Some aspects of the physics of water-table rise and salt movement in the soil under irrigated conditions

Proceedings - Mathematical Sciences -     

On non-simply connected manifolds with non-trivial parallel spinors

We examine the possibilities of the full holonomy groups of locally irreducible but not necessarily complete Riemannian spin manifolds admitting a non-trivial parallel spinor and discuss some applications of this classification.partially supported by NSERC Grant No. OPG0009421     

International Intercomparison of Solar UVR Spectral Measurement Systems in Melbourne in 2013

Monitoring ambient solar UVR levels provides information on how much there is in both real time and historically. Quality assurance of ambient measurements of solar UVR is critical to ensuring accuracy and stability and this can be achieved by regular intercomparisons of spectral measurement systems with those of other organizations. In October and November of 2013 a solar UVR spectroradiometer from Public Health England (PHE) was brought to Melbourne for a campaign of intercomparisons with a new Bentham spectrometer of Australian Radiation Protection and Nuclear Safety Agency (ARPANSA) and one at the Australian Bureau of Meteorology (BOM), supported by New Zealand's National Institute for Water and Atmosphere (NIWA). Given all three spectroradiometers have calibrations that are traceable to various national standards, the intercomparison provides a chance to determine measurement uncertainties and traceability that support UV measurement networks in Australia, New Zealand and the UK. UV Index measurements from all three systems were compared and ratios determined for clear sky conditions when the scans from each instrument were within 2 min of each other. While wavelengths below 305 nm showed substantial differences between the PHE unit and the two other systems, overall the intercomparison results were encouraging, with mean differences in measured UV Index between the BOM/NIWA and those of PHE and ARPANSA of <0.1% and 7.5%, respectively.     

Quantum entanglement between electronic and vibrational degrees of freedom in molecules

We consider the quantum entanglement of the electronic and vibrational degrees of freedom in molecules with tendencies towards double welled potentials. In these bipartite systems, the von Neumann entropy of the reduced density matrix is used to quantify the electron-vibration entanglement for the lowest two vibronic wavefunctions obtained from a model Hamiltonian based on coupled harmonic diabatic potential-energy surfaces. Significant entanglement is found only in the region in which the ground vibronic state contains a density profile that is bimodal (i.e., contains two separate local maxima). However, in this region two distinct types of density and entanglement profiles are found: one type arises purely from the degeneracy of energy levels in the two potential wells and is destroyed by slight asymmetry, while the other arises through strong interactions between the diabatic levels of each well and is relatively insensitive to asymmetry. These two distinct types are termed fragile degeneracy-induced entanglement and persistent entanglement, respectively. Six classic molecular systems describable by two diabatic states are considered: ammonia, benzene, BNB, pyridine excited triplet states, the Creutz-Taube ion, and the radical cation of the "special pair" of chlorophylls involved in photosynthesis. These chemically diverse systems are all treated using the same general formalism and the nature of the entanglement that they embody is elucidated.     

Tunability of the M(II)M(III)/M(II)(2) and M(III)(2)/M(II)M(III) (M=Mn, Co) couples in bis-μ-O,O'-carboxylato-μ-OR bridged complexes

A comparison of the electrochemical properties of a series of dinuclear complexes [M(2)(L)(RCO(2))(2)](+) with M = Mn or Co, L = 2,6-bis(N,N-bis-(2-pyridylmethyl)-sulfonamido)-4-methylphenolato (bpsmp(-)) or 2,6-bis(N,N-bis(2-pyridylmethyl)aminomethyl)-4-tert-butylphenolato (bpbp(-)) and R = H, CH(3), CF(3) or 3,4-dimethoxybenzoate demonstrates: (i) The electron-withdrawing sulfonyl groups in the backbone of bpsmp(-) stabilize the [M(2)(bpsmp)(RCO(2))(2)](+) complexes in their M(II)(2) oxidation state compared to their [M(2)(bpbp)(RCO(2))(2)](+) analogues. Manganese complexes are stabilised by approximately 550 mV and cobalt complexes by 650 mV. (ii) The auxiliary bridging carboxylato ligands further attenuate the metal-based redox chemistry. Substitution of two acetato for two trifluoroacetato ligands shifts redox couples by 300-400 mV. Within the working potential window, reversible or quasi-reversible M(II)M(III)? M(II)(2) processes range from 0.31 to 1.41 V for the [Co(2)(L)(RCO(2))(2)](+/2+) complexes and from 0.54 to 1.41 V for the [Mn(2)(L)(RCO(2))(2)](+/2+) complexes versus Ag/AgCl for E(M(II)M(III)/M(II)(2)). The extreme limits are defined by the complexes [M(2)(bpbp)(CH(3)CO(2))(2)](+) and [M(2)(bpsmp)(CF(3)CO(2))(2)](+) for both metal ions. Thus, tuning the ligand field in these dinuclear complexes makes possible a range of around 0.9 V and 1.49 V for the one-electron E(M(II)M(III)/M(II)(2)) couple of the Mn and Co complexes, respectively. The second one-electron process, M(II)M(III)? M(III)(2) was also observed in some cases. The lowest potential recorded for the E°(M(III)(2)/M(II)M(III)) couple was 0.63 V for [Co(2)(bpbp)(CH(3)CO(2))(2)](2+) and the highest measurable potential was 2.23 V versus Ag/AgCl for [Co(2)(bpsmp)(CF(3)CO(2))(2)](2+).     

