On the diffraction of acoustic waves by a quarter-plane

This paper follows the work of A.V. Shanin on diffraction by an ideal quarter-plane. Shanin's theory, based on embedding formulae, the acoustic uniqueness theorem and spherical edge Green's functions, leads to three modified Smyshlyaev formulae, which partially solve the far-field problem of scattering of an incident plane wave by a quarter-plane in the Dirichlet case. In this paper, we present similar formulae in the Neumann case, and describe a numerical method allowing a fast computation of the diffraction coefficient using Shanin's third modified Smyshlyaev formula. The method requires knowledge of the eigenvalues of the Laplace-Beltrami operator on the unit sphere with a cut, and we also describe a way of computing these eigenvalues. Numerical results are given for different directions of incident plane wave in the Dirichlet and the Neumann cases, emphasising the superiority of the third modified Smyshlyaev formula over the other two. © 2011 Elsevier B.V.

Construction of nonparametric Bayesian models from parametric Bayes equations

We consider the general problem of constructing nonparametric Bayesian models on infinite-dimensional random objects, such as functions, infinite graphs or infinite permutations. The problem has generated much interest in machine learning, where it is treated heuristically, but has not been studied in full generality in non-parametric Bayesian statistics, which tends to focus on models over probability distributions. Our approach applies a standard tool of stochastic process theory, the construction of stochastic processes from their finite-dimensional marginal distributions. The main contribution of the paper is a generalization of the classic Kolmogorov extension theorem to conditional probabilities. This extension allows a rigorous construction of nonparametric Bayesian models from systems of finite-dimensional, parametric Bayes equations. Using this approach, we show (i) how existence of a conjugate posterior for the nonparametric model can be guaranteed by choosing conjugate finite-dimensional models in the construction, (ii) how the mapping to the posterior parameters of the nonparametric model can be explicitly determined, and (iii) that the construction of conjugate models in essence requires the finite-dimensional models to be in the exponential family. As an application of our constructive framework, we derive a model on infinite permutations, the nonparametric Bayesian analogue of a model recently proposed for the analysis of rank data.

Effects of multi-scattering on the performance of a single-beam acoustic manipulation device.

The effects of multiple scattering on acoustic manipulation of spherical particles using helicoidal Bessel-beams are discussed. A closed-form analytical solution is developed to calculate the acoustic radiation force resulting from a Bessel-beam on an acoustically reflective sphere, in the presence of an adjacent spherical particle, immersed in an unbounded fluid medium. The solution is based on the standard Fourier decomposition method and the effect of multi-scattering is taken into account using the addition theorem for spherical coordinates. Of particular interest here is the investigation of the effects of multiple scattering on the emergence of negative axial forces. To investigate the effects, the radiation force applied on the target particle resulting from a helicoidal Bessel-beam of different azimuthal indexes (m = 1 to 4), at different conical angles, is computed. Results are presented for soft and rigid spheres of various sizes, separated by a finite distance. Results have shown that the emergence of negative force regions is very sensitive to the level of cross-scattering between the particles. It has also been shown that in multiple scattering media, the negative axial force may occur at much smaller conical angles than previously reported for single particles, and that acoustic manipulation of soft spheres in such media may also become possible.

Large scale heterogeneous networks, the Davis-Wielandt shell, and graph separation

We consider a large scale network of interconnected heterogeneous dynamical components. Scalable stability conditions are derived that involve the input/output properties of individual subsystems and the interconnection matrix. The analysis is based on the Davis-Wielandt shell, a higher dimensional version of the numerical range with important convexity properties. This can be used to allow heterogeneity in the agent dynamics while relaxing normality and symmetry assumptions on the interconnection matrix. The results include small gain and passivity approaches as special cases, with the three dimensional shell shown to be inherently connected with corresponding graph separation arguments. © 2012 Society for Industrial and Applied Mathematics.

