen adsorption in chapter 4 and correlate adsorption strength against popular descriptors for catalytic activity, such as the d-band centre approach. This approach is possible because of work which will be described in chapter 3 to implement angular momentum projected density of states calculations in ONETEP. The effects of oxygen coverage on the Pt55 and Pt147 cuboctahedral nanoparticles will also be analysed, which serves to advance our simulations towards realistic conditions. We show in our investigation into half monolayer, hemispherical oxygen coverage on platinum nanoparticles that oxygen tends to gravitate towards the edges and lower coordinated sites in the nanoparticle and away from the centres of facets. This effect correlates with the site specific, single oxygen adsorption energies on Pt309 and experimental platinum nanoparticles which is presented in chapter 5. We show that when subdividing the binding of monolayers of oxygen into only (111) and (100) facets that these have a lower adsorption strength per oxygen atom than combined (100) and (111) facets as well as lower binding strength than single oxygen adsoprtion. In the next part of the study, which is discussed in chapter 5, we show large scale DFT calculations on real platinum nanoparticles, which were measured by the Nellist group at Oxford materials using advanced electron microscopy techniques. These DFT calculations provide the electronic structure of the experimentally measured nanoparticles, which allowed us to apply electron density based catalytic activity descriptors to the nanoparticles, such as the d-band centre approach, or our own electronic density based descriptor described in chapter 3. We find that surface roughness of the experimental nanoparticles contributes to more potential oxygen binding sites with low electron density, which correlatates with stronger oxygen adsorption strength in our model, when compared with the relative smoothness of cuboctahedral and truncated octahedral facets. In the analysis which is presented in chapter 5, the proportion of sites which lie within 0.2 eV of the oxygen binding strength required for optimum catalytic activity is predicted with high efficiency, based on our catalytic activity descriptor. Finally, in chapter 6 we describe a new method for large scale DFT calculations on metallic systems which we call the AQuA-FOE method. We show how this method can have a computational cost which increases effectively linearly with the number of atoms. The AQuA-FOE method works by implicitly heating and quenching the electrons in the system to find the oneparticle density matrix, while conserving the electron number. We show validation of this method inside the EDFT procedure by comparing numerically with the diagonalisation based EDFT that is already implemented in ONETEP showing agreement in the energies to better than 10⁻⁵ EH per atom. We will also demonstrate the effectively linear-scaling computational cost of our method with calculation times on regular truncated octahedral Palladium nanoparticles ranging from 2,406 to 12,934 atoms.
41
Song, Yang. "Correcting density functional theory with supplemental potentials." Thesis, Boston University, 2013. https://hdl.handle.net/2144/12850.
Анотація:
Thesis (Ph.D.)--Boston University
PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you.Density Functional Theory (DFT) is a widely used method in quantum mechanics for modeling atoms and molecules. Commonly used DFT functionals have many shortcomings that include a poor description of dispersion, molecular geometries, exchange-repulsion, and hydrogen-bond interactions. To improve the quality of DFT, one popular idea is to apply empirical corrections to existing density functionals. Such an approach is both conceptually simple and computationally affordable. Despite many successful applications, most existing DFT empirical correction methods focus only on the dispersion corrections. In this thesis, we introduce system-specific empirical corrections to DFT. Our method not only provides corrections for dispersion, but also addresses problems such as deficiencies with molecular geometries, exchange-repulsion, and hydrogen bonding. The empirical correction, named "supplemental potential" (SP), is created by fitting the force differences between a functional and a high quality post-Hartree-Fock method. We tested the performance of SPs for three types of systems: water, methane-water, and molecular crystals. For the water system, the Becke-Lee-Yang-Parr (BLYP) functional description ofthe water potential energy surface (PES) can be improved to coupled-cluster quality with our water SP. For (H20)n (n=l-6), the relative cluster energies, cluster binding energies, and optimized energy structures are correctly predicted with the water SP correction. The developed methane-water SP is able to improve the BLYP PES to coupled-cluster quality in the study of methane water system. In the molecular crystal studies, the DFT-SP method correctly predict the most stable crystal structures among the sets of low-energy polymorphs, for four out of five studied organic molecules.
