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- Broman, David, 1977-
(författare)
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Meta-Languages and Semantics for Equation-Based Modeling and Simulation
- 2010
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Performing computational experiments on mathematical models instead of building and testing physical prototypes can drastically reduce the develop cost for complex systems such as automobiles, aircraft, and powerplants. In the past three decades, a new category of equation-based modeling languages has appeared that is based on acausal and object-oriented modeling principles, enabling good reuse of models. However, the modeling languages within this category have grown to be large and complex, where the specifications of the language's semantics are informally defined, typically described in natural languages. The lack of a formal semantics makes these languages hard to interpret unambiguously and to reason about. This thesis concerns the problem of designing the semantics of such equation-based modeling languages in a way that allows formal reasoning and increased correctness. The work is presented in two parts.In the first part we study the state-of-the-art modeling language Modelica. We analyze the concepts of types in Modelica and conclude that there are two kinds of type concepts: class types and object types. Moreover, a concept called structural constraint delta is proposed, which is used for isolating the faults of an over- or under-determined model.In the second part, we introduce a new research language called the Modeling Kernel Language (MKL). By introducing the concept of higher-order acausal models (HOAMs), we show that it is possible to create expressive modeling libraries in a manner analogous to Modelica, but using a small and simple language concept. In contrast to the current state-of-the-art modeling languages, the semantics of how to use the models, including meta operations on models, are also specified in MKL libraries. This enables extensible formal executable specifications where important language features are expressed through libraries rather than by adding completely new language constructs. MKL is a statically typed language based on a typed lambda calculus. We define the core of the language formally using operational semantics and prove type safety. An MKL interpreter is implemented and verified in comparison with a Modelica environment.
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| 2. |
- Norman, Patrick, 1968-
(författare)
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Nonlinear Optical Properties of Fullerenes, Oligomers, and Solutions
- 1998
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This work presents development and applications of modern tools in ab initio quantum chemistry for obtaining linear and nonlinear response properties of molecules in the gas phase and in solution. The external perturbing fields are primarily electric in nature with frequencies in the optical region.The framework for this achievement is denoted response theory, a formulation of time-dependent perturbation theory, which has been extended to include fourth-order properties fully analytically for self-consistent field (SCF) and multi-configurational SCF (MCSCF) reference states. This extension refers both to the vacuum theory as well as to a self-consistent reaction field model for properties in solution.Applications are presented, displaying both the possibilities and limitations of the theory. Highly electron correlated MCSCF reference states are used for small molecules both in the gas phase and in solution to obtain accurate values of ground and excited state polarizabilities $\alpha$, and ground state hyperpolarizabilities $\beta$ and $\gamma$. Excited state properties are addressed without explicit optimization of the state in question but instead by computing a double residue of the cubic response function. We have in some cases considered both the electronic and the vibrational contributions to these properties. Another direction that has been pursued is to, at the random phase approximation (RPA) level, extend the range of applications for large-scale systems by means of direct atomic orbital driven routines in a parallel scheme. In this context, we address structure-to-property relations for two-dimensional hydrocarbon oligomers, and electron-delocalization of fullerenes. With small we mean molecules with up to 15 atoms and with large-scale we mean molecules with up to 150 atoms.
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