Lift and the leading edge vortex

Leading edge vortices are considered to be important in generating the high lift coefficients observed in insect flight and may therefore be relevant to micro-air vehicles. A potential flow model of an impulsively started flat plate, featuring a leading edge vortex (LEV) and a trailing edge vortex (TEV) is fitted to experimental data in order to provide insight into the mechanisms that influence the convection of the LEV and to study how the LEV contributes to lift. The potential flow model fits the experimental data best with no bound circulation, which is in accordance with Kelvin's circulation theorem. The lift-to-drag ratio is well approximated by the function 'cot α' for α > 15°, which supports the tentative conclusion that shortly after an impulsive start, at post-stall angles of attack, lift is caused non-circulatory forces and by the action of the LEV as opposed to bound circulation. Copyright © 2012 by C. W. Pitt Ford.

Closely correlating lower and upper bound plastic analysis of real slabs

An engineer assessing the load-carrying capacity of an existing reinforced concrete slab is likely to use elastic analysis to check the load at which the structure might be expected to fail in flexure or in shear. In practice, many reinforced concrete slabs are highly ductile in flexure, so an elastic analysis greatly underestimates the loads at which they fail in this mode. The use of conservative elastic analysis has led engineers to incorrectly condemn many slabs and therefore to specify unnecessary and wasteful flexural strengthening or replacement. The lower bound theorem is based on the same principles as the upper bound theorem used in yield line analysis, but any solution that rigorously satisfies the lower bound theorem is guaranteed to be a safe underestimate of the collapse load. Jackson presented a rigorous lower bound method that obtains very accurate results for complex real slabs.

Lift and the leading-edge vortex

Flapping wings often feature a leading-edge vortex (LEV) that is thought to enhance the lift generated by the wing. Here the lift on a wing featuring a leading-edge vortex is considered by performing experiments on a translating flat-plate aerofoil that is accelerated from rest in a water towing tank at a fixed angle of attack of 15°. The unsteady flow is investigated with dye flow visualization, particle image velocimetry (PIV) and force measurements. Leading-and trailing-edge vortex circulation and position are calculated directly from the velocity vectors obtained using PIV. In order to determine the most appropriate value of bound circulation, a two-dimensional potential flow model is employed and flow fields are calculated for a range of values of bound circulation. In this way, the value of bound circulation is selected to give the best fit between the experimental velocity field and the potential flow field. Early in the trajectory, the value of bound circulation calculated using this potential flow method is in accordance with Kelvin's circulation theorem, but differs from the values predicted by Wagner's growth of bound circulation and the Kutta condition. Later the Kutta condition is established but the bound circulation remains small; most of the circulation is contained instead in the LEVs. The growth of wake circulation can be approximated by Wagner's circulation curve. Superimposing the non-circulatory lift, approximated from the potential flow model, and Wagner's lift curve gives a first-order approximation of the measured lift. Lift is generated by inertial effects and the slow buildup of circulation, which is contained in shed vortices rather than bound circulation. © 2013 Cambridge University Press.

An experimental study on engine dynamics model based in-cylinder pressure estimation

The information provided by the in-cylinder pressure signal is of great importance for modern engine management systems. The obtained information is implemented to improve the control and diagnostics of the combustion process in order to meet the stringent emission regulations and to improve vehicle reliability and drivability. The work presented in this paper covers the experimental study and proposes a comprehensive and practical solution for the estimation of the in-cylinder pressure from the crankshaft speed fluctuation. Also, the paper emphasizes the feasibility and practicality aspects of the estimation techniques, for the real-time online application. In this study an engine dynamics model based estimation method is proposed. A discrete-time transformed form of a rigid-body crankshaft dynamics model is constructed based on the kinetic energy theorem, as the basis expression for total torque estimation. The major difficulties, including load torque estimation and separation of pressure profile from adjacent-firing cylinders, are addressed in this work and solutions to each problem are given respectively. The experimental results conducted on a multi-cylinder diesel engine have shown that the proposed method successfully estimate a more accurate cylinder pressure over a wider range of crankshaft angles. Copyright © 2012 SAE International.

Contraction and observer design on cones

We consider the problem of positive observer design for positive systems defined on solid cones in Banach spaces. The design is based on the Hilbert metric and convergence properties are analyzed in the light of the Birkhoff theorem. Two main applications are discussed: positive observers for systems defined in the positive orthant, and positive observers on the cone of positive semi-definite matrices with a view on quantum systems. © 2011 IEEE.

