DISCONTINUOUS GALERKIN METHODS FOR COMPRESSIBLE MISCIBLE DISPLACEMENTS AND APPLICATIONS IN RESERVOIR SIMULATION

This dissertation contains research on discontinuous Galerkin (DG) methods applied to the system of compressible miscible displacements, which is widely adopted to model surfactant flooding in enhanced oil recovery (EOR) techniques. In most scenarios, DG methods can effectively simulate problems in miscible displacements.However, if the problem setting is complex, the oscillations in the numerical results can be detrimental, with severe overshoots leading to nonphysical numerical approximations. The first way to address this issue is to apply the bound-preservingtechnique. Therefore, we adopt a bound-preserving Discontinuous Galerkin methodwith a Second-order Implicit Pressure Explicit Concentration (SIPEC) time marchingmethod to compute the system of two-component compressible miscible displacement in our first work. The Implicit Pressure Explicit Concentration (IMPEC) method is one of the most prevalent time marching approaches used in reservoir simulation for solving coupled flow systems in porous media. The main idea of IMPEC is to treat the pressure equation implicitly and the concentration equations explicitly. However, this treatment results in a first-order accurate scheme. To improve the order of accuracy of the scheme, we propose a correction stage to compensate for the second-order accuracy in each time step, thus naming it the SIPEC method. The SIPEC method is a crucial innovation based on the traditional second-order strong-stability-preserving Runge-Kutta (SSP-RK2) method. However, the SIPEC method is limited to second-order accuracy and cannot efficiently simulate viscous fingering phenomena. High-order numerical methods are preferred to reduce numerical artifacts and mesh dependence. In our second work, we adopt the IMPEC method based on the implicit-explicit Runge-Kutta (IMEX-RK) Butcher tableau to achieve higher order temporal accuracy while also ensuring stability. The high-order discontinuous Galerkin method is employed to simulate the viscous fingering fluid instabilities in a coupled nonlinear system of compressible miscible displacements. Although the bound-preserving techniques can effectively yield physically relevant numerical approximations, their success depends heavily on theoretical analysis, which is not straightforward for high-order methods. Therefore, we introduce an oscillation-free damping term to effectively suppress the spurious oscillations near discontinuities in high-order DG methods. As indicated by the numerical experiments, the incorporation of the bound-preserving DG method with SIPEC time marching and high-order OFDG with IMPEC time marching provides satisfactory results for simulating fluid flow in reservoirs

Three essays on monetary policy in the UK

The dissertation studies monetary policy in the UK and specifically three topics: the monetary policy reaction function of the Bank of England, the influence of QE on nominal income and the determination of inflation and the role of money in it. In the study of the reaction function of the Bank of England in chapter 2 (which draws on Cobham and Kang, 2012a), there are two issues involved a comparison of two different approaches: the GMM approach and the ex ante forecast approach. The first issue is the time horizons for inflation and the output gap. The estimations using the GMM method indicate that the best fit is for inflation one year ahead and for the output gap one quarter ahead. The estimations in the ex ante forecast approach indicate the best fit should be for inflation two years ahead and output growth one quarter ahead, which is closer to the Bank of England’s view. The second issue is about the smoothing behaviour in interest rate decisions. The GMM method suggests smoothing behaviour incorporated in a lagged dependent variable while the ex ante forecast method suggests no smoothing since the lagged change of the interest rate is not significant in the regression. The latter suggestion is also closer to former policy makers’ views. In addition, the GMM method may suffer from a weak instruments problem and the ex ante forecast approach is a better method to estimate the monetary policy reaction function. I also try to apply the ex ante forecast approach to the reaction function of the European Central Bank, with results which are less precise but still closer to what the ECB claims to do. The third and the fourth chapters address the monetary aggregates, which have been ignored in monetary policy research for a long time but fluctuated strongly during the financial crisis period and after QE was implemented. What’s more, while most work in recent years focuses on the fluctuations in financial markets, the dissertation discusses the influence of the crisis and QE on macroeconomic activity. In chapter 3 (which draws on Cobham and Kang, 2012b), a flow of funds matrix is used to illustrate the monetary developments. This is followed by regressions of a naïve ad hoc reduced form model which considers the growth of nominal spending as determined by the growth of nominal money and other variables. The results of the regression suggest that money has had a bigger role since the crisis and under QE. Then various counterfactual assumptions about money growth are made and the counterfactual paths of nominal spending are calculated by using the estimated parameters of the regression above. The comparison of those counterfactuals indicates that QE has had a considerable influence on nominal spending. In the fourth chapter, money growth is studied in a long-run perspective, in terms of its relation with inflation. In a reduced-form Phillips curve, inflation is explained by variables at different frequencies. The money growth, GDP growth and interest rate change which are included in the Quantity Theory of Money are expected to link inflation at low frequency while the output gap as well as exchange rate and import price has a relation with inflation at high frequency. The frequency-domain technique is used in this process. The estimated results suggest money has a relationship with inflation only at low frequency while the output gap, on the other hand, relates inflation at high frequency. Then regressions on low frequency and high frequency are also run. Frequency-wise causality measures follow to support the indications. From the results given by the third and fourth chapters, it is suggested that it is the time to pay attention to money again in monetary policy research. And it would be useful to incorporate money or credit into wider macroeconometric models of the UK economy

