Proofs for free - parametricity for dependent types

Reynolds' abstraction theorem shows how a typing judgement in System F can be translated into a relational statement (in second order predicate logic) about inhabitants of the type. We obtain a similar result for pure type systems: for any PTS used as a programming language, there is a PTS that can be used as a logic for parametricity. Types in the source PTS are translated to relations (expressed as types) in the target. Similarly, values of a given type are translated to proofs that the values satisfy the relational interpretation. We extend the result to inductive families. We also show that the assumption that every term satisfies the parametricity condition generated by its type is consistent with the generated logic

Approaching exact hyperpolarizabilities via sum-over-states Monte Carlo configuration interaction

We propose using sum-over-states calculations with the compact wavefunctions of Monte Carlo configuration interaction to approach accurate values for higher-order dipole properties up to second hyperpolarizabilities in a controlled way. We apply the approach to small systems that can generally be compared with full configuration interaction (FCI) results. We consider hydrogen fluoride with a 6-31g basis and then look at results, including frequency dependent properties, in an aug-cc-pVDZ basis. We extend one calculation beyond FCI by using an aug-cc-pVTZ basis. The properties of an H$_{4}$ molecule with multireference character are calculated in an aug-cc-pVDZ basis. We then investigate this method on a strongly multireference system with a larger FCI space by modelling the properties of carbon monoxide with a stretched geometry. The behavior of the approach with increasing basis size is considered by calculating results for the neon atom using aug-cc-pVDZ to aug-cc-pVQZ. We finally test if the unusual change in polarizability between the first two states of molecular oxygen can be reproduced by this method in a 6-31g basis.Comment: 11 pages, 14 figure

Characterizing a configuration interaction excited state using natural transition geminals

We introduce natural transition geminals as a means to qualitatively understand a transition where double excitations are important. The first two $A_{1}$ singlet states of the CH cation are used as an initial example. We calculate these states with configuration interaction singles (CIS) and state-averaged Monte Carlo configuration interaction (SA-MCCI). For each method we compare the important natural transition geminals with the dominant natural transition orbitals. We then compare SA-MCCI and full configuration interaction (FCI) with regards to the natural transition geminals using the beryllium atom. We compare using the natural transition geminals with analyzing the important configurations in the CI expansion to give the dominant transition for the beryllium atom and the carbon dimer. Finally we calculate the natural transition geminals for two electronic excitations of formamide.Comment: 15 pages, 2 figures. Mol. Phys. (2013

Applying Monte Carlo configuration interaction to transition metal dimers: exploring the balance between static and dynamic correlation

We calculate potential curves for transition metal dimers using Monte Carlo configuration interaction (MCCI). These results, and their associated spectroscopic values, are compared with experimental and computational studies. The multireference nature of the MCCI wavefunction is quantified and we estimate the important orbitals. We initially consider the ground state of the chromium dimer. Next we calculate potential curves for Sc$_{2}$ where we contrast the lowest triplet and quintet states. We look at the molybdenum dimer where we compare non-relativistic results with the partial inclusion of relativistic effects via effective core potentials, and report results for scandium nickel.Comment: 9 pages and 8 figure

High temperature, short term tensile strength of C6000/PMR-15 composites

Tensile tests were conducted on 0 unidirectionally reinforced Celion 6000 graphite fibers in PMR-15 polyimide matrix. Tensile strengths for coupons subjected to short and long term uniform temperatures were obtained. Thick coupons, heated on one side to produce significant transient through thickness temperature gradients, were tested and compared to the strength of specimens with uniform temperature distributions. All coupons were radiantly heated and reached maximum test temperatures within 15 sec. Tensile loads were applied to the coupons after 15 sec of elevated temperature exposure. Loading rates were selected so that specimen failures occurred within a maximum of 45 sec after reaching the test temperature. Results indicate that significant tensile strength remains beyond the material post cure temperature

Reducing the external environmental costs of pastoral farming in New Zealand: experiences from the Te Arawa lakes, Rotorua