Consensus in non-commutative spaces

Convergence analysis of consensus algorithms is revisited in the light of the Hilbert distance. The Lyapunov function used in the early analysis by Tsitsiklis is shown to be the Hilbert distance to consensus in log coordinates. Birkhoff theorem, which proves contraction of the Hilbert metric for any positive homogeneous monotone map, provides an early yet general convergence result for consensus algorithms. Because Birkhoff theorem holds in arbitrary cones, we extend consensus algorithms to the cone of positive definite matrices. The proposed generalization finds applications in the convergence analysis of quantum stochastic maps, which are a generalization of stochastic maps to non-commutative probability spaces. ©2010 IEEE.

A differential lyapunov framework for contraction analysis

Lyapunov's second theorem is an essential tool for stability analysis of differential equations. The paper provides an analog theorem for incremental stability analysis by lifting the Lyapunov function to the tangent bundle. The Lyapunov function endows the state-space with a Finsler structure. Incremental stability is inferred from infinitesimal contraction of the Finsler metrics through integration along solutions curves. © 2013 IEEE.

Analysis of lateral current spreading in solar cell devices by spatially-resolved electroluminescence

Spatially-resolved electroluminescence (EL) images from solar cells contain information of local current distribution. By theoretical analysis of the EL intensity distribution, the current density distribution under a certain current bias and the sheet resistance can be obtained quantitatively. Two-dimensional numerical simulation of the current density distribution is employed to a GaInP cell, which agrees very well with the experimental results. A reciprocity theorem for current spreading is found and used to interpret the EL images from the viewpoint of current extraction. The optimization of front electrodes is discussed based on the results. (C) 2010 American Institute of Physics. [doi:10.1063/1.3431390]

Dynamics of quantum dissipation systems interacting with fermion and boson grand canonical bath ensembles: Hierarchical equations of motion approach

A hierarchical equations of motion formalism for a quantum dissipation system in a grand canonical bath ensemble surrounding is constructed on the basis of the calculus-on-path-integral algorithm, together with the parametrization of arbitrary non-Markovian bath that satisfies fluctuation-dissipation theorem. The influence functionals for both the fermion or boson bath interaction are found to be of the same path integral expression as the canonical bath, assuming they all satisfy the Gaussian statistics. However, the equation of motion formalism is different due to the fluctuation-dissipation theories that are distinct and used explicitly. The implications of the present work to quantum transport through molecular wires and electron transfer in complex molecular systems are discussed. (c) 2007 American Institute of Physics.

Quantum master equation scheme of time-dependent density functional theory to time-dependent transport in nanoelectronic devices

In this work a practical scheme is developed for the first-principles study of time-dependent quantum transport. The basic idea is to combine the transport master equation with the well-known time-dependent density functional theory. The key ingredients of this paper include (i) the partitioning-free initial condition and the consideration of the time-dependent bias voltages which base our treatment on the Runge-Gross existence theorem; (ii) the non-Markovian master equation for the reduced (many-body) central system (i.e., the device); and (iii) the construction of Kohn-Sham master equations for the reduced single-particle density matrix, where a number of auxiliary functions are introduced and their equations of motion (EOMs) are established based on the technique of spectral decomposition. As a result, starting with a well-defined initial state, the time-dependent transport current can be calculated simultaneously along with the propagation of the Kohn-Sham master equation and the EOMs of the auxiliary functions.

Formal specification and refinement of a safe train control function

Motivated by the design and development challenges of the BART case study, an approach for developing and analyzing a formal model for reactive systems is presented. The approach makes use of a domain specific language for specifying control algorithms able to satisfy competing properties such as safety and optimality. The domain language, called SPC, offers several key abstractions such as the state, the profile, and the constraint to facilitate problem specification. Using a high-level program transformation system such as HATS being developed at the University of Nebraska at Omaha, specifications in this modelling language can be transformed to ML code. The resulting executable specification can be further refined by applying generic transformations to the abstractions provided by the domain language. Problem dependent transformations utilizing the domain specific knowledge and properties may also be applied. The result is a significantly more efficient implementation which can be used for simulation and gaining deeper insight into design decisions and various control policies. The correctness of transformations can be established using a rewrite-rule based induction theorem prover Rewrite Rule Laboratory developed at the University of New Mexico.