| 1. |
- Almanasreh, Hasan, 1981
(författare)
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The Dirac Operator; From Numerics to the Theory of G-convergence
- 2010
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- We consider two main issues concerning the Dirac operator, the first is widely known as the appearance of spurious eigenvalues within the spectrum. The second is the study of the asymptotic behavior of the eigenvalues for a family of Dirac operators with oscillatory potential added to the Coulomb-Dirac Hamiltonian. In the first problem a stable Finite element scheme is used to treat the problem of spuriousity of the radial Dirac operator with a Coulomb potential. The numerical accuracy depends strongly on the derivation of a fine-intrinsic stability parameter. In the second problem we consider the Coulomb-Dirac operator with addition to an abstract oscillating potential. Using the spectral measure of operators we project into the positive part of the perturbed Hamiltonian. By using G-convergence theory of positive self-adjoint operators in Hilbert spaces and ¡- convergence of the associated quadratic functionals we prove G-compactness for a family of positive Dirac operators under certain assumptions on the potentials.
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| 2. |
- Antipov, Sergey V., 1986
(författare)
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Radiative association of C(3 P) and N(4 S) atoms: From semi-classical theory to coupled-states quantum dynamics
- 2010
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In the present work formation of the CN radical through radiative association is simulated using both semi-classical and quantum mechanical theories. The rate coefficient for temperatures from 40 K to 1900 K has been computed using the Breit-Wigner theory to account for the resonances. Comparison with the results obtained by the semi-classical method, which completely omits the shape resonances, is accurate to within 25% above room temperature. Furthermore, the role of the spin-orbit and rotational couplings is investigated. Comparison of the energy-dependent rate coefficients calculated with and without spin-orbit and rotational couplings shows that the couplings effect the low-energy part of the rate coefficient.
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| 3. |
- Li, Huaqing, 1983
(författare)
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Classical Wigner Method with an Effective Quantum Force
- 2010
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this work, I will present an effective way to study the dynamics in phase space and obtain the rate constants. Our method is based on the Classical Wigner (CW) model, which is an approximate method for including quantum mechanical effects into molecular simulations. The Classical Wigner model propagates each trajectory independently under a classical force. It becomes poorer when the temperature decreases, because it can not describe the dynamical interference effects. The mechanism of the CW model needs to be improved. We manage to solve this problem by using a parameter denoted 0, which is the characteristic distance between forward and backward Feynman paths that enter the expression of the correlation function[1]. We use this parameter to construct an effective force to substitute for the classical force. This new method still keeps the simplicity of the CW model and improves the accuracy. The new method is named Classical Wigner method with an effective quantum force (CWEQF). This new force has the ability to approximately contain the quantum effects in the dynamics. Also, we have a new way to interpret the tunneling effects, especially for the quasi-bound situation. Thus, we are able to describe a consistent mechanism for the quantum leak out effect exemplified for a cubic potential. Then we implement the CWEQF on the two-dimensional H + H2 reaction to obtain the rate constant. All the applications return consistently improved results compared to the ordinary CW model. There is still room for us to improve this method. However, from the pedagogical point of view, this method is really a good candidate to understand the quantum effect in phase space.
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| 4. |
- Lärkäng, Richard, 1985
(författare)
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Residue currents on analytic spaces
- 2010
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis concerns residue currents on analytic spaces. In the first paper, we construct Coleff-Herrera products and Bochner-Martinelli type currents associated with a weakly holomorphic mapping, and show that these currents satisfy well-known properties from the strongly holomorphic case. This includes the transformation law, the Poincaré-Lelong formula and the equivalence of the Coleff-Herrera product and the Bochner-Martinelli current associated with a complete intersection of weakly holomorphic functions. In the second paper, we discuss the duality theorem on singular varieties. In the case of a complex manifold, the duality theorem, proven by Dickenstein-Sessa and Passare, says that the annihilator of the Coleff-Herrera product associated with a complete intersection $f$ equals the ideal generated by $f$. We give sufficient and in many cases necessary conditions in terms of certain singularity subvarieties of the sheaf $\mathcal{O}_Z$ for when the duality theorem holds on a singular variety $Z$.
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| 5. |
- Ryding, Mauritz Johan, 1981
(författare)
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Interactions of ionic molecular clusters H+(H2O)n, H+(NH3)1(H2O)n and H+(pyridine)1-3(H2O)n with heavy water in cluster beam experiments
- 2010
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Molecular cluster ions are fascinating subjects of study. Bridging the size gap between molecules and bulk, they often display non-trivial size dependent behavior and properties. Clusters—apart from being interesting in their own right and serving as useful model system in a number of applications—have a very real and important role in the atmosphere. Clusters acts as precursors for atmospheric particle formation, and as such, any uncertainties regarding clusters have a significant impact on the current estimates of global warming. This work investigates the properties of some ionic molecular clusters: H+(H2O)n, H+(NH3)1(H2O)n and H+(pyridine)1-3(H2O)n, as well as their reactions with gas phase heavy water, D2O. This is done in a cluster beam experiment, using a setup consisting of a quadrupole mass filter, a collision cell, and a time-of-flight mass spectrometer. The relative reaction cross section between the clusters and D2O was investigated; it was found that the pure water clusters and ammonia containing cluster have similar cross sections. Furthermore, the cross sections of the pyridine containing clusters differed from those of the pure water clusters and ammonia containing clusters. However, among the pyridine containing clusters, the reaction cross section depended only on the water content and not on the number of pyridine molecules. Previous studies in the field have concluded that the proton mobility in a cationic pure water cluster is large, leading to a H/D scrambling process during the lifetime of the reaction intermediate formed upon collision of the cluster with D2O. This is seen also in the experiments presented here. However, some of the cluster types investigated—H+(NH3)1(H2O)n and H+(pyridine)1(H2O)n —do not show this behavior. For these clusters, the high proton affinity of the basic molecule leads to the proton being locked in place by the nitrogen atom. Surprisingly, it was found that adding additional pyridine molecules to the latter cluster types negates this effect, thus H+(pyridine)2-3(H2O)n clusters exhibit H/D scrambling just like pure protonated water clusters. Quantum chemical calculations show that for H+(pyridine)2(H2O)4-6 there are stable structures where the proton is found on a water molecule. Although these structures are higher in energy compared to the most stable ones (with the proton situated on a pyridine molecule), the thermodynamical barrier for transferring the proton from a pyridine molecule to a water molecule is likely to decrease with cluster size, thus allowing hydronium containing stable cluster isomers.