Reversible and selective O2 chemisorption in a porous metal-organic host material

The metal-organic host material [{Co(III)(2)(bpbp)(O(2))}(2)bdc](PF(6))(4) (1·2O(2); bpbp(-) = 2,6-bis(N,N-bis(2-pyridylmethyl)aminomethyl)-4-tert-butylphenolato; bdc(2-) = 1,4-benzenedicarboxylato) displays reversible chemisorptive desorption and resorption of dioxygen through conversion to the deoxygenated Co(II) form [{Co(II)(2)(bpbp)}(2)bdc](PF(6))(4) (1). Single crystal X-ray diffraction analysis indicates that the host lattice 1·2O(2), achieved through desorption of included water guests from the as-synthesized phase 1·2O(2)·3H(2)O, consists of an ionic lattice containing discrete tetranuclear complexes, between which lie void regions that allow the migration of dioxygen and other guests. Powder X-ray diffraction analyses indicate that the host material retains crystallinity through the dioxygen desorption/chemisorption processes. Dioxygen chemisorption measurements on 1 show near-stoichiometric uptake of dioxygen at 5 mbar and 25 °C, and this capacity is largely retained at temperatures above 100 °C. Gas adsorption isotherms of major atmospheric gases on both 1 and 1·2O(2) indicate the potential suitability of this material for air separation, with a O(2)/N(2) selectivity factor of 38 at 1 atm. Comparison of oxygen binding in solution and in the solid state indicates a dramatic increase in binding affinity to the complex when it is incorporated in a porous solid.     

Bond alternation, polarizability, and resonance detuning in methine dyes

We derive structure-property relationships for methine ("Brooker") dyes relating the color of the dye and its symmetric parents to its bond alternation in the ground state and also to the dipole properties associated with its low-lying charge-resonance (or charge-transfer) transition. We calibrate and test these relationships on an array of different protonation states of the green fluorescent protein chromophore motif (an asymmetric halochromic methine dye) and its symmetric parent dyes. The relationships rely on the assumption that the diabatic states that define the Platt model for methine dye color [J. R. Platt, J. Chem. Phys. 25, 80 (1956)] can also be distinguished by their single-double bond alternation and by their charge localization character. These assumptions are independent of the primary constraint that defines the diabatic states in the Platt model--specifically, the Brooker deviation rule for methine dyes [L. G. S. Brooker, Rev. Mod. Phys. 14, 275 (1942)]. Taking these assumptions, we show that the Platt model offers an alternate route to known structure-property relationships between the bond length alternation and the quadratic nonlinear polarizability β. We show also that the Platt model can be parameterized without the need for synthesis of the symmetric parents of a given dye, using the dipole data obtained through spectroscopic measurements. This suggests that the Platt model parameters may be used as independent variables in free-energy relationships for chromophores whose symmetric parents cannot be synthesized or chromophores strongly bound to biomolecular environments. The latter category includes several recently characterized biomolecular probe constructs. We illustrate these concepts by an analysis of previously reported electroabsorption and second-harmonic generation experiments on green fluorescent proteins.     

Finite equational bases for congruence modular varieties

In this paper it is proved that a variety generated by a finite algebraic system with finitely many operations is finitely axiomatizable, provided that the variety is congruence modular and residually small. This result is an extension to congruence modular varieties of a well known theorem for congruence distributive varieties, due to K. A. Baker. Also, under somewhat less restrictive hypotheses, (which are satisfied by finite groups and rings) it is proved that a finite algebraic system belongs to a finitely axiomatizable locally finite variety.Research supported by National Science Foundation Grant No. DMS-8302295.Presented by George Gratzer.