42
Zawadzki, Krissia de. "Density-functional theory for single-electron transistors." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/76/76131/tde-24102018-165237/.
Анотація:
The study of transport in nano-structured devices and molecular junctions has become a topic of great interest with the recent call for quantum technologies. Most of our knowledge has been guided by experimental and theoretical studies of the single-electron transistor (SET), an elementary device constituted by a quantum dot coupled to two otherwise independent free electron gases. The SET is particularly interesting because its transport properties at low temperatures are governed by the Kondo effect. A methodological difficulty has nonetheless barred theoretical progress in describing accurately realistic devices. On the one hand, Density-Functional Theory (DFT), the most convenient tool to obtain the electronic structure of complex materials, yields only qualitatively descriptions of the low-temperature physical properties of quantum dot devices. On the other hand, a quantitative description of low-temperature transport properties of the SET, such that obtained through the solution of the Anderson model via exact methods, is nonetheless unable to account for realistic features of experimental devices, such as geometry, band structure and electron-electron interactions in the electron gases. DFT describes the electron gases very well, but proves inadequate to treat the electronic correlations introduced by the quantum dot. This thesis proposes a way out of this frustrating dilemma. Our contribution is founded on renormalization-group (RG) concepts. Specifically, we show that, under conditions of experimental interest, the high and low temperatures regimes of a SET corresponds to the weakly-coupling and strongly-coupling fixed points of the Anderson Hamiltonian. Based on an RG analysis, we argue that, at this low-temperature fixed point, the entanglement between impurity and gas-electron spins introduces non-local correlations that lie beyond the reach of local- or quasi-local-density approximations, hence rendering inadequate approximations for the exchange-correlation energy functional. By contrast, the weak-coupling fixed point is within the reach of local-density approximations. With a view to describing realistic properties of quantum dot devices, we therefore propose a hybrid self-consistent procedure that starts with the weak-coupling fixed point and takes advantage of a reliable numerical method to drive the Hamiltonian to the strong-coupling fixed point. Our approach employs traditional DFT to treat the weak-coupling system and the Numerical Renormalization-Group (NRG) method to obtain properties in the strongcoupling regime. As an illustration, we apply the procedure to a single-electron transistor modeled by a generalized one-dimensional Hubbard Hamiltonian. We analyze the thermal dependence of the conductance in the SET and discuss its behavior at low-temperatures, comparing our results with other self-consistent approaches and with experimental data.O estudo de propriedades de transporte em dispositivos nano estruturados e junções moleculares tornou-se um tópico de grande interesse com a recente demanda por novas tecnologias quânticas. Grande parte do nosso conhecimento tem sido guiado por trabalhos experimentais e teóricos de um dispositivo conhecido como transístor de um elétron (SET), o qual é constituído por um ponto quântico acoplado a dois gases de elétrons independentes. O SET é particularmente interessante devido as suas propriedades de transporte a baixas temperaturas, as quais são governadas pelo efeito Kondo. Uma dificuldade metodológica, no entanto, tem barrado novos avanços teóricos para se obter uma descrição precisa de dispositivos realistas. Por um lado, a teoria do funcional da densidade (DFT), uma das ferramentas mais convenientes para calcular a estrutura eletrônica de materiais complexos, provê uma descrição apenas qualitativa das propriedades de transporte de transístores quânticos a baixas temperaturas. Por outro lado, uma descrição quantitativa satisfatória do SET a baixas temperaturas, tal como a modelagem e solução do modelo de Anderson via métodos exatos, é incapaz de levar em conta características realistas de dispositivos complexos, tal como geometria, estrutura de bandas e interações inter eletrônicas nos gases de elétrons. Embora a DFT os descreva bem, ela é inadequada para tratar correlações introduzidas pelo ponto quântico. Na presente tese propomos uma alternativa