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| 6. |
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| 7. |
- Sznajdman, Jacob, 1983
(författare)
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Some Analytic generalizations of the Briancon-Skoda Theorem
- 2010
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The Brian\c con-Skoda theorem appears in many variations in recent literature. The common denominator is that the theorem gives a sufficient condition that implies a membership $\phi\in \ideala^l$, where $\ideala$ is an ideal of some ring $R$. In the analytic interpretation $R$ is the local ring of an analytic space $Z$, and the condition is that $|\phi|\leq C|\ideala|^{N+l}$ holds on the space $Z$. The theorem thus relates the rate of vanishing of $\phi$ along the locus of $\ideala$ to actual membership of (powers of) the ideal. The smallest integer $N$ that works for all $\ideala \subset R$ and all $l\geq 1$ simultaneously will be called the Brian\c con-Skoda number of the ring $R$. The thesis contains three papers. The first one gives an elementary proof of the original Brian\c con-Skoda theorem. This case is simply $Z=\C^n$. The second paper contains an analytic proof of a generalization by Huneke. The result is also sharper when $\ideala$ has few generators if the geometry is not to complicated in a certain sense. Moreover, the method can give upper bounds for the Brian\c con-Skoda number for some varieties such as for example the cusp $z^p = w^q$. In the third paper non-reduced analytic spaces are considered. In this setting Huneke's generalization must be modified to remain valid. More precisely, $\phi$ belongs to $\ideala^l$ if one requires that $|L \phi| \leq C |\ideala|^{N+l}$ holds on $Z$ for a given family of holomorphic differential operators on $Z$. We impose the assumption that the local ring $\O_Z$ is Cohen-Macaulay for technical reasons.
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| 8. |
- Säfström, Ida, 1984
(författare)
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Tensor Products of Highest Weight Representations and Skew-Symmetric Matrix Equations A+B+C=0
- 2010
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The question of characterizing the eigenvalues for the sum of two Hermitian matrices, was solved in 1999, after almost a century of efforts. The saturation conjecture for GL_C(n) was proven by Knutson and Tao, filling in the last gap in Horn’s conjecture. Under certain conditions, this problem is equivalent to decomposing the tensor product of two finite dimensional irreducible highest weight representations of GL_C(n). In the first part of this thesis we use the methods of moment maps and coadjoint orbits to find equivalence between the eigenvalue problem for skew-symmetric matrices and the decomposition of tensor products of irreducible highest weight representations of SO_C(2k). We characterize the eigenvalues in the cases k = 2,3, where we can take advantage of Lie algebra isomorphisms. In the second part, we consider irreducible, infinite dimensional, unitary highest weight representations of GL_C(n + 1) as representations on spaces of vector valued polynomials, and we find irreducible factors in the tensor product of two such representations.
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| 9. |
- Cronie, Ottmar, 1979
(författare)
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Different Aspects of Inference for Spatio-Temporal Point Processes
- 2010
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis deals with inference problems related to the Renshaw-Särkkä growth interaction model (RS-model). It is a continuous time spatio-temporal point process with time dependent interacting marks, in which the immigrationdeath process (a continuous time Markov chain) controls the arrivals of new marked points as well as their potential life-times. The data considered are marked point patterns sampled at fixed time points. First we propose three edge correction methods for discretely sampled (marked) spatio-temporal point processes. These are all based on the idea of placing an approximated expected behaviour of our process at hand (based on simulated realisations) outside the study region, which in turn interacts with the data during the estimation. We study the methods and evaluate them numerically in the context of the RS-model. The parameters related to the development of the marks are estimated using the least-squares approach. Secondly, we propose (approximate) maximum likelihood (ML) estimators for the two parameters of the immigration-death process; the arrival intensity and the death rate. The arrival intensity is assumed to be constant and the death rate is assumed to be proportional to a function of the current mark size of a point. The arrival intensity estimator is constructed to compensate for the (unobserved) individuals arriving and dying between two sampled time points. When assumed that the death rate is constant we can derive the transition probabilities of the immigration-death process. These in turn give us the exact likelihood of its parameter pair. We are able to reduce the likelihood maximisation problem from two dimensions to one dimension. Furthermore, under the condition that the parameter pair lies in some compact subset of the positive part of the real plane, we manage to show the consistency and the asymptotic normality of its ML-estimator under an equidistant sampling scheme. These results are also evaluated numerically.
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| 10. |
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