On the theory of complex rays

The article surveys the application of complex-ray theory to the scalar Helmholtz equation in two dimensions. The first objective is to motivate a framework within which complex rays may be used to make predictions about wavefields in a wide variety of geometrical configurations. A crucial ingredient in this framework is the role played by Sp{} in determining the regions of existence of complex rays. The identification of the Stokes surfaces emerges as a key step in the approximation procedure, and this leads to the consideration of the many characterizations of Stokes surfaces, including the adaptation and application of recent developments in exponential asymptotics to the complex Wentzel--Kramers--Brilbuin expansion of these wavefields

Downsizing assessment of automotive Stirling engines

A 67 kW (90 hp) Stirling engine design, sized for use in a 1984 1440 kg (3170 lb) automobile was the focal point for developing automotive Stirling engine technology. Since recent trends are towards lighter vehicles, an assessment was made of the applicability of the Stirling technology being developed for smaller, lower power engines. Using both the Philips scaling laws and a Lewis Research Center (Lewis) Stirling engine performance code, dimensional and performance characteristics were determined for a 26 kW (35 hp) and a 37 kW (50 hp) engine for use in a nominal 907 kg (2000 lb) vehicle. Key engine elements were sized and stressed and mechanical layouts were made to ensure mechanical fit and integrity of the engines. Fuel economy estimates indicated that the Stirling engine would maintain a 30 to 45 percent fuel economy advantage comparable spark ignition and diesel powered vehicles in the 1984 period

Explicitly correlated plane waves: Accelerating convergence in periodic wavefunction expansions

We present an investigation into the use of an explicitly correlated plane wave basis for periodic wavefunction expansions at the level of second-order M{\o}ller-Plesset perturbation theory (MP2). The convergence of the electronic correlation energy with respect to the one-electron basis set is investigated and compared to conventional MP2 theory in a finite homogeneous electron gas model. In addition to the widely used Slater-type geminal correlation factor, we also derive and investigate a novel correlation factor that we term Yukawa-Coulomb. The Yukawa-Coulomb correlation factor is motivated by analytic results for two electrons in a box and allows for a further improved convergence of the correlation energies with respect to the employed basis set. We find the combination of the infinitely delocalized plane waves and local short-ranged geminals provides a complementary, and rapidly convergent basis for the description of periodic wavefunctions. We hope that this approach will expand the scope of discrete wavefunction expansions in periodic systems.Comment: 15 pages, 13 figure

The SISO CSPI PDG standard for commercial off-the-shelf simulation package interoperability reference models

For many years discrete-event simulation has been used to analyze production and logistics problems in manufactur-ing and defense. Commercial-off-the-shelf Simulation Packages (CSPs), visual interactive modelling environ-ments such as Arena, Anylogic, Flexsim, Simul8, Witness, etc., support the development, experimentation and visua-lization of simulation models. There have been various attempts to create distributed simulations with these CSPs and their tools, some with the High Level Architecture (HLA). These are complex and it is quite difficult to assess how a set of models/CSP are actually interoperating. As the first in a series of standards aimed at standardizing how the HLA is used to support CSP distributed simula-tions, the Simulation Interoperability Standards Organiza-tion’s (SISO) CSP Interoperability Product Development Group (CSPI PDG) has developed and standardized a set of Interoperability Reference Models (IRM) that are in-tended to clearly identify the interoperability capabilities of CSP distributed simulations

Optimization of Turbine Rim Seals

Experiments are being conducted to gain an understanding of the physics of rim scale cavity ingestion in a turbine stage with the high-work, single-stage characteristics envisioned for Advanced Subsonic Transport (AST) aircraft gas turbine engines fo the early 21st century. Initial experimental measurements to be presented include time-averaged turbine rim cavity and main gas path static pressure measurements for rim seal coolant to main gas path mass flow ratios between 0 and 0.02. The ultimate objective of this work is develop improved rim seal design concepts for use in modern high-work, single sage turbines n order to minimize the use of secondary coolant flow. Toward this objective the time averaged and unsteady data to be obtained in these experiments will be used to 1) Quantify the impact of the rim cavity cooling air on the ingestion process. 2) Quantify the film cooling benefits of the rim cavity purge flow in the main gas path. 3) Quantify the impact of the cooling air on turbine efficiency. 4) Develop/evaluate both 3D CFD and analytical models of the ingestion/cooling process