para este dilema. Nossa contribuição é fundamentada em conceitos de grupo de renormalização (RG). Especificamente, mostramos que, em condições de interesse experimental, os regimes de altas e baixas temperaturas em um SET correspondem aos pontos fixos de acoplamento fraco e forte do Hamiltoniano de Anderson. Baseando-nos em na análise do RG, mostramos que, no ponto fixo de baixas temperaturas, o emaranhamento entre a impureza e os spins dos gases eletrônicos introduz correlações não-locais que não podem ser descritas com abordagens DFT baseadas em aproximações locais ou quase locais para o potencial de troca e correlação. Em contraste, o ponto fixo de acoplamento fraco pode ser descrito por aproximações locais. Com o objetivo de obter uma descrição realista das propriedades de transístores quânticos, propomos um procedimento auto-consistente que começa do ponto fixo de acoplamento fraco e se aproveita de um método numérico eficiente para levar o Hamiltoniano para o ponto fixo de acoplamento forte. Nossa abordagem emprega DFT para tratar o sistema no limite de acoplamento fraco e o método de Grupo de Renormalização Numérico (NRG) para obter propriedades no regime de acoplamento forte. Como ilustração, aplicamos o procedimento para um transístor de um elétron modelado através do Hamiltoniano de Hubbard generalizado. Analisamos a dependência térmica da condutância no SET discutindo seu comportamento a baixas temperatura e comparamos nossos resultados com outras abordagens auto-consistentes e resultados experimentais.
43
Sargolzaei, Mahdi. "Orbital Polarization in Relativistic Density Functional Theory." Doctoral thesis, Technische Universität Dresden, 2006. https://tud.qucosa.de/id/qucosa%3A24939.
Анотація:
The description of the magnetic properties of interacting many-particle systems has been one of the most important goals of physics. The problem is to derive the magnetic properties of such systems from quantum mechanical principles. It is well understood that the magnetization in an atom described by quantum numbers, spin (S), orbital (L), and total angular momentum (J) of its electrons. A set of guidelines, known as Hund's rules, discovered by Friedrich Hermann Hunds help us to determine the quantum numbers for the ground states of free atoms. The question ``to which extent are Hund's rules applicable on different systems such as molecules and solids?'' is still on the agenda. The main problem is that of finding the ground state of the considered system. Density functional theory (DFT) methods apparently are the most widely spread self-consistent methods to investigate the ground state properties. This is due to their high computational efficiency and very good accuracy. In the framework of DFT, usually the total energy is decomposed into kinetic energy, Coulomb energy, and a term called the exchange-correlation energy. Taking into account the relativistic kinetic energy leads to direct and indirect relativistic effects on the electronic structure of a solid. The most pronounced direct effect (although not the biggest in magnitude) is the spin-orbit splitting of band states. A well-known indirect relativistic effect is the change of screening of valence electrons from the nuclear charge by inner-shell electrons. One can ask that how relativistic effects come into play in ordinary density functional theory. Of course ordinary density functional theory does not include those effect. Four-current density functional theory (CDFT), the quantum electrodynamic version of the Hohenberg-Kohn theory is a powerful tool to treat relativistic effects. Although it is principally designed for systems in strong magnetic fields, CDFT can also be applied in situations where currents are present without external magnetic fields. As already pointed out by Rajagopal and Callaway (1973), the most natural way to incorporate magnetism into DFT is the generalization to CDFT. These authors, however, treated its most simple approximation, the spin density functional theory (SDFT), which keeps the spin current only and neglects completely correlation effects of orbital currents. By using the Kohn-Sham-Dirac (KSD) equation, spin-orbit coupling is introduced kinematically. The part of the orbital magnetism that is a consequence of Hund's second rule coupling is absent in this theory and there is not any more a one-to-one mapping of spin densities onto external fields. In solids, in particular in metals, the importance of Hund's second rule coupling (orbital polarization) and Hund's third rule (spin-orbit coupling) is