Unified form language: A domain-specific language for weak formulations of partial differential equations

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.

New space-time trellis codes for two-antenna quasi-static channels

New space-time trellis codes with four- and eight-level phase-shift keying (PSK) and 16-phase quadrature amplitude modulation (QAM) for two transmit antennas in slow-fading channels are presented in this paper. Unlike most of the codes that are reported in the literature, the proposed codes are specifically designed to minimize the frame error probability from a union-bound perspective. The performance of the proposed codes with various memory orders and receive antennas is evaluated by simulation. It is shown that the proposed codes outperform previously known codes in all studied cases.

Measurements of triggering and transient growth in a model lean-premixed gas turbine combustor

Instability triggering and transient growth of thermoacoustic oscillations were experimentally investigated in combination with linear/nonlinear flame transfer function (FTF) methodology in a model lean-premixed gas turbine combustor operated with CH 4 and air at atmospheric pressure. A fully premixed flame with 10kW thermal power and an equivalence ratio of 0.60 was chosen for detailed characterization of the nonlinear transient behaviors. Flame transfer functions were experimentally determined by simultaneous measurements of inlet velocity fluctuations and heat release rate oscillations using a constant temperature anemometer and OH */CH * chemiluminescence emissions, respectively. The phase-resolved variation of the local flame structure at a limit cycle was measured by planar laser-induced fluorescence of OH. Simultaneous measurements of inlet velocity, OH */CH * emission, and acoustic pressure were performed to investigate the temporal evolution of the system from a stable to a limit cycle operation. This measurement allows us to describe an unsteady instability triggering event in terms of several distinct stages: (i) initiation of a small perturbation, (ii) exponential amplification, (iii) saturation, (iv) nonlinear evolution of the perturbations towards a new unstable periodic state, (v) quasi-steady low-amplitude periodic oscillation, and (vi) fully-developed high-amplitude limit cycle oscillation. Phase-plane portraits of instantaneous inlet velocity and heat release rate clearly show the presence of two different attractors. Depending on its initial position in phase space at infinitesimally small amplitude, the system evolves towards either a high-amplitude oscillatory state or a low-amplitude oscillatory state. This transient phenomenon was analyzed using frequency- and amplitude-dependent damping mechanisms, and compared to subcritical and supercritical bifurcation theories. The results presented in this paper experimentally demonstrate the hypothesis proposed by Preetham et al. based on analytical and computational solutions of the nonlinear G-equation [J. Propul. Power 24 (2008) 1390-1402]. Good quantitative agreement was obtained between measurements and predictions in terms of the conditions for the onset of triggering and the amplitude of triggered combustion instabilities. © 2011 The Combustion Institute.

Effects of initial soil fabric and mode of shearing on quasi-steady state line for monotonic undrained behavior

The effects of initial soil fabric and mode of shearing on quasi-steady state line in void ratiostress space are studied by employing the Distinct Element Method numerical analysis. The results show that the initial soil fabric and the mode of shearing have a profound effect on the location of the quasi-steady state line. The evolution of the soil fabric during the course of undrained shearing shows that the specimens with different initial soil fabrics reach quasi-steady state at various soil fabric conditions. At quasi-steady state, the soil fabric has a significant adjustment to change its behavior from contractive to dilative. As the stress state approaches the steady state, the soil fabrics of different initial conditions become similar. The numerical analysis results are compared qualitatively with the published experimental data and the effects of specimen reconstitution methods and mode of shearing found in the experimental studies canbe systematically explained by the numerical analysis. © 2009 Taylor & Francis Group.

When will a flame describing function approach to thermoacoustics work well?