Stokes phenomenon and matched asymptotic expansions

This paper describes the use of matched asymptotic expansions to illuminate the description of functions exhibiting Stokes phenomenon. In particular the approach highlights the way in which the local structure and the possibility of finding Stokes multipliers explicitly depend on the behaviour of the coefficients of the relevant asymptotic expansions

Asymptotics of near-cloaking

This paper describes how asymptotic analysis can be used to gain new insights into the theory of cloaking of spherical and cylindrical targets within the context of acoustic waves in a class of linear elastic materials. In certain cases these configurations allow solutions to be written down in terms of eigenfunction expansions from which high-frequency asymptotics can be extracted systematically. These asymptotics are compared with the predictions of ray theory and are used to describe the scattering that occurs when perfect cloaking models are regularised

Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression

Solution of the time-dependent Schro ̈dinger equation using a linear combination of basis functions, such as Gaussian wavepackets (GWPs), requires costly evaluation of integrals over the entire potential energy surface (PES) of the system. The standard approach, motivated by computational tractability for direct dynamics, is to approx- imate the PES with a second order Taylor expansion, for example centred at each GWP. In this Article, we propose an alternative method for approximating PES ma- trix elements based on PES interpolation using Gaussian process regression (GPR). Our GPR scheme requires only single-point evaluations of the PES at a limited num- ber of configurations in each time-step; the necessity of performing often-expensive evaluations of the Hessian matrix is completely avoided. In applications to 2-, 5- and 10-dimensional benchmark models describing a tunnelling coordinate coupled non-linearly to a set of harmonic oscillators, we find that our GPR method results in PES matrix elements for which the average error is, in the best case, two orders-of- magnitude smaller and, in the worst case, directly comparable to that determined by any other Taylor expansion method, without requiring additional PES evaluations or Hessian matrices. Given the computational simplicity of GPR, as well as the op- portunities for further refinement of the procedure highlighted herein, we argue that our GPR methodology should replace methods for evaluating PES matrix elements using Taylor expansions in quantum dynamics simulations

Interaction between LiH molecule and Li atom from state-of-the-art electronic structure calculations

State-of-the-art ab initio techniques have been applied to compute the potential energy surface for the lithium atom interacting with the lithium hydride molecule in the Born–Oppenheimer approximation. The interaction potential was obtained using a combination of the explicitly correlated unrestricted coupled-cluster method with single, double, and noniterative triple excitations [UCCSD(T)-F12] for the core–core and core–valence correlation and full configuration interaction for the valence–valence correlation. The potential energy surface has a global minimum 8743 cm−1 deep if the Li–H bond length is held fixed at the monomer equilibrium distance or 8825 cm−1 deep if it is allowed to vary. In order to evaluate the performance of the conventional CCSD(T) approach, calculations were carried out using correlation-consistent polarized valence X-tuple-zeta basis sets, with X ranging from 2 to 5, and a very large set of bond functions. Using simple two-point extrapolations based on the single-power laws X−2 and X−3 for the orbital basis sets, we were able to reproduce the CCSD(T)–F12 results for the characteristic points of the potential with an error of 0.49% at worst. The contribution beyond the CCSD(T)–F12 model, obtained from full configuration interaction calculations for the valence–valence correlation, was shown to be very small, and the error bars on the potential were estimated. At linear LiH–Li geometries, the ground-state potential shows an avoided crossing with an ion-pair potential. The energy difference between the ground-state and excited-state potentials at the avoided crossing is only 94 cm−1. Using both adiabatic and diabatic pictures, we analyze the interaction between the two potential energy surfaces and its possible impact on the collisional dynamics. When the Li–H bond is allowed to vary, a seam of conical intersections appears at C2v geometries. At the linear LiH–Li geometry, the conical intersection is at a Li–H distance which is only slightly larger than the monomer equilibrium distance, but for nonlinear geometries it quickly shifts to Li–H distances that are well outside the classical turning points of the ground-state potential of LiH. This suggests that the conical intersection will have little impact on the dynamics of Li–LiH collisions at ultralow temperatures. Finally, the reaction channels for the exchange and insertion reactions are also analyzed and found to be unimportant for the dynamics