Compactification of moduli spaces and mirror symmetry

textOlsson gives modular compactifications of the moduli of toric pairs and the moduli of polarized abelian varieties A [subscript g,δ] in (Ols08). We give alternative constructions of these compactifications by using mirror symmetry. Our constructions are toroidal compactifications. The data needed for a toroidal compactification is a collection of fans. We obtain the collection of fans from the Mori fans of the minimal models of the mirror families. Moreover, we reinterpretate the compactification of A [subscript g,δ] in terms of KSBA stable pairs. We find that there is a canonical set of divisors S(K₂) associated with each cusp. Near the cusp, a polarized semiabelic scheme (X, G, L) is the canonical degeneration given by the compactification if and only if (X, G, Θ) is an object in A P [subscript g,d] for any Θ ∈ S(K₂). The two compactifications presented here are a part of a general program of applying mirror symmetry to the compactification problem of the moduli of Calabi–Yau manifolds. This thesis contains the results in (Zhu14b) and (Zhu14a).Mathematic

Light Controlling at Subwavelength Scales in Nanophotonic Systems: Physics and Applications

The capability of controlling light at scales that are much smaller than the operating wave-length enables new optical functionalities, and opens up a wide range of applications. Such a capability is out of the realm of conventional optical approaches. This dissertation aims to explore the light-matter interactions at nanometer scale, and to investigate the novel scien-tific and industrial applications. In particular, we will explain how to detect nanoparticles using an ultra-sensitive nano-sensor; we will also describe a photonic diode which gener-ates a unidirectional flow of single photons; Moreover, in an one-dimensional waveguide QED system where the fermionic degree of freedom is present, we will show that strong photon-photon interactions can be generated through scattering means, leading to photonic bunching and anti-bunching with various applications. Finally, we will introduce a mecha-nism to achieve super-resolution to discern fine features that are orders of magnitude smaller than the illuminating wavelength. These research projects incorporate recent advances in quantum nanophotonics, nanotechnologies, imaging reconstruction techniques, and rigorous numerical simulations

Graph Neural Network for Stress Predictions in Stiffened Panels Under Uniform Loading

Machine learning (ML) and deep learning (DL) techniques have gained significant attention as reduced order models (ROMs) to computationally expensive structural analysis methods, such as finite element analysis (FEA). Graph neural network (GNN) is a particular type of neural network which processes data that can be represented as graphs. This allows for efficient representation of complex geometries that can change during conceptual design of a structure or a product. In this study, we propose a novel graph embedding technique for efficient representation of 3D stiffened panels by considering separate plate domains as vertices. This approach is considered using Graph Sampling and Aggregation (GraphSAGE) to predict stress distributions in stiffened panels with varying geometries. A comparison between a finite-element-vertex graph representation is conducted to demonstrate the effectiveness of the proposed approach. A comprehensive parametric study is performed to examine the effect of structural geometry on the prediction performance. Our results demonstrate the immense potential of graph neural networks with the proposed graph embedding method as robust reduced-order models for 3D structures.Comment: 20 pages; 7 figure

Probing dynamics of dark energy with latest observations

We examine the validity of the $\Lambda$CDM model, and probe for the dynamics of dark energy using latest astronomical observations. Using the $Om(z)$ diagnosis, we find that different kinds of observational data are in tension within the $\Lambda$CDM framework. We then allow for dynamics of dark energy and investigate the constraint on dark energy parameters. We find that for two different kinds of parametrisations of the equation of state parameter $w$, a combination of current data mildly favours an evolving $w$, although the significance is not sufficient for it to be supported by the Bayesian evidence. A forecast of the DESI survey shows that the dynamics of dark energy could be detected at $7\sigma$ confidence level, and will be decisively supported by the Bayesian evidence, if the best fit model of $w$ derived from current data is the true model.Comment: 4.5 pages, 3 figures, 1 table; references adde

An Enhanced Technology Acceptance Model for Web-Based Learning

Although information technology (IT) has played an increasingly important role in contemporary education, resistance to IT remains significant in the education sector. This study attempts to identify additional key determinants of the IT acceptance in the education sector based on a study in which. 280 full-time teachers who were part-time students of a bachelor degree program participated. The current technology acceptance model (TAM) and the social cognitive theory (SCT) are combined to provide a new framework for this analysis. Results of the study are consistent with the TAM factors for explaining behavioral intention. The study also indicates that the computer self-efficacy (CSE) has substantial influence on the teachers\u27 technology acceptance. Implications of the resulting factors are discussed within the context of education

Using phase-change materials to switch the direction of reflectionless light propagation in non-PT-symmetric structures

We introduce a non-parity-time-symmetric three-layer structure, consisting of a gain medium layer sandwiched between two phase-change medium layers for switching of the direction of reflectionless light propagation. We show that for this structure unidirectional reflectionlessness in the forward direction can be switched to unidirectional reflectionlessness in the backward direction at the optical communication wavelength by switching the phase-change material Ge2Sb2Te5 (GST) from its amorphous to its crystalline phase. We also show that it is the existence of exceptional points for this structure with GST in both its amorphous and crystalline phases which leads to unidirectional reflectionless propagation in the forward direction for GST in its amorphous phase, and in the backward direction for GST in its crystalline phase. Our results could be potentially important for developing a new generation of compact active free-space optical devices. We also show that phase-change materials can be used to switch photonic nanostructures between cloaking and superscattering regimes at mid-infrared wavelengths. More specifically, we investigate the scattering properties of subwavelength three-layer cylindrical structures in which the material in the outer shell is the phase-change material GST. We first show that, when GST is switched between its amorphous and crystalline phases, properly designed electrically small structures can switch between resonant scattering and cloaking invisibility regimes. The contrast ratio between the scattering cross sections of the cloaking invisibility and resonant scattering regimes reaches almost unity. We then also show that larger, moderately small cylindrical structures can be designed to switch between superscattering and cloaking invisibility regimes, when GST is switched between its crystalline and amorphous phases. The contrast ratio between the scattering cross sections of cloaking invisibility and superscattering regimes can be as high as ~ 93%. Our results could be potentially important for developing a new generation of compact reconfigurable optical devices