In any thermoacoustic analysis, it is important not only to predict linear frequencies and growth rates, but also the amplitude and frequencies of any limit cycles. The Flame Describing Function (FDF) approach is a quasi-linear analysis which allows the prediction of both the linear and nonlinear behaviour of a thermoacoustic system. This means that one can predict linear growth rates and frequencies, and also the amplitudes and frequencies of any limit cycles. The FDF achieves this by assuming that the acoustics are linear and that the flame, which is the only nonlinear element in the thermoacoustic system, can be adequately described by considering only its response at the frequency at which it is forced. Therefore any harmonics generated by the flame's nonlinear response are not considered. This implies that these nonlinear harmonics are small or that they are sufficiently filtered out by the linear dynamics of the system (the low-pass filter assumption). In this paper, a flame model with a simple saturation nonlinearity is coupled to simple duct acoustics, and the success of the FDF in predicting limit cycles is studied over a range of flame positions and acoustic damping parameters. Although these two parameters affect only the linear acoustics and not the nonlinear flame dynamics, they determine the validity of the low-pass filter assumption made in applying the flame describing function approach. Their importance is highlighted by studying the level of success of an FDF-based analysis as they are varied. This is achieved by comparing the FDF's prediction of limit-cycle amplitudes to the amplitudes seen in time domain simulations.

Development of a time and space resolved sampling probe diagnostic for engine exhaust hydrocarbons

In order to understand how unburned hydrocarbons emerge from SI engines and, in particular, how non-fuel hydrocarbons are formed and oxidized, a new gas sampling technique has been developed. A sampling unit, based on a combination of techniques used in the Fast Flame Ionization Detector (FFID) and wall-mounted sampling valves, was designed and built to capture a sample of exhaust gas during a specific period of the exhaust process and from a specific location within the exhaust port. The sampling unit consists of a transfer tube with one end in the exhaust port and the other connected to a three-way valve that leads, on one side, to a FFID and, on the other, to a vacuum chamber with a high-speed solenoid valve. Exhaust gas, drawn by the pressure drop into the vacuum chamber, impinges on the face of the solenoid valve and flows radially outward. Once per cycle during a specified crank angle interval, the solenoid valve opens and traps exhaust gas in a storage unit, from which gas chromatography (GC) measurements are made. The port end of the transfer tube can be moved to different locations longitudinally or radially, thus allowing spatial resolution and capturing any concentration differences between port walls and the center of the flow stream. Further, the solenoid valve's opening and closing times can be adjusted to allow sampling over a window as small as 0.6 ms during any portion of the cycle, allowing resolution of a crank angle interval as small as 15°CA. Cycle averaged total HC concentration measured by the FFID and that measured by the sampling unit are in good agreement, while the sampling unit goes one step further than the FFID by providing species concentrations. Comparison with previous measurements using wall-mounted sampling valves suggests that this sampling unit is fully capable of providing species concentration information as a function of air/fuel ratio, load, and engine speed at specific crank angles. © Copyright 1996 Society of Automotive Engineers, Inc.

Scalable, low-energy hybrid photonic space switch

A scalable monolithically integrated photonic space switch is proposed which uses a combination of Mach-Zehnder modulators and semiconductor optical amplifiers (SOAs) for improved crosstalk performance and reduced switch loss. This architecture enables the design of high-capacity, high-speed, large-port count, low-energy switches. Extremely low crosstalk of better than -50 dB can be achieved using a 2 × 2 dilated hybrid switch module. A 'building block' approach is applied to make large port count optical switches possible. Detailed physical layer multiwavelength simulations are used to investigate the viability of a 64 × 64 port switch. Optical signal degradation is estimated as a function of switch size and waveguide induced crosstalk. A comparison between hybrid and SOA switching fabrics highlights the power-efficient, high-performance nature of the hybrid switch design, which consumes less than one-third of the energy of an equivalent SOA-based switch. The significantly reduced impairments resulting from this switch design enable scaling of the port count, compared to conventional SOA-based switches. © 1983-2012 IEEE.

Bayesian inference and learning in Gaussian process state-space models with Particle MCMC

State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference and learning (i.e. state estimation and system identification) in nonlinear nonparametric state-space models. We place a Gaussian process prior over the state transition dynamics, resulting in a flexible model able to capture complex dynamical phenomena. To enable efficient inference, we marginalize over the transition dynamics function and, instead, infer directly the joint smoothing distribution using specially tailored Particle Markov Chain Monte Carlo samplers. Once a sample from the smoothing distribution is computed, the state transition predictive distribution can be formulated analytically. Our approach preserves the full nonparametric expressivity of the model and can make use of sparse Gaussian processes to greatly reduce computational complexity.