Orthogonal Polynomials from Hermitian Matrices

A unified theory of orthogonal polynomials of a discrete variable is presented through the eigenvalue problem of hermitian matrices of finite or infinite dimensions. It can be considered as a matrix version of exactly solvable Schr\"odinger equations. The hermitian matrices (factorisable Hamiltonians) are real symmetric tri-diagonal (Jacobi) matrices corresponding to second order difference equations. By solving the eigenvalue problem in two different ways, the duality relation of the eigenpolynomials and their dual polynomials is explicitly established. Through the techniques of exact Heisenberg operator solution and shape invariance, various quantities, the two types of eigenvalues (the eigenvalues and the sinusoidal coordinates), the coefficients of the three term recurrence, the normalisation measures and the normalisation constants etc. are determined explicitly.Comment: 53 pages, no figures. Several sentences and a reference are added. To be published in J. Math. Phy

Monte Carlo simulations of infinitely dilute solutions of amphiphilic diblock star copolymers

Single-chain Monte Carlo simulations of amphiphilic diblock star copolymers were carried out in continuous space using implicit solvents. Two distinct architectures were studied: stars with the hydrophobic blocks attached to the core, and stars with the polar blocks attached to the core, with all arms being of equal length. The ratio of the lengths of the hydrophobic block to the length of the polar block was varied from 0 to 1. Stars with 3, 6, 9 or 12 arms, each of length 10, 15, 25, 50, 75 and 100 Kuhn segments were analysed. Four distinct types of conformations were observed for these systems. These, apart from studying the snapshots from the simulations, have been quantitatively characterised in terms of the mean-squared radii of gyration, mean-squared distances of monomers from the centre-of-mass, asphericity indices, static scattering form factors in the Kratky representation as well as the intra-chain monomer-monomer radial distribution functions.Comment: 12 pages, 11 ps figures. Accepted for publication in J. Chem. Phy

Linking horizontal and vertical transports of biomass fire emissions to the Tropical Atlantic Ozone Paradox during the Northern Hemisphere winter season: climatology

International audienceDuring the Northern hemisphere winter season, biomass burning is widespread in West Africa, yet the total tropospheric column ozone values (<30 DU) over much of the Tropical Atlantic Ocean (15° N?5° S) are relatively low. At the same time, the tropospheric column ozone values in the Southern Tropical Atlantic are higher than those in the Northern Hemisphere (ozone paradox). We examine the causes for low tropospheric column ozone values by considering the horizontal and vertical transport of biomass fire emissions in West Africa during November through March, using observed data which characterizes fires, aerosols, horizontal winds, precipitation, lightning and outgoing longwave radiation. We have found that easterly winds prevail in the lower troposphere but transition to westerly winds at pressure levels lower than 500 hPa. A persistent anticyclone over West Africa at 700 hPa is responsible for strong easterly winds, which causes a net outflow of ozone/ozone precursors from biomass burning in West Africa across the Atlantic Ocean towards South America. The lowest outgoing longwave radiation (OLR) and highest precipitation rates are generally found over the central Atlantic, some distance downstream of fires in West Africa making the vertical transport of ozone and ozone precursors less likely and ozone destruction more likely. However, lightning over land areas in Central Africa and South America can lead to enhanced ozone levels in the upper troposphere especially over the Southern tropical Atlantic during the Northern Hemisphere winter season

Space-borne observations link the tropical atlantic ozone maximum and paradox to lightning

International audienceThe potential enhancement of tropospheric column ozone values over the Tropical Atlantic Ocean on a seasonal basis by lightning is investigated using satellite derived ozone data, TRMM lightning data, ozonesonde data and NCEP reanalysis during 1998-2001. Our results show that the number of lightning flashes in Africa and South America reach a maximum during September, October and November (SON). The spatial patterns of winds in combination with lightning from West Africa, Central Africa and South America is likely responsible for enriching middle/upper troposphere ozone over the Tropical South Atlantic during SON. Moreover, lightning flashes are high in the hemisphere opposite to biomass burning during December, January, and February (DJF) and June, July and August (JJA). This pattern leads to an enrichment of ozone in the middle/upper troposphere in the Southern Hemisphere Tropics during DJF and the Northern Hemisphere Tropics during JJA. During JJA the largest numbers of lightning flashes are observed in West Africa, enriching tropospheric column ozone to the north of 5S in the absence of biomass burning. During DJF, lightning is concentrated in South America and Central Africa enriching tropospheric column ozone south of the Equator in the absence of biomass burning

