13 resultados para Dunkl operators
em Cambridge University Engineering Department Publications Database
Resumo:
We describe a method to explore the configurational phase space of chemical systems. It is based on the nested sampling algorithm recently proposed by Skilling (AIP Conf. Proc. 2004, 395; J. Bayesian Anal. 2006, 1, 833) and allows us to explore the entire potential energy surface (PES) efficiently in an unbiased way. The algorithm has two parameters which directly control the trade-off between the resolution with which the space is explored and the computational cost. We demonstrate the use of nested sampling on Lennard-Jones (LJ) clusters. Nested sampling provides a straightforward approximation for the partition function; thus, evaluating expectation values of arbitrary smooth operators at arbitrary temperatures becomes a simple postprocessing step. Access to absolute free energies allows us to determine the temperature-density phase diagram for LJ cluster stability. Even for relatively small clusters, the efficiency gain over parallel tempering in calculating the heat capacity is an order of magnitude or more. Furthermore, by analyzing the topology of the resulting samples, we are able to visualize the PES in a new and illuminating way. We identify a discretely valued order parameter with basins and suprabasins of the PES, allowing a straightforward and unambiguous definition of macroscopic states of an atomistic system and the evaluation of the associated free energies.
Resumo:
We present the Unified Form Language (UFL), which is a domain-specific language for representing weak formulations of partial differential equations with a view to numerical approximation. Features of UFL include support for variational forms and functionals, automatic differentiation of forms and expressions, arbitrary function space hierarchies formultifield problems, general differential operators and flexible tensor algebra. With these features, UFL has been used to effortlessly express finite element methods for complex systems of partial differential equations in near-mathematical notation, resulting in compact, intuitive and readable programs. We present in this work the language and its construction. An implementation of UFL is freely available as an open-source software library. The library generates abstract syntax tree representations of variational problems, which are used by other software libraries to generate concrete low-level implementations. Some application examples are presented and libraries that support UFL are highlighted. © 2014 ACM.
Resumo:
BACKGROUND: Central Venous Catheterisation (CVC) has occasionally been associated with cases of retained guidewires in patients after surgery. In theory, this is a completely avoidable complication; however, as with any human procedure, operator error leading to guidewires being occasionally retained cannot be fully eliminated. OBJECTIVE: The work described here investigated the issue in an attempt to better understand it both from an operator and a systems perspective, and to ultimately recommend appropriate safe design solutions that reduce guidewire retention errors. METHODS: Nine distinct methods were used: observations of the procedure, a literature review, interviewing CVC end-users, task analysis construction, CVC procedural audits, two human reliability assessments, usability heuristics and a comprehensive solution survey with CVC end-users. RESULTS: The three solutions that operators rated most highly, in terms of both practicality and effectiveness, were: making trainees better aware of the potential guidewire complications and strongly emphasising guidewire removal in CVC training, actively checking that the guidewire is present in the waste tray for disposal, and standardising purchase of central line sets so that differences that may affect chances of guidewire loss is minimised. CONCLUSIONS: Further work to eliminate/engineer out the possibility of guidewires being retained is proposed.