Multiresolution approximation of the vector fields on T^3

Multiresolution approximation (MRA) of the vector fields on T^3 is studied. We introduced in the Fourier space a triad of vector fields called helical vectors which derived from the spherical coordinate system basis. Utilizing the helical vectors, we proved the orthogonal decomposition of L^2(T^3) which is a synthesis of the Hodge decomposition of the differential 1- or 2-form on T^3 and the Beltrami decomposition that decompose the space of solenoidal vector fields into the eigenspaces of curl operator. In the course of proof, a general construction procedure of the divergence-free orthonormal complete basis from the basis of scalar function space is presented. Applying this procedure to MRA of L^2(T^3), we discussed the MRA of vector fields on T^3 and the analyticity and regularity of vector wavelets. It is conjectured that the solenoidal wavelet basis must break r-regular condition, i.e. some wavelet functions cannot be rapidly decreasing function because of the inevitable singularities of helical vectors. The localization property and spatial structure of solenoidal wavelets derived from the Littlewood-Paley type MRA (Meyer's wavelet) are also investigated numerically.Comment: LaTeX, 33 Pages, 3 figures. submitted to J. Math. Phy

Dynamical mean field theory of optical third harmonic generation

We formulate the third harmonic generation (THG) within the dynamical mean field theory (DMFT) approximation of the Hubbard model. In the limit of large dimensions, where DMFT becomes exact, the vertex corrections to current vertices are identically zero, and hence the calculation of the THG spectrum reduces to a time-ordered convolution, followd by appropriate analytic continuuation. We present the typical THG spectrum of the Hubbard model obtained by this method. Within our DMFT calculation, we observe a nontrivial approximate {\em scaling} function describing the THG spectra in all Mott insulators, independent of the gap magnitude.Comment: 4 eps figure

Nonlinear Optical Response in two-dimensional Mott Insulators

We study the third-order nonlinear optical susceptibility $\chi^{(3)}$ and photoexcited states of two-dimensional (2D) Mott insulators by using an effective model in the strong-coupling limit of a half-filled Hubbard model. In the numerically exact diagonalization calculations on finite-size clusters, we find that the coupling of charge and spin degrees of freedom plays a crucial role in the distribution of the dipole-allowed states with odd parity and the dipole-forbidden states with even parity in the photoexcited states. This is in contrast with the photoexcited states in one dimension, where the charge and spin degrees of freedom are decoupled. In the third-harmonic generation (THG) spectrum, main contribution is found to come from the process of three-photon resonance associated with the odd-parity states. As a result, the two-photon resonance process is less pronounced in the THG spectrum. The calculated THG spectrum is compared with recent experimental data. We also find that $\chi^{(3)}$ with cross-polarized configuration of pump and probe photons shows spectral distributions similar to $\chi^{(3)}$ with co-polarized configuration, although the weight is small. These findings will help the analyses of the experimental data of $\chi^{(3)}$ in the 2D Mott insulators.Comment: 9 pages,5 figures,RevTeX

Comment on "Origin of Giant Optical Nonlinearity in Charge-Transfer--Mott Insulators: A New Paradigm for Nonlinear Optics"

Comment on Phys. Rev. Lett. 86, 2086 (2001)Comment: 1 page, 1 eps figur

Bioengineering the ameloblastoma tumour to study its effect on bone nodule formation

Ameloblastoma is a benign, epithelial cancer of the jawbone, which causes bone resorption and disfigurement to patients affected. The interaction of ameloblastoma with its tumour stroma drives invasion and progression. We used stiff collagen matrices to engineer active bone forming stroma, to probe the interaction of ameloblastoma with its native tumour bone microenvironment. This bone-stroma was assessed by nano-CT, transmission electron microscopy (TEM), Raman spectroscopy and gene analysis. Furthermore, we investigated gene correlation between bone forming 3D bone stroma and ameloblastoma introduced 3D bone stroma. Ameloblastoma cells increased expression of MMP-2 and -9 and RANK temporally in 3D compared to 2D. Our 3D biomimetic model formed bone nodules of an average surface area of 0.1 mm2 and average height of 92.37 ± 7.96 μm over 21 days. We demonstrate a woven bone phenotype with distinct mineral and matrix components and increased expression of bone formation genes in our engineered bone. Introducing ameloblastoma to the bone stroma, completely inhibited bone formation, in a spatially specific manner. Multivariate gene analysis showed that ameloblastoma cells downregulate bone formation genes such as RUNX2. Through the development of a comprehensive bone stroma, we show that an ameloblastoma tumour mass prevents osteoblasts from forming new bone nodules and severely restricted the growth of existing bone nodules. We have identified potential pathways for this inhibition. More critically, we present novel findings on the interaction of stromal osteoblasts with ameloblastoma

Nonlinear Optical Response Functions of Mott Insulators Based on Dynamical Mean Field Approximation

We investigate the nonlinear optical susceptibilities of Mott insulators with the dynamical mean field approximation. The two-photon absorption (TPA) and the third-harmonic generation (THG) spectra are calculated, and the classification by the types of coupling to external fields shows different behavior from conventional semiconductors. The direct transition terms are predominant both in the TPA and THG spectra, and the importance of taking all types of interaction with the external field into account is illustrated in connection with the THG spectrum and dcKerr effect. The dependence of the TPA and THG spectra on the Coulomb interaction indicate a scaling relation. We apply this relation to the quantitative evaluation and obtain results comparable to those of experiments.Comment: 14 pages, 12 figure

In vivo precision of the GE Lunar iDXA for the measurement of visceral adipose tissue in adults: the influence of body mass index.

CoreScan is a new software for the GE Lunar iDXA, which provides a quantification of visceral adipose tissue (VAT). The objective of this study was to determine the in vivo precision of CoreScan for the measurement of VAT mass in a heterogeneous group of adults. Forty-five adults (aged 34.6 (8.6) years), ranging widely in body mass index (BMI 26.0 (5.2)  kg/m(2); 16.7-42.4 kg/m(2)), received two consecutive total body scans with repositioning. The sample was divided into two subgroups based on BMI, normal-weight and overweight/obese, for precision analyses. Subgroup analyses revealed that precision errors (RMSSD:%CV; root mean square standard deviation:% coefficient of variation) for VAT mass were 20.9 g:17.0% in the normal-weight group and 43.7 g:5.4% in overweight/obese groups. Our findings indicate that precision for DXA-VAT mass measurements increases with BMI, but caution should be used with %CV-derived precision error in normal BMI subjects.European Journal of Clinical Nutrition advance online publication, 15 October 2014; doi:10.1038/ejcn.2014.213