Abstract:
The proximity effect is a central feature of superconducting junctions as it underlies many important applications in devices and can be exploited in the design of new systems with novel quantum functionality. Recently, exotic proximity effects have been observed in various systems, such as superconductor-metallic nanowires and graphene-superconductor structures. However, it is still not clear how superconducting order propagates spatially in a heterogeneous superconductor system. Here we report intriguing influences of junction geometry on the proximity effect for a 2D heterogeneous superconductor system comprised of 2D superconducting islands on top of a surface metal. Depending on the local geometry, the superconducting gap induced in the surface metal region can either be confined to the boundary of the superconductor, in which the gap decays within a short distance (~ 15 nm), or can be observed nearly uniformly over a distance of many coherence lengths due to non-local proximity effects.

Abstract:
We systematically address superconductivity of Pb nano-islands with different thicknesses and lateral sizes via a scanning tunneling microscopy/spectroscopy. Reduction of the superconducting gap is observed even when the island is larger than the bulk coherence length and becomes very fast below ~ 50 nm lateral size. The suppression of gap with size depends to a good approximation only on the volume of the island and is independent of its shape. Theoretical analysis indicates that the universal quenching behavior is primarily manifested by the mean number of electronic orbitals within the pairing energy window.

Abstract:
A three-dimensional (3D) topological insulator (TI) is a quantum state of matter with a gapped insulating bulk yet a conducting surface hosting topologically-protected gapless surface states. One of the most distinct electronic transport signatures predicted for such topological surface states (TSS) is a well-defined half-integer quantum Hall effect (QHE) in a magnetic field, where the surface Hall conductivities become quantized in units of (1/2)e2/h (e being the electron charge, h the Planck constant) concomitant with vanishing resistance. Here, we observe well-developed QHE arising from TSS in an intrinsic TI of BiSbTeSe2. Our samples exhibit surface dominated conduction even close to room temperature, while the bulk conduction is negligible. At low temperatures and high magnetic fields perpendicular to the top and bottom surfaces, we observe well-developed integer quantized Hall plateaus, where the two parallel surfaces each contributing a half integer e2/h quantized Hall (QH) conductance, accompanied by vanishing longitudinal resistance. When the bottom surface is gated to match the top surface in carrier density, only odd integer QH plateaus are observed, representing a half-integer QHE of two degenerate Dirac gases. This system provides an excellent platform to pursue a plethora of exotic physics and novel device applications predicted for TIs, ranging from magnetic monopoles and Majorana particles to dissipationless electronics and fault-tolerant quantum computers.

Abstract:
The electron density dependence of the electron spin relaxation time in a system of electrons interacting with phonons through phonon-modulated spin-orbit coupling was calculated using the formula for electron spin resonance derived by the projection-reduction method. The electron spin relaxation time in GaAs increased with increasing electron density, and the electron density was found to affect the electron spin relaxation differently according to temperature. The electron spin in GaAs was relaxed mainly by optical phonon scattering at high electron densities and piezoelectric phonon scattering at relatively low electron densities.

Abstract:
The world population has been increasing while, similarly, both the number of environmental disasters and the loss resulting from those have been on the rise. It is also expected that the trend will continue. Especially, what is noticeable is that more and more people and property concentrate on cities. In fact, urbanization is a major global trend simply because most people want to get their jobs, raise and educate their children, and enjoy riches of diverse cultures, recreation activities, and entertainment, which cities can provide to them. Urbanization always involves transforming the natural environment into a man-made environment, contributing to changes in land use and land cover patterns as well as in landscape and hydrology in the built-up areas. These changes, in turn, negatively influence the natural environment because those changes almost always tend to result in the disruption of its fragile ecosystems in balance. In addition, the changes mean the land used, for example, for a natural ecosystem may be converted into an impervious land, which can increase human vulnerability to floods, causing human and property losses. There has been some research done to investigate the relationship between land use/land cover change and environmental hazards. However, little research has been conducted to test direct effects of land cover change on environmental disasters such as floods, hurricanes, and hazardous material releases by using GIS and remote sensing technologies. Therefore, this research aimed to analyze the effect of land cover change on floods. More specifically, the research tested whether land cover change is related to flood disasters in Texas from 1993 to 2012. One of the main findings of this research is that both decrease in forest areas and increase in urban built-up areas contributed to the property damage resulting from flood events.

