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We have applied a fluids density functional theory based on that of Yu and Wu [J. Chem. Phys. 116, 7094 (2002)] to treat reversible supramolecular polymers near a hard surface. This approach combines a hard-sphere fluids density functional theory with the first-order thermodynamic perturbation theory of Wertheim. The supramolecular polymers are represented in the theory by hard-spheres with two associating sites. We explore the effects of the bonding scheme, monomer concentration, and association energy upon the equilibrium chain sizes and the depletion lengths. This study is performed on simple systems containing two-site monomers and binary mixtures of two-site monomers combined with end stopper monomers which have only a single association site. Our model has correct behavior in the dilute and overlap regimes and the bulk results can be easily connected to simpler random-flight models. We find that there is a nonmonotonic behavior of the depletion length of the polymers as a function of concentration and that this depletion length can be controlled through the concentration of end stoppers. These results are applicable to the study of colloidal dispersions in supramolecular polymer solutions.

To keep up with the growing demand for oil and gas, the oil and gas industry ventures into deeper waters. For a deep water pipeline project, South Stream, a pipeline test program is developed. Part of this program is the investigation of the resistance of an externally pressurised pipeline against local buckling collapse. This is a decisive factor in design of marine pipelines. Local buckling of a pipeline is the buckling behaviour within its cross section. Buckling is defined as the state of a structure for which a relatively small increment in load leads to a relatively large increment in displacement. Generally this is reflected in a change in deformation shape and possibly a loss of stability. A perturbation theory, first developed by Koiter [1], is applied to model this behaviour. The response of a geometrically imperfect structure is obtained by using the response of an initially perfect structure, e.g. a straight beam or a perfect ring. From the principle of minimum potential energy an equilibrium state can be obtained. For a certain load, the bifurcation load, multiple equilibrium configurations are possible. The nature of this equilibrium state is investigated by expanding the load around this bifurcation load and expanding the displacement functions around their fundamental solutions. The value and sign of the post-bifurcation load coefficients determine the system’s initial post-bifurcation stability. Introduction of initial imperfections leads to modified post-bifurcation load coefficients. Generality is enhanced by using dimensionless identities. System collapse can occur in the elastic domain for unstable initial post-buckling behaviour or in the plastic domain due to material yielding. It is likely that collapse of a system with (small) initial geometric imperfections occurs due to an interaction of elastic and plastic buckling. Buckling leads to relatively large displacements that induce material yielding. This can lead to loss of stiffness and can induce collapse. Relatively thin walled rings and cylinders tend to collapse more in the elastic domain, while relatively thick walled rings and cylinders tend to collapse more in the plastic domain. This is due to the fact that thin walled structures require more deformation to induce yielding than thick walled structures. When performing a collapse test, end caps are attached to a pipeline specimen. This is modelled by boundary constraints. End caps are very stiff and modelled as being rigid. Their influence on the bifurcation and collapse behaviour of a cylinder is investigated. The constraints introduce boundary layer behaviour in the regions close the end caps. It is found that these constraints increase the buckling load of a cylinder with respect to an infinitely long cylinder (ring under plane strain condition). Besides, for relatively short cylinders, the buckling mode is altered. While a long cylinder prefers to collapse in an oval shape mode (described by 2 lobes), a short cylinder prefers to collapse in a mode shape described by a higher number of lobes. A collapse test is performed to estimate the collapse behaviour of a real life pipeline. Hence it is required that the collapse shape that is observed in the test matches the oval collapse shape of a long real life pipeline. This results to a minimum required length of a tested pipeline specimen. A relation for the required length is obtained. An analytical method has been developed to determine the buckling load and mode of a constrained cylinder. Finally, the analytically obtained results have been verified using finite element analysis (FEA) and experimental results obtained from literature. [1] W.T. Koiter. Over de stabiliteit van het elastisch evenwicht. PhD Thesis, TH Delft, 1945

