Spatial-Temporal Models for Processes on the Sphere and their Application in Climate Problem

There have been noticeable advancements in developing parametric covariance models for spatial and spatial-temporal data in climate science. However, literature on covariance models for processes on the surface of a sphere is still sparse, due to its mathematical difficulties. In this dissertation, we study random fields and spatial-temporal covariance functions on the surface of a sphere. At first, smooth climate variables need smooth covariance functions. We develop a methodology to construct parametric covariance functions using the great circle distance for spatial processes, geared towards smooth processes on the surface of a sphere. We integrate a non-differential process over a small neighborhood on the surface of a sphere, which result in a smoother process. The resulting model is isotropic and positive definite on the surface of a sphere with the great circle distance, with a natural extension for nonstationarity case. Extensive numerical comparisons of our model, with a Matérn covariance model using the great circle distance as well as the chordal distance, are presented. Next, utilizing the one-to-one mapping between the Euclidean distance and the great circle distance, isotropic and positive definite functions in a Euclidean space can be used as covariance functions on the surface of a sphere. However, this approach may result in physically unrealistic distortion on the sphere especially for large distances. We consider several classes of covariance functions on the surface of a sphere, defined with either the great circle distance or the Euclidean distance, and investigate their impact upon prediction. We demonstrate that covariance functions originally defined in the Euclidean distance may not be adequate for some global data. Finally, climate variables often vary in both space and time and it has become popular to model multiple processes jointly. We consider the extension of the bivariate Matérn covariance models for spatial-temporal processes on the surface of a sphere. Since data sets have large dimension, a number of challenges arise when performing parameter estimation and prediction. To overcome the computational challenges, we consider the Discrete Fourier Transformation (DFT). We present a method to compute the approximate likelihood efficiently for the case of regularly spaced data of large dimension

Investigating the spatio-temporal variation of hepatitis A in Korea using a Bayesian model

Hepatitis A is a water-borne infectious disease that frequently occurs in unsanitary environments. However, paradoxically, those who have spent their infancy in a sanitary environment are more susceptible to hepatitis A because they do not have the opportunity to acquire natural immunity. In Korea, hepatitis A is prevalent because of the distribution of uncooked seafood, especially during hot and humid summers. In general, the transmission of hepatitis A is known to be dynamically affected by socioeconomic, environmental, and weather-related factors and is heterogeneous in time and space. In this study, we aimed to investigate the spatio-temporal variation of hepatitis A and the effects of socioeconomic and weather-related factors in Korea using a flexible spatio-temporal model. We propose a Bayesian Poisson regression model coupled with spatio-temporal variability to estimate the effects of risk factors. We used weekly hepatitis A incidence data across 250 districts in Korea from 2016 to 2019. We found spatial and temporal autocorrelations of hepatitis A indicating that the spatial distribution of hepatitis A varied dynamically over time. From the estimation results, we noticed that the districts with large proportions of males and foreigners correspond to higher incidences. The average temperature was positively correlated with the incidence, which is in agreement with other studies showing that the incidences in Korea are noticeable in spring and summer due to the increased outdoor activity and intake of stale seafood. To the best of our knowledge, this study is the first to suggest a spatio-temporal model for hepatitis A across the entirety of Korean. The proposed model could be useful for predicting, preventing, and controlling the spread of hepatitis A

Hexagonal RMnO3: a model system for two-dimensional triangular lattice antiferromagnets

The hexagonal RMnO3(h-RMnO3) are multiferroic materials, which exhibit the coexistence of a magnetic order and ferroelectricity. Their distinction is in their geometry that both results in an unusual mechanism to break inversion symmetry and also produces a two-dimensional triangular lattice of Mn spins, which is subject to geometrical magnetic frustration due to the antiferromagnetic interactions between nearest-neighbor Mn ions. This unique combination makes the h-RMnO3 a model system to test ideas of spin-lattice coupling, particularly when both the improper ferroelectricity and the Mn trimerization that appears to determine the symmetry of the magnetic structure arise from the same structure distortion. In this review we demonstrate how the use of both neutron and X-ray diffraction and inelastic neutron scattering techniques have been essential to paint this comprehensive and coherent picture of h-RMnO3. (c) 2016 International Union of Crystallography110111scopu

Dynamic Spin Fluctuations in the Frustrated A-site Spinel CuAl2O4

We performed nuclear magnetic resonance (NMR) and muon spin relaxation ({\mu}SR) experiments to identify the magnetic ground state of the frustrated quantum A-site spinel, CuAl2O4. Our results verify that the ground state does not exhibit a long-range magnetic ordering, but a glass-like transition manifests at T*=2.3 K. However, the Gaussian shape and the weak longitudinal field dependence of {\mu}SR spectra below T* show that the ground state has dynamic spin fluctuations, distinct from those of conventional spin-glasses.Comment: 22 pages, 7 figure

Antiferromagnetic Kitaev interaction in J_\rm{eff}=1/2 cobalt honeycomb materials Na3_3Co2_2SbO6_6 and Na2_2Co2_2TeO6_6

Finding new materials with antiferromagnetic (AFM) Kitaev interaction is an urgent issue to broaden and enrich the quantum magnetism research significantly. By carrying out inelastic neutron scattering experiments and subsequent analysis, we conclude that Na$_3$Co$_2$SbO$_6$ and Na$_2$Co$_2$TeO$_6$ are new honeycomb cobalt-based AFM Kitaev systems. The spin-orbit excitons at 20-28~meV in both compounds strongly supports the idea that Co$^{2+}$ ions of both compounds have a spin-orbital entangled J_\rm{eff}=1/2 state. Furthermore, we found that a generalized Kitaev-Heisenberg Hamiltonian can well describe the spin-wave excitations of both compounds with additional 3rd nearest-neighbor interaction. Our best-fit parameters show large AFM Kitaev terms and off-diagonal symmetric anisotropy terms of a similar magnitude in both compounds. We should stress that our parameters' optimized magnetic structures are consistent with the magnetic structures reported from neutron diffraction studies. Moreover, there is also the magnon-damping effect at the higher energy part of the spin waves, as usually observed in other Kitaev magnets. We demonstrate that Na$_3$Co$_2$SbO$_6$ and Na$_2$Co$_2$TeO$_6$ are the first experimental realization of AFM Kitaev magnets based on the systematic studies of the spin waves and analysis.Comment: 28 pages, 9 figure