The Heun equation and the Calogero-Moser-Sutherland system V: generalized Darboux transformations

We obtain isomonodromic transformations for Heun's equation by generalizing Darboux transformation, and we find pairs and triplets of Heun's equation which have the same monodromy structure. By composing generalized Darboux transformations, we establish a new construction of the commuting operator which ensures finite-gap property. As an application, we prove conjectures in part III.Comment: 24 page

Out-of-plane dielectric constant and insulator-superconductor transition in Bi_2Sr_2Dy_{1-x}Er_xCu_2O_8 single crystals

The out-of-plane dielectric constant of the parent insulator of the high-temperature superconductor Bi_2Sr_2(Dy,Er)Cu_2O_8 was measured and analysed from 80 to 300 K in the frequency range of 10^6-10^9 Hz. All the samples were found to show a fairly large value of 10-60, implying some kind of charge inhomogeneity in the CuO_2 plane. Considering that the superconducting sample Bi_2Sr_2(Ca,Pr)Cu_2O_8 also shows a similar dielectric constant, the charge inhomogeneity plays an important role in the insulator-superconductor transition.Comment: RevTex4 format, 5 pages, 3 figures, submitted to J. Phys. Condens. Ma

A study of uncertainties in the sulfate distribution and its radiative forcing associated with sulfur chemistry in a global aerosol model

The direct radiative forcing by sulfate aerosols is still uncertain, mainly because the uncertainties are largely derived from differences in sulfate column burdens and its vertical distributions among global aerosol models. One possible reason for the large difference in the computed values is that the radiative forcing delicately depends on various simplifications of the sulfur processes made in the models. In this study, therefore, we investigated impacts of different parts of the sulfur chemistry module in a global aerosol model, SPRINTARS, on the sulfate distribution and its radiative forcing. Important studies were effects of simplified and more physical-based sulfur processes in terms of treatment of sulfur chemistry, oxidant chemistry, and dry deposition process of sulfur components. The results showed that the difference in the aqueous-phase sulfur chemistry among these treatments has the largest impact on the sulfate distribution. Introduction of all the improvements mentioned above brought the model values noticeably closer to in-situ measurements than those in the simplified methods used in the original SPRINTARS model. At the same time, these improvements also brought the computed sulfate column burdens and its vertical distributions into good agreement with other AEROCOM model values. The global annual mean radiative forcing due to the direct effect of anthropogenic sulfate aerosol was thus estimated to be −0.26 W m<sup>−2</sup> (−0.30 W m<sup>−2</sup> with a different SO<sub>2</sub> inventory), whereas the original SPRINTARS model showed −0.18 W m<sup>−2</sup> (−0.21 W m<sup>−2</sup> with a different SO<sub>2</sub> inventory). The magnitude of the difference between original and improved methods was approximately 50% of the uncertainty among estimates by the world's global aerosol models reported by the IPCC-AR4 assessment report. Findings in the present study, therefore, may suggest that the model differences in the simplifications of the sulfur processes are still a part of the large uncertainty in their simulated radiative forcings

The decomposition of level-1 irreducible highest weight modules with respect to the level-0 actions of the quantum affine algebra Uq′(sl^n)U'_q(\hat{sl}_n)

We decompose the level-1 irreducible highest weight modules of the quantum affine algebra $U_q(\hat{sl}_n)$ with respect to the level-0 $U'_q (\hat{sl}_n)$--action defined in q-alg/9702024. The decomposition is parameterized by the skew Young diagrams of the border strip type.Comment: 22 pages, AMSLaTe

Simulation of aerosol optical properties over a tropical urban site in India using a global model and its comparison with ground measurements

Aerosols have great impacts on atmospheric environment, human health, and earth's climate. Therefore, information on their spatial and temporal distribution is of paramount importance. Despite numerous studies have examined the variation and trends of BC and AOD over India, only very few have focused on their spatial distribution or even correlating the observations with model simulations. In the present study, a three-dimensional aerosol transport-radiation model coupled with a general circulation model. SPRINTARS, simulated atmospheric aerosol distributions including BC and aerosol optical properties, i.e., aerosol optical thickness (AOT), Ångström Exponent (AE), and single scattering albedo (SSA). The simulated results are compared with both BC measurements by aethalometer and aerosol optical properties measured by ground-based skyradiometer and by satellite sensor, MODIS/Terra over Hyderabad, which is a tropical urban area of India, for the year 2008. The simulated AOT and AE in Hyderabad are found to be comparable to ground-based measured ones. The simulated SSA tends to be higher than the ground-based measurements. Both these comparisons of aerosol optical properties between the simulations with different emission inventories and the measurements indicate that, firstly the model uncertainties derived from aerosol emission inventory cannot explain the gaps between the simulations and the measurements and secondly the vertical transport of BC and the treatment of BC-containing particles can be the main issue in the global model to solve the gap

Comparative study of macroscopic quantum tunneling in Bi_2Sr_2CaCu_2O_y intrinsic Josephson junctions with different device structures

We investigated macroscopic quantum tunneling (MQT) of Bi$_2$Sr$_2$CaCu$_2$O$_y$ intrinsic Josephson junctions (IJJs) with two device structures. One is a nanometer-thick small mesa structure with only two or three IJJs and the other is a stack of a few hundreds of IJJs on a narrow bridge structure. Experimental results of switching current distribution for the first switching events from zero-voltage state showed a good agreement with the conventional theory for a single Josephson junction, indicating that a crossover temperature from thermal activation to MQT regime for the former device structure was as high as that for the latter device structure. Together with the observation of multiphoton transitions between quantized energy levels in MQT regime, these results strongly suggest that the observed MQT behavior is intrinsic to a single IJJ in high-$T_c$ cuprates, independent of device structures. The switching current distribution for the second switching events from the first resistive state, which were carefully distinguished from the first switchings, was also compared between two device structures. In spite of the difference in the heat transfer environment, the second switching events for both devices were found to show a similar temperature-independent behavior up to a much higher temperature than the crossover temperature for the first switching. We argue that it cannot be explained in terms of the self-heating owing to dissipative currents after the first switching. As possible candidates, the MQT process for the second switching and the effective increase of electronic temperature due to quasiparticle injection are discussed.Comment: 10pages, 7figures, submitted to Phys. Rev.

Particle Propagator of Spin Calogero-Sutherland Model

Explicit-exact expressions for the particle propagator of the spin 1/2 Calogero-Sutherland model are derived for the system of a finite number of particles and for that in the thermodynamic limit. Derivation of the expression in the thermodynamic limit is also presented in detail. Combining this result with the hole propagator obtained in earlier studies, we calculate the spectral function of the single particle Green's function in the full range of the energy and momentum space. The resultant spectral function exhibits power-law singularity characteristic to correlated particle systems in one dimension.Comment: 43 pages, 6 figure

Markov basis and Groebner basis of Segre-Veronese configuration for testing independence in group-wise selections

We consider testing independence in group-wise selections with some restrictions on combinations of choices. We present models for frequency data of selections for which it is easy to perform conditional tests by Markov chain Monte Carlo (MCMC) methods. When the restrictions on the combinations can be described in terms of a Segre-Veronese configuration, an explicit form of a Gr\"obner basis consisting of moves of degree two is readily available for performing a Markov chain. We illustrate our setting with the National Center Test for university entrance examinations in Japan. We also apply our method to testing independence hypotheses involving genotypes at more than one locus or haplotypes of alleles on the same chromosome.Comment: 25 pages, 5 figure