A multiscale approach to liquid crystal nematics via statistical field theory

We propose an approach to a multiscale problem in the theory of thermotropic uniaxial nematics based on the method of statistical field theory. This approach enables us to relate the coefficients $A$, $B$, $C$, $L_1$ and $L_2$ of the Landau-de Gennes free energy for the isotropic-nematic phase transition to the parameters of a molecular model of uniaxial nematics, which we take to be a lattice gas model of nematogenic molecules interacting via a short-ranged potential. We obtain general constraints on the temperature and volume fraction of nematogens for the Landau-de Gennes theory to be stable against molecular orientation fluctuations at quartic order. In particular, for the case of a fully occupied lattice, we compute the values of the isotropic-nematic transition temperature and the order parameter discontinuity predicted by (i) a continuum approximation of the nearest-neighbor Lebwohl-Lasher model and (ii) a Lebwohl-Lasher-type model with a nematogenic interaction of finite range. We find that the predictions of (i) are in reasonably good agreement with known results of MC simulation.Comment: 12 pages, 2 figure

Van der Waals torque and force between anisotropic topological insulator slabs

We investigate the character of the van der Waals (vdW) torque and force between two coplanar and dielectrically anisotropic topological insulator (TI) slabs separated by a vacuum gap in the non-retardation regime, where the optic axes of the slabs are each perpendicular to the normal direction to the slab-gap interface and also generally differently oriented from each other. We find that in addition to the magnetoelectric coupling strength, the anisotropy can also influence the sign of the vdW force, viz., a repulsive vdW force can become attractive if the anistropy is increased sufficiently. In addition, the vdW force oscillates as a function of the angular difference between the optic axes of the TI slabs, being most repulsive/least attractive (least repulsive/most attractive) for angular differences that are integer (half-integer) multiples of $\pi$. Our third finding is that the vdW torque for TI slabs is generally weaker than that for ordinary dielectric slabs. Our work provides the first instance in which the vector potential appears in a calculation of the vdW interaction for which the limit is non-retarded or static.Comment: 10 pages, 4 figure

Two Essays on International Capital Flows and Cross-Listings

This dissertation explores two interesting issues: international capital flows and cross-listings. With high volatility of capital flows and imbalance of capital flows between emerging and advanced economies, the topic of capital flow management is always attractive to researchers and policy makers. The first essay explore how capital flows in G20 countries are significantly impacted by pull and push factors. The results show that international capital flows are significantly associated with domestic financial development, which is measured by stock market liquidity and domestic credit. Moreover, international capital flows are affected by some push factors such as, the growth of world economy and fluctuations of crude oil price. Finally, this study controls for real interest rate, foreign currency, and capital restriction because government and macroprudential policies are key to stabilizing capital flows. The second essay addresses two research questions: 1) how cross-listing activities are associated with domestic financial development, and 2) why do firms choose different types of DRs? The first section shows a threshold effect of financial development on country’s demands for DRs. When financial development is at a much lower stage, some countries have no explicit demands for cross-listing; when local stock markets become well-developed, most countries have great demands for cross-listings; however, after local stock market develop at very strong level, domestic financial development has less influence on demands of cross-listings.The second section shows difference in abnormal returns of domestic shares because of different choices of DRs. In the event study, the results show that developed countries earn positive abnormal returns around the ADR and GDR listing, but developing countries earn negative abnormal returns around GDR listing. Level I and unsponsored DRs bring positive abnormal returns to domestic shares, but Level II&III DRs come with some negative abnormal returns. And then, it explains that how choices of DRs are affected by domestic financial development, and it also controls for domestic disclosure index, political stability, cultural distance, and firm characteristics. Countries with lower financial development, worse disclosure requirements, political instability, and cultural similarity, are more likely to issue GDRs, Level II&III DRs, and sponsored DRs, which is consistent with the bonding and proximity hypotheses

Statistical physics of isotropic-genesis nematic elastomers: I. Structure and correlations at high temperatures

Isotropic-genesis nematic elastomers (IGNEs) are liquid crystalline polymers (LCPs) that have been randomly, permanently cross-linked in the high-temperature state so as to form an equilibrium random solid. Thus, instead of being free to diffuse throughout the entire volume, as they would be in the liquid state, the constituent LCPs in an IGNE are mobile only over a finite length-scale controlled by the density of cross-links. We address the effects that such network-induced localization have on the liquid-crystalline characteristics of an IGNE, as probed via measurements made at high temperatures. In contrast with the case of uncross-linked LCPs, for IGNEs these characteristics are determined not only by thermal fluctuations but also by the quenched disorder associated with the cross-link constraints. To study IGNEs, we consider a microscopic model of dimer nematogens in which the dimers interact via orientation-dependent excluded volume forces. The dimers are, furthermore, randomly, permanently cross-linked via short Hookean springs, the statistics of which we model by means of a Deam-Edwards type of distribution. We show that at length-scales larger than the size of the nematogens this approach leads to a recently proposed phenomenological Landau theory of IGNEs [Lu et al., Phys. Rev. Lett. 108, 257803 (2012)], and hence predicts a regime of short-ranged oscillatory spatial correlations in the nematic alignment, of both thermal and glassy types. In addition, we consider two alternative microscopic models of IGNEs: (i) a wormlike chain model of IGNEs that are formed via the cross-linking of side-chain LCPs; and (ii) a jointed chain model of IGNEs that are formed via the cross-linking of main-chain LCPs. At large length-scales, both of these models give rise to liquid-crystalline characteristics that are qualitatively in line with those predicted by the dimer-and-springs model.Comment: 33 pages, 6 figures, 6 appendice