A new class of (2+1)(2+1)-d topological superconductor with Z8\mathbb{Z}_8 topological classification

The classification of topological states of matter depends on spatial dimension and symmetry class. For non-interacting topological insulators and superconductors the topological classification is obtained systematically and nontrivial topological insulators are classified by either integer or $Z_2$. The classification of interacting topological states of matter is much more complicated and only special cases are understood. In this paper we study a new class of topological superconductors in $(2+1)$ dimensions which has time-reversal symmetry and a $\mathbb{Z}_2$ spin conservation symmetry. We demonstrate that the superconductors in this class is classified by $\mathbb{Z}_8$ when electron interaction is considered, while the classification is $\mathbb{Z}$ without interaction.Comment: 5 pages main text and 3 pages appendix. 1 figur

Selective copper extraction by multi-modified mesoporous silica material, SBA-15

© 2018 Selective copper (Cu) recovery from wastewater mitigates environmental pollution and is economically valuable. Mesoporous silica adsorbents, SBA-15, with amine-grafting (SBA-15-NH2) and manganese loading along with amine-grafting (Mn-SBA-15-NH2) were fabricated using KMnO4 and 3-aminopropyltriethoxysilane. The characteristics of the synthesized adsorbents were evaluated in detail in terms of its crystal structure peaks, surface area and pore size distribution, transmission electron microscope and X-ray photoelectron spectroscopy. The results established the 2.08 mmol/g of Cu adsorption capacity on Mn-SBA-15-NH2. Furthermore, in a mixed heavy metal solution, high selective Cu adsorption capacity on Mn-SBA-15-NH2 (2.01 mmol/g) was achieved while maintaining 96% adsorption amount as that of a single Cu solution. Comparatively, Cu adsorption on SBA-15-NH2 decreased by half due to high competition with other heavy metals. Optimal Cu adsorption occurred at pH 5. This pH condition enabled grafted amine group in Mn-SBA-15-NH2 to form strong chelating bonds with Cu, avoiding protonation of amine group (below pH 5) as well as precipitation (above pH 5). The adsorption equilibrium well fitted to Langmuir and Freundlich isotherm models, while kinetic results were represented by models of linear driving force approximation (LDFA) and pore diffusion model (PDM). High regeneration and reuse capacity of Mn-SBA-15-NH2 were well established by its capacity to maintain 90% adsorption capacity in a multiple adsorption-desorption cycle. Cu was selectively extracted from Mn-SBA-15-NH2 with an acid solution

Equation of State in Numerical Relativistic Hydrodynamics

Relativistic temperature of gas raises the issue of the equation of state (EoS) in relativistic hydrodynamics. We study the EoS for numerical relativistic hydrodynamics, and propose a new EoS that is simple and yet approximates very closely the EoS of the single-component perfect gas in relativistic regime. We also discuss the calculation of primitive variables from conservative ones for the EoS's considered in the paper, and present the eigenstructure of relativistic hydrodynamics for a general EoS, in a way that they can be used to build numerical codes. Tests with a code based on the Total Variation Diminishing (TVD) scheme are presented to highlight the differences induced by different EoS's.Comment: To appear in the ApJS September 2006, v166n1 issue. Pdf with full resolution figures can be downloaded from http://canopus.cnu.ac.kr/ryu/ryuetal.pd

Spin Berry phase in the Fermi arc states

Unusual electronic property of a Weyl semi-metallic nanowire is revealed. Its band dispersion exhibits multiple subbands of partially flat dispersion, originating from the Fermi arc states. Remarkably, the lowest energy flat subbands bear a finite size energy gap, implying that electrons in the Fermi arc surface states are susceptible of the spin Berry phase. This is shown to be a consequence of spin-to-surface locking in the surface electronic states. We verify this behavior and the existence of spin Berry phase in the low-energy effective theory of Fermi arc surface states on a cylindrical nanowire by deriving the latter from a bulk Weyl Hamiltonian. We point out that in any surface state exhibiting a spin Berry phase pi, a zero-energy bound state is formed along a magnetic flux tube of strength, hc/(2e). This effect is highlighted in a surfaceless bulk system pierced by a dislocation line, which shows a 1D chiral mode along the dislocation line.Comment: 9 pages, 9 figure