usually interchanged in comparison to atoms. Thus, in applications of the relativistic CDFT to solids, the usual way has been to keep the spin-orbit coupling in the KSD equation (an extension to ordinary Kohn-Sham (KS) equation) and to neglect the orbital contribution to the total current density and approximate exchange-correlation energy functional with spin density only. This scheme includes a spontaneous exchange and correlation spin polarization. Orbital polarization, on the other hand, comes into play not as a correlation effect but also as an effect due to the interplay of spin polarization and spin-orbit coupling: In the presence of both couplings, time reversal symmetry is broken and a non-zero orbital current density may occur. Application of this scheme to 3d and 4f magnets yields orbital moments that are smaller than related experimental values by typically a factor of two. Orbital magnetism in a solid is strongly influenced by the ligand field, originating from the structural environment and geometry of the solid. The orbital moments in a solid with cubic symmetry are expected to be quenched if spin-orbit coupling is neglected. However, spin-orbit coupling induces orbital moments, accordingly. The relativistic nature of the spin-orbit coupling requires orbital magnetism to be treated within QED, and the treatment of QED in solids is possible in the frame of current density functional theory. The kinematic spin-orbit coupling is accounted for in many DFT calculations of magnetic systems within the LSDA. However, a strong deviation of the LSDA orbital moments from experiment is found in such approaches. To avoid such deviations, orbital polarization corrections would be desirable. In this Thesis, those corrections have been investigated in the framework of CDFT. After a short review for CDFT in Chapter 2, in Chapter 3, an "ad hoc" OP correction term (OPB) suggested by Brooks and Eriksson is given. This correction in some cases gives quite reasonable corrections to orbital moments of magnetic materials. Another OP correction (OPE), which has been introduced recently, was derived from the CDFT in the non-relativistic limit. Unfortunately, the program can only incompletely be carried through, as there are reasonable but uncontrolled approximations to be made in two steps of the derivation. Nevertheless, the result is quite close to the "ad hoc"ansatz. The calculated OPE energies for 3d and 4f free ions are in qualitative agreement with OPB energies. In Chapter 4, both corrections are implemented in the FPLO scheme to calculate orbital moments in solids. We found that both OPB and OPE corrections implemented in FPLO method, yield reasonably well the orbital magnetic moments of bcc Fe, hcp Co and fcc Ni compared with experiment. In Chapter 5, the effect of spin-orbit coupling and orbital polarization corrections on the spin and orbital magnetism of full-Heusler alloys is investigated by means of local spin density calculations. It is demonstrated, that OP corrections are needed to explain the experimental orbital moments. Model calculations employing one ligand field parameter yield the correct order of magnitude of the orbital moments, but do not account for its quantitative composition dependence. The spin-orbit coupling reduces the degree of spin polarization of the density of states at Fermi level by a few percent. We have shown that the orbital polarization corrections do not change significantly the spin polarization degree at the Fermi level. We also provide arguments that Co2FeSi might not be a half-metal as suggested by recent experiments. In Chapter 6, to understand recent XMCD data for Co impurities in gold, the electronic structure of Co impurities inside gold has been calculated in the framework of local spin density approximation. The orbital and spin magnetic moment have been evaluated. In agreement with experimental findings, the orbital moment is enhanced with respect to Co metal. On the other hand, internal relaxations are found to reduce the orbital moment considerably, whereas the spin moment is less affected. Both OPB and OPE yield a large orbital moment for Co impurities. However, those calculated orbital moments are almost by a factor of two larger than the experimental values. We also found that the orbital magnetic moment of Co may strongly depend on pressure.
44
Laestadius, Andre. "Foundation of Density Functionals in the Presence of Magnetic Field." Doctoral thesis, KTH, Matematik (Avd.), 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-145546.
