Skeletonization by crystallization

A skeleton of a planar contour is a set of centres of bitangent circles lying inside the contour. If contour of a planar shape was made up of a spatial distribution of sodium acetate crystals the propagating crystallization patterns would implement distance transformation, or thinning, of the contour. In such a case, boundaries between colliding patterns represent skeleton of the planar shape. In laboratory experiments we demonstrate that a supersaturated solution of a sodium acetate is a massively parallel processor. In this sodium-acetate processor data are inputted as spatial distribution of nucleation sites, information is transmitted via propagating patterns of crystallization and results of computation are represented by boundaries between stationary domains of crystals.     

An improved parallel compact scheme for domain-decoupled simulation of turbulence

An improved domain-decoupled compact scheme for first and second spatial derivatives is proposed for domain-decomposition-based parallel computational fluid dynamics. The method improves the accuracy of previously developed decoupled schemes and preserves the accuracy and bandwidth properties of fully coupled compact schemes, even for a very large degree of parallelism, and enables the Navier-Stokes equations to be solved independently on each processor. The scheme is analysed using Fourier analysis and error analysis, and tested on one-dimensional wave-packet propagation, a two-dimensional vortex convection problem, and in the direct numerical simulation of the three-dimensional Taylor-Green vortex problem and turbulent channel flow. Our results demonstrate the scheme's effectiveness in performing direct numerical simulation of turbulence in terms of accuracy and scalability.     

Unsteady response of chain-branching premixed-flames to pressure waves

Motivated by some recent experimental results that are incompatible with the standard one-step model, we present an analytical study of the unsteady response of flames to acoustic waves in the framework of a simple two-step chemistry model, using conditions that are appropriate to approximately describe lean methane–air flames. The calculated response functions are qualitatively different from those obtained with the standard one-step model. The results are sufficiently encouraging to suggest that the analysis should be extended in the near future to more detailed kinetics schemes.     

The pushing gate in a planar Coulomb crystal using a flat-top laser beam

We propose a pushing gate for entangling two ions in a planar Coulomb crystal in the view of realizing large-scale quantum simulations. A tightly focused laser is irradiated from the direction perpendicular to the crystal plane and its spatial intensity profile generates a state-dependent force. We analyze the error sources in this scheme and obtain low infidelity.     

A hybrid Padé ADI scheme of higher‐order for convection–diffusion problems

A high‐order Padé alternating direction implicit (ADI) scheme is proposed for solving unsteady convection–diffusion problems. The scheme employs standard high‐order Padé approximations for spatial first and second derivatives in the convection‐diffusion equation. Linear multistep (LM) methods combined with the approximate factorization introduced by Beam and Warming (J. Comput. Phys. 1976; 22 : 87–110) are applied for the time integration. The approximate factorization imposes a second‐order temporal accuracy limitation on the ADI scheme independent of the accuracy of the LM method chosen for the time integration. To achieve a higher‐order temporal accuracy, we introduce a correction term that reduces the splitting error. The resulting scheme is carried out by repeatedly solving a series of pentadiagonal linear systems producing a computationally cost effective solver. The effects of the approximate factorization and the correction term on the stability of the scheme are examined. A modified wave number analysis is performed to examine the dispersive and dissipative properties of the scheme. In contrast to the HOC‐based schemes in which the phase and amplitude characteristics of a solution are altered by the variation of cell Reynolds number, the present scheme retains the characteristics of the modified wave numbers for spatial derivatives regardless of the magnitude of cell Reynolds number. The superiority of the proposed scheme compared with other high‐order ADI schemes for solving unsteady convection‐diffusion problems is discussed. A comparison of different time discretizations based on LM methods is given. Copyright © 2009 John Wiley & Sons, Ltd.     

A high-accuracy temporal–spatial pseudospectral method for time-periodic unsteady fluid flow and heat transfer problems

A temporal–spatial pseudospectral (TSP) method is proposed for the high-accuracy solutions of time-periodic unsteady fluid flow and heat transfer problems. In this method, both the spatial and temporal derivative terms in the governing equations are computed by pseudospectral method. The spatial derivatives are computed through Chebyshev and Lagrange polynomials while the time derivatives are computed by Fourier series. The TSP method is capable of directly finding out the periodic state solutions without the necessity to resolve the initial transient state solutions, hence holds high computational efficiency and high numerical accuracy properties for the time-periodic problems. This method is validated by three 2D benchmark problems: the time-periodic incompressible flow with exact solutions; the natural convection in enclosure with time-periodic temperature on one sidewall, and on both sidewalls. The TSP results fit well the exact solutions or the benchmark solutions and the TSP accuracy is much higher than the time marching spatial pseudospectral accuracy. Some time-dependent fluid flow and heat transfer characteristic parameters are analysed. The proposed TSP method could be further extended to more complex time-periodic unsteady fluid flow and heat transfer problems where high-accuracy results are required.     

The Dempster–Shafer calculus for statisticians

The Dempster–Shafer (DS) theory of probabilistic reasoning is presented in terms of a semantics whereby every meaningful formal assertion is associated with a triple (p, q, r) where p is the probability “for” the assertion, q is the probability “against” the assertion, and r is the probability of “don’t know”. Arguments are presented for the necessity of “don’t know”. Elements of the calculus are sketched, including the extension of a DS model from a margin to a full state space, and DS combination of independent DS uncertainty assessments on the full space. The methodology is applied to inference and prediction from Poisson counts, including an introduction to the use of join-tree model structure to simplify and shorten computation. The relation of DS theory to statistical significance testing is elaborated, introducing along the way the new concept of “dull” null hypothesis.     

Introducing unsteady non‐uniform source terms into the lattice Boltzmann model

Taking body forces into account is not new for the lattice Boltzmann method, yet most of the existing approaches can only treat steady and uniform body forces. To manage situations with time‐ and space‐dependent body forces or source terms, this paper proposes a new approach through theoretical derivation and numerical verification. The method by attaching an extra term to the lattice Boltzmann equation is still used, but the expression of the extra term is modified. It is the modified extra term that achieves the particularity of the new approach. This approach can not only introduce unsteady and non‐uniform body forces into momentum equations, but is also able to add an arbitrary source term to the continuity equation. Both the macroscopic equations from multi‐scale analysis and the simulated results of typical examples show that the accuracy with second‐order convergence can be guaranteed within incompressible limit. Copyright © 2007 John Wiley & Sons, Ltd.