Decades of nutrient pollution have caused water quality to decline in the nationally iconic Te Arawa (Rotorua) lakes in New Zealand. Pastoral agriculture is a major nutrient source, and therefore this degradation represents an external environmental cost to intensive farming. This cost is borne by the wider community, and a major publically funded remediation programme is now under way. This article describes the range of actions being taken to reduce nutrient loads from internal (lake bed sediments) and external (primarily diffuse) sources in the lake catchments. The high economic cost and uncertain efficacy of engineering-based actions to reduce internal nutrient loads is highlighted. Major changes to land management practices to control diffuse nutrient pollution are required throughout New Zealand if the need for costly and lengthy remediation programmes elsewhere is to be avoided. More action to educate farmers and the public about eutrophication issues, development and enforcement of environmental standards, and further consideration of the use of market-based instruments are proposed as ways to correct the current market failure

Reducing the external environmental costs of pastoral farming in New Zealand: experiences from the Te Arawa lakes, Rotorua

Decades of nutrient pollution have caused water quality to decline in the nationally iconic Te Arawa (Rotorua) lakes in New Zealand. Pastoral agriculture is a major nutrient source, and therefore this degradation represents an external environmental cost to intensive farming. This cost is borne by the wider community, and a major publically funded remediation programme is now under way. This article describes the range of actions being taken to reduce nutrient loads from internal (lake bed sediments) and external (primarily diffuse) sources in the lake catchments. The high economic cost and uncertain efficacy of engineering-based actions to reduce internal nutrient loads is highlighted. Major changes to land management practices to control diffuse nutrient pollution are required throughout New Zealand if the need for costly and lengthy remediation programmes elsewhere is to be avoided. More action to educate farmers and the public about eutrophication issues, development and enforcement of environmental standards, and further consideration of the use of market-based instruments are proposed as ways to correct the current market failure

Calculations of Potential Energy Surfaces Using Monte Carlo Configuration Interaction

We apply the method of Monte Carlo configuration interaction (MCCI) to calculate ground-state potential energy curves for a range of small molecules and compare the results with full configuration interaction. We show that the MCCI potential energy curve can be calculated to relatively good accuracy, as quantified using the non-parallelity error, using only a very small fraction of the FCI space. In most cases the potential curve is of better accuracy than its constituent single-point energies. We finally test the MCCI program on systems with basis sets beyond full configuration interaction: a lattice of fifty hydrogen atoms and ethylene. The results for ethylene agree fairly well with other computational work while for the lattice of fifty hydrogens we find that the fraction of the full configuration interaction space we were able to consider appears to be too small as, although some qualitative features are reproduced, the potential curve is less accurate.Comment: 14 pages, 22 figure

Monte Carlo configuration interaction applied to multipole moments, ionisation energies and electron affinities

The method of Monte Carlo configuration interaction (MCCI) [1,2] is applied to the calculation of multipole moments. We look at the ground and excited state dipole moments in carbon monoxide. We then consider the dipole of NO, the quadrupole of the nitrogen molecule and of BH. An octupole of methane is also calculated. We consider experimental geometries and also stretched bonds. We show that these non-variational quantities may be found to relatively good accuracy when compared with FCI results, yet using only a small fraction of the full configuration interaction space. MCCI results in the aug-cc-pVDZ basis are seen to generally have reasonably good agreement with experiment. We also investigate the performance of MCCI when applied to ionisation energies and electron affinities of atoms in an aug-cc-pVQZ basis. We compare the MCCI results with full configuration-interaction quantum Monte Carlo [3,4] and `exact' non-relativistic results [3,4]. We show that MCCI could be a useful alternative for the calculation of atomic ionisation energies however electron affinities appear much more challenging for MCCI. Due to the small magnitude of the electron affinities their percentage errors can be high, but with regards to absolute errors MCCI performs similarly for ionisation energies and electron affinities.Comment: 12 pages, 20 figure