Анотація:
This thesis contains four articles related to mathematical aspects of Density Functional Theory. In Paper A, the theoretical justification of density methods formulated with current densities is addressed. It is shown that the set of ground-states is determined by the ensemble-representable particle and paramagnetic current density. Furthermore, it is demonstrated that the Schrödinger equation with a magnetic field is not uniquely determined by its ground-state solution. Thus, a wavefunction may be the ground-state of two different Hamiltonians, where the Hamiltonians differ by more than a gauge transformation. This implies that the particle and paramagnetic current density do not determine the potentials of the system and, consequently, no Hohenberg-Kohn theorem exists for Current Density Functional Theory formulated with the paramagnetic current density. On the other hand, by instead using the particle density as data, we show that the scalar potential in the system's Hamiltonian is determined for a fixed magnetic field. This means that the Hohenberg-Kohn theorem continues to hold in the presence of a magnetic field, if the magnetic field has been fixed. Paper B deals with N-representable density functionals that also depend on the paramagnetic current density. Here the Levy-Lieb density functional is generalized to include the paramagnetic current density. It is shown that a wavefunction exists that minimizes the "free" Hamiltonian subject to the constraints that the particle and paramagnetic current density are held fixed. Furthermore, a convex and universal current density functional is introduced and shown to equal the convex envelope of the generalized Levy-Lieb density functional. Since this functional is convex, the problem of finding the particle and paramagnetic current density that minimize the energy is related to a set of Euler-Lagrange equations. In Paper C, an N-representable Kohn-Sham approach is developed that also include the paramagnetic current density. It is demonstrated that a wavefunction exists that minimizes the kinetic energy subject to the constraint that only determinant wavefunctions are considered, as well as that the particle and paramagnetic current density are held fixed. Using this result, it is then shown that the ground-state energy can be obtained by minimizing an energy functional over all determinant wavefunctions that have finite kinetic energy. Moreover, the minimum is achieved and this determinant wavefunction gives the ground-state particle and paramagnetic current density. Lastly, Paper D addresses the issue of a Hohenberg-Kohn variational principle for Current Density Functional Theory formulated with the total current density. Under the assumption that a Hohenberg-Kohn theorem exists formulated with the total current density, it is shown that the map from particle and total current density to the vector potential enters explicitly in the energy functional to be minimized. Thus, no variational principle as that of Hohenberg and Kohn exists for density methods formulated with the total current density.QC 20140523
45
Reinhard, Teresa Elisabeth [Verfasser], and Angel [Akademischer Betreuer] Rubio. "Density Matrix Embedding Theory : Foundations, Applications and Connection to Functional Theories / Teresa Elisabeth Reinhard ; Betreuer: Angel Rubio." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2019. http://d-nb.info/1186891157/34.
46
Karlsson, Daniel. "Nuclear density functional theory calculations for the r-process nucleosynthesis : Nuclear density functional theory calculations for the r-process nucleosynthesis." Thesis, KTH, Fysik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-250775.
47
Sayin, Ceren Sibel. "Density Functional Theory Investigation Of Tio2 Anatase Nanosheets." Master's thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/12611075/index.pdf.
Анотація:
In this thesis, the electronic properties of nanosheets derived from TiO2 anatase structure which acts as a photocatalyst, are investigated using the density functional theory. We examine bulk constrained properties of the nanosheets derived from the (001) surface and obtain their optimized geometries. We investigate properties of lepidocrocite-type TiO2 nanosheets and nanotubes of different sizes formed by rolling the lepidocrocite nanosheets. We show that the stability and the band gaps of the considered nanotubes increase with increasing diameter. We also study adsorption of
Aun clusters with (n=1,2,3,4) on the clean and oxygen depleted lepidocrocite surface. Through systematic investigation of various cases we conclude that Au preferres O
vacancy sites rather than clean surface in accordance with previous metal adsorption studies on TiO2 surfaces. For the clean surface, we observe that Au clusters with an odd number of atoms are weakly bonded and metallizes the system while even number of Au atoms results in small band gap semiconductors with relatively higher binding energies.
48
Iusan, Diana Mihaela. "Density Functional Theory Applied to Materials for Spintronics." Doctoral thesis, Uppsala universitet, Materialteori, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-119887.