LHC τ\tau-rich Tests of Lepton-specific 2HDM for (g−2)μ(g-2)_\mu

The lepton-sepcific (or type X) 2HDM (L2HDM) is an attractive new physics candidate explaining the muon $g-2$ anomaly requiring a light CP-odd boson $A$ and large $\tan\beta$. This scenario leads to $\tau$-rich signatures, such as $3\tau$, $4\tau$ and $4\tau+W/Z$, which can be readily accessible at the LHC. We first study the whole L2HDM parameter space to identify allowed regions of extra Higgs boson masses as well as two couplings $\lambda_{hAA}$ and $\xi_h^l$ which determine the 125 GeV Higgs boson decays $h\to \tau^+\tau^-$ and $h\to AA/AA^*(\tau^+\tau^-)$, respectively. This motivates us to set up two regions of interest: (A) $m_A \ll m_{H} \sim m_{H^\pm}$, and (B) m_A \sim m_{H^\pm} \sim {\cal O}(100) \mbox{GeV} \ll m_H, for which derive the current constraints by adopting the chargino-neutralino search at the LHC8, and then analyze the LHC14 prospects by implementing $\tau$-tagging algorithm. A correlated study of the upcoming precision determination of the 125 GeV Higgs boson decay properties as well as the observation of multi-tau events at the next runs of LHC will be able to shed light on the L2HDM option for the muon $g-2$.Comment: 21 pages, 9 figure

Angiogenesis and Vasculogenesis at 7-Day of Reperfused Acute Myocardial Infarction

Objectives 
This study is to investigate the angiogenesis and vasculogenesis at the first week of reperfused acute myocardial infarction (AMI).
Methods 
16 of mini-swines (20 to 30 Kg) were randomly assigned to the sham-operated group and the AMI group. The acute myocardial infarction and reperfusion model was created and the pig tail catheter was performed to monitor hemodynamics before left anterior descending coronary artery (LAD) occlusion, 90 min of LAD occlusion and 120 min of LAD reperfusion. Pathologic myocardial tissue was collected at 7-day of LAD reperfusion and further assessed by immunochemistry, dual immunochemistry, in-situ hybridization, real-time quantitative polymerase chain reaction and western blot. 
Results 
The infarcted area had higher FLK1 mRNA expression than sham-operated area and the normal area (all P<0.05), and the infarcted and marginal areas showed higher CD146 protein expression than the sham-operated area (all P<0.05), but the microvessel density (CD31 positive expression of microvessels/HP) was not significantly different between the infarcted area and the sham-operated area (8.92±3.05 vs 6.43±1.54) at 7-day of reperfused acute myocardial infarction (P>0.05). 
Conclusions 
FLK1 and CD146 expression significantly increase in the infarcted and marginal areas, and the microvessel density is not significantly different between the infarcted area and the sham-operated area, suggesting that angiogenesis and vasculogenesis in the infarcted area appear to high frequency of increase in 7-day of reperfused myocardial infarction. 
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