Stochastic Porous Media Equation on General Measure Spaces with Increasing Lipschitz Nonlinearties

We prove the existence and uniqueness of probabilistically strong solutions to stochastic porous media equations driven by time-dependent multiplicative noise on a general measure space $(E, \mathscr{B}(E), \mu)$, and the Laplacian replaced by a self-adjoint operator $L$. In the case of Lipschitz nonlinearities $\Psi$, we in particular generalize previous results for open $E\subset \mathbb{R}^d$ and $L\!\!=$Laplacian to fractional Laplacians. We also generalize known results on general measure spaces, where we succeeded in dropping the transience assumption on $L$, in extending the set of allowed initial data and in avoiding the restriction to superlinear behavior of $\Psi$ at infinity for $L^2(\mu)$-initial data.Comment: 18page

Design and performance of cost-effective ultra-high performance concrete for prefabricated elements

This study presented in this thesis aims to: (1) develop a mixture design methodology for cost-effective ultra-high-performance concrete (UHPC) incorporating high volume of supplementary cementitious materials and conventional concrete and masonry sands; (2) developed UHPC with adapted rheology incorporating lightweight sand, hybrid fibers, and nanomaterials with improved properties; (3) design prefabricated UHPC panels with fiber-reinforced polymers (FRP) for enhanced flexural properties of stay-in-place panels made with optimized UHPC; and (4) explore potential applications of such UHPC elements. The proposed design methodology produced UHPC mixtures with 28-days compressive strengths higher than 125 and 168 MPa under standard water curing and 1-d steam curing at 90 ⁰C. To further improve the properties, internal curing using pre-saturated lightweight sand, rheology control of the suspending mortar before steel fibers addition, and reinforcement of hybrid fibers and carbon nanomaterials, were employed. The outcome indicated: (a) the optimum replacement ratio of lightweight sand to river sand in the UHPC was 25% to increase mechanical properties and reduce shrinkage; (b) at steel fiber content of 2%, the optimal plastic viscosity of the suspending mortar was 53 ± 3 Pa·s to secure favorable fiber distribution and enhance flexural properties of the UHPC; (c) through use of hybrid steel fibers, the flexural strength, tensile strength, and autogenous shrinkage of UHPC can increase by up to 20%, 25%, and reduced by 40%, respectively; (d) adding nanomaterials at a volume fraction of 0.3% increased the tensile strength and energy absorption capacity of the UHPC by 55% and 185%, respectively. In the end, novel applications of the developed reinforced and non-reinforced UHPC-FRP systems were explored for various applications --Abstract, page iii

Prospects of Observing the Decay B_c -> J/psi + pi and the Alignment Performance in the ATLAS Experiment

This thesis contains two main aspects of my research work towards physics in proton-proton collisions in the ATLAS experiment at the LHC. First, a Monte Carlo based analysis of the event yield and the mass shape for the ground state of the B_c meson in the hadronic decay channel B_c -> J/psi + pi was studied. The selection criteria have been optimised, the total number of signal events, and the significance of the observation have been estimated for the detector configuration and backgrounds expected at the centre-of-mass energy of 10 TeV with 1 fb^{-1} of integrated luminosity. As the momenta of these decay products are relatively low, compared with the main objectives of the ATLAS physics program, the performance of the inner detector is crucial for the low p_T tracking. As a result, the second part of the thesis is focused on the impact of the inner detector alignment on physics. Monte Carlo studies were performed by looking at the reconstructions of the well-known resonances, K_s^0, J/psi, Upsilon and Z^0 in misalignments, particularly the systematic misalignments. Then the performance of two different alignments that have been applied subsequently in ATLAS since the start up of the LHC were investigated using K_s^0 -> pi^+ pi^- events in the current 7 TeV collisions. Finally, I summarise the performance of the inner detector on the early J/psi -> µ^+ µ^- reconstruction in collisions, which is essential for the coming B physics measurements

The economic impact of credit default swap on credit markets

This study conducts a comprehensive analysis of the economic benefits and costs of credit default swap (CDS) in credit markets since its inception. Consistent with its role of insuring credit risk, the introduction of CDS reduces illiquidity and liquidity risk more for speculative grade bonds with high credit risk than investment grade ones. More importantly, CDS significantly improves the price convergence between investment grade bonds and CDS spreads through a popular trading strategy—CDS-bond basis arbitrage in normal period. In the recent crisis, however, CDS fails to reduce the prolonged price divergence between the two markets plausibly due to the lack of arbitrage. Overall, the economic impact of CDS is dependent on the prevailing trading strategies in the credit markets