11,271 research outputs found
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 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
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 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
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