This research concerns the fuel cycle and safety aspects of a Gas Cooled Fast Reactor, one of the so-called "Generation IV" nuclear reactor designs. The Generation IV Gas Cooled Fast Reactor uses helium as coolant at high temperature. The goal of the GCFR is to obtain a "closed nuclear fuel cycle", where only natural uranium is used as raw material, and only fission products are discharged to a repository. Uranium and heavier isotopes (plutonium, americium, etc) are recycled in the reactor and are eventually fissioned. Since the heavy isotopes determine the long-term radiotoxicity of the nuclear waste, application of a closed fuel cycle maximizes the energy output of the fuel material, and can significantly reduce the lifetime of nuclear waste. It is shown that it is possible to obtain a closed fuel cycle with the GCFR. Coated particle fuel and ceramic plate fuel are discussed as fuel candidates for GCFR. A theoretical framework is derived using a combination of eigenvalue perturbation theory and nuclide perturbation theory to estimate the Breeding Gain of the reactor, and the change of Breeding Gain due to changes of the initial fuel composition. It is shown that the GCFR has some potential as an actinide transmutation reactor. To increase the safety of the GCFR, passive elements have been designed to automatically shut down the reactor in case of incidents. These elements use liquid Li-6, which is introduced into special assemblies if necessary. It has been shown that with these elements the reactor can withstand transients without damage to the fuel. The research has been performed in a European framework.

This thesis discusses the use of perturbation theory in the context of financial mathematics, in particular on the use of matched asymptotic expansions in option pricing. Our methods are applied to the ordinary Black-Scholes model for illustration. In this simple example of the Black-Scholes model an exact solution is available, so it is in fact not neccessary to apply the method of asymptotic expansions on this model. However, in case we do apply the method, two artificial layers have to be constructed. Making smart choices for the local variables leads to a transformation of the equations into a heat equation, which can easily be solved. Finally, the results are compared to a Taylor expansion of the exact solution to see that this method is very accurate. After this first instructive model, the method of matched asymptotic expansions is applied to two more advanced models based on papers by Sam Howison and Patrick Hagan et al.. Here, different choices for the scalings are made. The former discusses a fast mean-reverting stochastic volatility model that turns out to have many open ends. In Howison's paper quite a lot of assumptions and simplifications are made. Unfortunately, often the motivation for them is not explicitly given in the paper, and in some cases we even think these assumptions and simplifications are incorrect. The latter examines a new three-parameter stochastic volatility model that successfully prices back the volatility smile as observed in the market nowadays, and that is commonly used. The derivation of this model is the main focus of this thesis. The resulting expression for the implied volatility under the SABR model is obtained by considering the forward and backward Kol-mogorov equations per order in epsilon, making some smart choices for local variables and functions in order to transform them into an equation that looks like a heat equation, which is easier to solve. Recommendations for further investigation on these models would be to consider several different choices for the scalings and see which one works best.

A Helmholtz energy functional for inhomogeneous fluid phases based on the perturbed-chain polar statistical associating fluid theory (PCP-SAFT) equation of state is proposed. The model is supplemented with a capillary wave contribution to the surface tension to account for long-wavelength fluctuations of a vapor-liquid interface. The functional for the dispersive attraction is based on a nonlocal perturbation theory for chain fluids and the difference of the perturbation theory to the dispersion term of the PCP-SAFT equation of state is treated with a local density approximation. This approach suggested by Gloor et al. [Fluid Phase Equilib. 194, 521 (2002)] leads to full compatibility with the PCP-SAFT equation of state. Several levels of approximation are compared for the nonlocal functional of the dispersive attractions. A first-order non-mean-field description is found to be superior to a mean-field treatment, whereas the inclusion of a second-order perturbation term does not contribute significantly to the results. The proposed functional gives excellent results for the surface tension of nonpolar or only moderately polar fluids, such as alkanes, aromatic substances, ethers, and ethanoates. A local density approximation for the polar interactions is sufficient for carbon dioxide as a strongly quadrupolar compound. The surface tension of acetone, as an archetype dipolar fluid, is overestimated, suggesting that a nonisotropic orientational distribution function across an interface should for strong dipolar substances be accounted for.