On Two Kinds of Differential Operators on General Smooth Surfaces

Two kinds of differential operators that can be generally defined on an arbitrary smooth surface in a finite dimensional Euclid space are studied, one is termed as surface gradient and the other one as Levi-Civita gradient. The surface gradient operator is originated from the differentiability of a tensor field defined on the surface. Some integral and differential identities have been theoretically studied that play the important role in the studies on continuous mediums whose geometrical configurations can be taken as surfaces and on interactions between fluids and deformable boundaries. The definition of Levi-Civita gradient is based on Levi-Civita connections generally defined on Riemann manifolds. It can be used to set up some differential identities in the intrinsic/coordiantes-independent form that play the essential role in the theory of vorticity dynamics for two dimensional flows on general fixed smooth surfaces

Interaction induced topological phase transition in Bernevig-Hughes-Zhang model

We study interaction induced topological phase transition in Bernevig-Hughes-Zhang model. Topological nature of the phase transition is revealed by directly calculating the Z2 index of the interacting system from the single-particle Green's function. The interacting Z2 index is also consistently checked through the edge spectra. Combined with ab initio methods, present approach is a useful tool searching for correlated topological insulating materials from the first-principle point of view.Comment: 4.5 pages, 4 figures, reference adde

Migration and Electropolymerization of Methyl Methacrylate in Hardened Cement Paste via Electrokinetic Treatment

Porous concrete structures are susceptible to the intrusion of chemical species, such as sulfates, chlorides, and carbon dioxide. Many technologies have been developed to repair or rehabilitate damaged concrete. These include cathodic protection, corrosion inhibitor addition, or the use of coatings and sealers. In recent years, a developing technology, electrokinetic nanoparticle treatment, has been shown to reduce concrete porosity, increase strength, promote corrosion resistance, and extend durability. This dissertation was conducted to explore a novel treatment to reduce the porosity of concrete via the application of electrokinetic transportation and electro-initiated polymerization of methyl methacrylate (MMA). Potassium persulfate (PSP) was used to help initiate polymerization of MMA electrochemically at the cathode. This was first attempted in beaker tests (involving just MMA and deionized water). FTIR-ATR analysis indicated that solid deposits obtained from the beaker tests were PMMA. Without the PSP in the beaker tests, no deposit was obtained. With the addition of PSP, the electrochemical treatment conducted on hardened cement paste (HCP) specimens yielded a yellowish, odorless, oil-like liquid. This liquid was extracted by acetone solvent exchange. FTIR-ATR analysis indicated that the liquid was likely to be the copolymer of MMA and methacrylic acid (MAA). An O-H bond was detected during the FTIR-ATR analysis indicating that the polymerization of MMA or MAA was initiated predominantly by OH radicals instead of sulfate radicals. Hydroxide ions are common in the caustic environment within HCP. The sulfate radicals could have reacted with hydroxide ions to produce sulfate ions and OH radicals. Without the addition of PSP, a similar organic liquid was also extracted from the MMA-treated HCP samples. FTIR-ATR analysis of the liquid indicated that it was likely to be an MMA/MAA copolymer. A strong O-H stretch was observed on the ATR spectrum of the liquid. This indicate that OH radicals may have initiated the polymerization of MMA/MAA. The corrosion potentials and current densities used in these treatments appeared to significantly influence the polymerization of MMA/MAA. A very limited amount of the liquid was extractable from the MMA-treated HCP in the low-voltage trials (+0.49 V vs. the Cu/CuSO4 reference electrode (CSE)). This was because the low voltages caused the reduction of hydroxide ions at the anode to decrease and the formation of OH radicals to drop as well. Apparently, a solid phase of PMMA did not form in the pores of HCP regardless of whether or not PSP was used. This may be attributed to the high-pH environment in HCP which could have caused the MMA or PMMA to hydrolyze and produce either MAA or a MAA/MMA copolymer. The lack of solids in the pores of MMA-treated HCP specimens resulted in no significant increase in strength or reduction in porosity. Future work is needed to investigate the impact of stabilizing inhibitors that are typically packed into industrial shipments of MMA monomer. Additionally, future work needs to examine the impact of lowering the pH of the treatment solution in order to facilitate a hydrolysisfree environment for reducing hydrolysis of MMA and PMMA. This could encourage the production of solid phase reactants that may enhance strength and durability