Анотація:
The properties of dilute magnetic semiconductors have been studied by combined ab initio, Monte Carlo, and experimental techniques. This class of materials could be very important for future spintronic devices, that offer enriched functionality by making use of both the spin and the charge of the electrons. The main part of the thesis concerns the transition metal doped ZnO. The role of defects on the magnetic interactions in Mn-doped ZnO was investigated. In the presence of acceptor defects such as zinc vacancies and oxygen substitution by nitrogen, the magnetic interactions are ferromagnetic. For dilute concentrations of Mn (~ 5%) the ordering temperature of the system is low, due to the short ranged character of the exchange interactions and disorder effects. The clustering tendency of the Co atoms in a ZnO matrix was also studied. The electronic structure, and in turn the magnetic interactions among the Co atoms, is strongly dependent on the exchange-correlation functional used. It is found that Co impurities tend to form nanoclusters and that the interactions among these atoms are antiferromagnetic within the local spin density approximation + Hubbard U approach. The electronic structure, as well as the chemical and magnetic interactions in Co and (Co,Al)-doped ZnO, was investigated by joined experimental and theoretical techniques. For a good agreement between the two, approximations beyond the local density approximation must be used. It is found that the Co atoms prefer to cluster within the semiconducting matrix, a tendency which is increased with Al co-doping. We envision that it is best to describe the system as superparamagnetic due to the formation of Co nanoclusters within which the interactions are antiferromagnetic. The magnetic anisotropy and evolution of magnetic domains in Fe81Ni19/Co(001) superlattices were investigated both experimentally, as well as using model spin dynamics. A magnetic reorientation transition was found.
49
Mills, Eric A. "Protein-solvent interactions and classical density functional theory." Thesis, University of British Columbia, 2015. http://hdl.handle.net/2429/55761.
Анотація:
We use classical density functional theory to investigate the interactions between solvents and proteins. We examine a diverse experimental literature to establish thermodynamic properties of protein-cosolute interaction, particularly the compensation between transfer entropy and transfer enthalpy. We develop a method of analysing the uncertainties in such measurements and use the method to resolve a long-standing debate over entropy-enthalpy compensation. We develop a classical density functional theory for interactions between proteins and cosolutes. The theory developed here ignores the solvent-solvent interaction but is nonetheless quite accurate. We use this approach to reproduce transfer free energies reported elsewhere, and show that the cDFT model captures the desolvation barrier and the temperature dependence of the transfer free energy. We use experimental values that we have analyzed to define the parameter space of a model density functional theory approach. We then extend the classical density functional theory to capture protein-water interactions, thus developing a new implicit solvent model. Along the way we give a proof that the free energy of a bath of particles in a finite external potential is independent of the external potential in the isothermal-isobaric ensemble. We finally discuss the challenges remaining in implementing our implicit solvent model.Science, Faculty of
Physics and Astronomy, Department of
Graduate
50
Manoli, Soheil Dimitri. "The generalized exchange local spin density-functional theory /." Thesis, McGill University, 1986. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=75359.
Анотація:
An orbital dependent local spin density-functional (LSD) scheme with a generated exchange, the LSD GX scheme, has been developed based on the correct normalization conditions of an electron gas. This scheme contains no adjustable parameters; the B$ sb1$, B$ sb2$ and $ alpha sp lim$ are constant for all atoms once the shape of the Fermi hole is chosen. These parameters are rigorously calculated using an unspecified Fermi hole correlation factor and they give an exchange density which reduces exactly to the homogeneous free electron gas one at the high electron density limit.The LSD GX exchange density is corrected for self-interaction (SI) by splitting the total Fermi hole correlation factor into pure-exchange and self-interaction holes.
These new LSD and SI corrected schemes are compared to each other. They also compare very well theoretically and numerically (total energies and eigenvalues) with other local schemes current in the literature.
New equations for the IP and electronegativities of the atoms in these local schemes are derived which give good results.