Abstract:
The assessment of potential health risks posed by formaldehyde in clothing to consumers is of increasing concern worldwide. Because of this, it is necessary to develop an exposure model that can realistically mimic clothes wearing conditions. This study aims to preliminarily develop a health risk assessment model for formaldehyde in clothing, and then to assess the potential health risk posed by formaldehyde in textiles to adults and infants in Vietnam using the model. Finally, this study aims to examine the plausibility of the adopted permissible values for formaldehyde in cloth- ing in Vietnam. In the model, two exposure factors for dermal exposure and overall exposure routes, i.e. sweat type and perspiration area, were considered. The margins of exposure (MOE) were calculated to estimate the health risks from worst case and average exposures. The assessment shows that acute exposure via inhalation can pose health risks to Vietnamese consumers in both cases. In regards to chronic exposure, dermal exposure is about four (for infants) and seven (for adults) times higher than exposure via inhalation, but no risks were found for average exposure. If a MOE of 100 is defined as ‘safe’ used, dermal and total chronic exposure to worst case cause potential risks, whereas no health risks were found for exposure to average case. With the model, the adopted Vietnamese permissible values for
formaldehyde in clothing were assessed as not posing a health risk to Vietnamese consumers, hence they are accepted.

Abstract:
For independent random variables, the order of growth of the convergent series Sn is studied in this paper. More specifically, if the series Sn converges almost surely to a random variable, the tail series is a well-defined sequence of random variables and converges to 0 almost surely. For the almost surely convergent series Sn, a tail series strong law of large numbers (SLLN) is constructed by investigating the duality between the limiting behavior of partial sums and that of tail series.

Abstract:
We consider the close relation between duality in N=2 SUSY gauge theories and integrable models. Various integrable models ranging from Toda lattices, Calogero models, spinning tops, and spin chains are related to the quantum moduli space of vacua of N=2 SUSY gauge theories. In particular, SU(3) gauge theories with two flavors of massless quarks in the fundamental representation can be related to the spectral curve of the Goryachev-Chaplygin top, which is a Nahm's equation in disguise. This can be generalized to the cases with massive quarks, and N_f = 0,1,2, where a system with seven dimensional phase space has the relevant hyperelliptic curve appear in the Painlev\'e test. To understand the stringy origin of the integrability of these theories we obtain exact nonperturbative point particle limit of type II string compactified on a Calabi-Yau manifold, which gives the hyperelliptic curve of SU(2) QCD with N_f=1 hypermultiplet.

Abstract:
There is a close relation between duality in $N=2$ SUSY gauge theories and integrable models. In particular, the quantum moduli space of vacua of $N=2$ SUSY $SU(3)$ gauge theories coupled to two flavors of massless quarks in the fundamental representation can be related to the spectral curve of the Goryachev-Chaplygin top. Generalizing this to the cases with {\it massive} quarks, and $N_f = 0,1,2$, we find a corresponding integrable system in seven dimensional phase space where a hyperelliptic curve appears in the Painlev\'e test. To understand the stringy origin of the integrability of these theories we obtain exact nonperturbative point particle limit of type II string compactified on a Calabi-Yau manifold, which gives the hyperelliptic curve of $SU(2)$ QCD with $N_f =1$ hypermultiplet.

Abstract:
We compute the one loop Casimir energy of an interacting scalar field in a compact noncommutative space of $R^{1,d}\times T^2_\theta$, where we have ordinary flat $1+d$ dimensional Minkowski space and two dimensional noncommuative torus. We find that next order correction due to the noncommutativity still contributes an attractive force and thus will have a quantum instability. However, the case of vector field in a periodic boundary condition gives repulsive force for $d>5$ and we expect a stabilized radius. This suggests a stabilization mechanism for a senario in Kaluza-Klein theory, where some of the extra dimensions are noncommutative.