A Smooth Finite Element Method Based on Reproducing Kernel DMS-Splines

The element-based piecewise smooth functional approximation in the conventional finite element method (FEM) results in discontinuous first and higher order derivatives across element boundaries Despite the significant advantages of the FEM in modelling complicated geometries, a motivation in developing mesh-free methods has been the ease with which higher order globally smooth shape functions can be derived via the reproduction of polynomials There is thus a case for combining these advantages in a so-called hybrid scheme or a `smooth FEM' that, whilst retaining the popular mesh-based discretization, obtains shape functions with uniform C-p (p >= 1) continuity One such recent attempt, a NURBS based parametric bridging method (Shaw et al 2008b), uses polynomial reproducing, tensor-product non-uniform rational B-splines (NURBS) over a typical FE mesh and relies upon a (possibly piecewise) bijective geometric map between the physical domain and a rectangular (cuboidal) parametric domain The present work aims at a significant extension and improvement of this concept by replacing NURBS with DMS-splines (say, of degree n > 0) that are defined over triangles and provide Cn-1 continuity across the triangle edges This relieves the need for a geometric map that could precipitate ill-conditioning of the discretized equations Delaunay triangulation is used to discretize the physical domain and shape functions are constructed via the polynomial reproduction condition, which quite remarkably relieves the solution of its sensitive dependence on the selected knotsets Derivatives of shape functions are also constructed based on the principle of reproduction of derivatives of polynomials (Shaw and Roy 2008a) Within the present scheme, the triangles also serve as background integration cells in weak formulations thereby overcoming non-conformability issues Numerical examples involving the evaluation of derivatives of targeted functions up to the fourth order and applications of the method to a few boundary value problems of general interest in solid mechanics over (non-simply connected) bounded domains in 2D are presented towards the end of the paper

Conformational studies of the triphenylphosphazenyl side chain in cyclophosphazenes. I. Crystal and molecular structure of N3P3C15(NPPh3)

The title compound, C t8H~sC15NaP4, crystallizes in the monoclinic space group P2~/n with a = 20.14 (2), b = 8.69 (1), c = 14.92 (2) A, fl = 98.8 (3) ° , Z = 4. The structure was determined from visual data and refined to R = 0-069 for 1450 reflections. The cyclophosphazene ring is non-planar. The exocyclic NPPh 3 group exhibits type I conformation [R. A. Shaw (1975). Pure Appl. Chem. 44, 317-341] in which the N-P bond is perpendicular to the adjacent P-CI bond.

The Reaction of N4P4Cl8 with Dibenzylamine: Formation of an Unusual Bicyclic Phosphazene, N4P4[N(CH2Ph)2]6(NCH2Ph), by Dealkylation

The reactions of halogenocyclotetraphosphazatetraenes N4P4X8, with nucleophiles have received little attention and only the reactions of the octachloride, N4P4Cl8, with amines have been investigated in any detail.1 Millington and Sowerby2 studied the reaction of N4P4Cl8 with dimethylamine and isolated the derivatives, N4P4Cl8-n (NMe2)n, n = 2,3,4,5,6,8;several N-methylanilino derivatives

Conformational studies of the phosphazenyl side chain in cyclophosphazenes. Part 3. Crystal and molecular structure of N3P3Cl4(NEt2)(NPPh3)

The crystal structure of N3P3Cl4(NEt2)(NPPh3) has been determined. The crystals are orthorhombic, space group Pbca, with a= 8.208(1), b= 21.890(1), c= 31.722(2)Å, Z= 8, and m.p. = 146.5 °C. The structure was solved by direct methods and refined to a final R value of 0.045 for 2 025 independent reflections. The analysis reveals significant variations in the ring P–N bond lengths. The two nitrogenous substituents, NPPh3 and NEt2, reside on the same phosphorus atom. The latter, NEt2, has an almost exact type II conformation (the plane NC2 almost perpendicular to the local NPN plane)(the first observed for a dialkylamino-group in cyclophosphazenes), the former, NPPh3, deviates from type II towards type III (in type III the plane Pring–N–Pexo makes an angle of ca. 45° with the local N–P–N ring plane). The present structure is compared with others of triphenylphosphazenyl-cyclophosphazenes and the conformation of the NPPh3 substituent and its electron supply in the ground and perturbed states are discussed.

Optimised form of acceleration correction algorithm within SPH-based simulations of impact mechanics

In the context of SPH-based simulations of impact dynamics, an optimised and automated form of the acceleration correction algorithm (Shaw and Reid, 2009a) is developed so as to remove spurious high frequency oscillations in computed responses whilst retaining the stabilizing characteristics of the artificial viscosity in the presence of shocks and layers with sharp gradients. A rational framework for an insightful characterisation of the erstwhile acceleration correction method is first set up. This is followed by the proposal of an optimised version of the method, wherein the strength of the correction term in the momentum balance and energy equations is optimised. For the first time, this leads to an automated procedure to arrive at the artificial viscosity term. In particular, this is achieved by taking a spatially varying response-dependent support size for the kernel function through which the correction term is computed. The optimum value of the support size is deduced by minimising the (spatially localised) total variation of the high oscillation in the acceleration term with respect to its (local) mean. The derivation of the method, its advantages over the heuristic method and issues related to its numerical implementation are discussed in detail. (C) 2011 Elsevier Ltd. All rights reserved.

Critical behavior at depinning of driven disordered vortex matter in 2H-NbS2

We report unusual jamming in driven ordered vortex flow in 2H-NbS2. Reinitiating movement in these jammed vortices with a higher driving force and halting it thereafter once again with a reduction in drive leads to a critical behavior centered around the depinning threshold via divergences in the lifetimes of transient states, validating the predictions of a recent simulation study Reichhardt and Olson Reichhardt, Phys. Rev. Lett. 103, 168301 (2009)] which also pointed out a correspondence between plastic depinning in vortex matter and the notion of random organization proposed Corte et al., Nat. Phys. 4, 420 (2008)] in the context of sheared colloids undergoing diffusive motion.

Stabilized SPH-based simulations of impact dynamics using acceleration-corrected artificial viscosity

Artificial viscosity in SPH-based computations of impact dynamics is a numerical artifice that helps stabilize spurious oscillations near the shock fronts and requires certain user-defined parameters. Improper choice of these parameters may lead to spurious entropy generation within the discretized system and make it over-dissipative. This is of particular concern in impact mechanics problems wherein the transient structural response may depend sensitively on the transfer of momentum and kinetic energy due to impact. In order to address this difficulty, an acceleration correction algorithm was proposed in Shaw and Reid (''Heuristic acceleration correction algorithm for use in SPH computations in impact mechanics'', Comput. Methods Appl. Mech. Engrg., 198, 3962-3974) and further rationalized in Shaw et al. (An Optimally Corrected Form of Acceleration Correction Algorithm within SPH-based Simulations of Solid Mechanics, submitted to Comput. Methods Appl. Mech. Engrg). It was shown that the acceleration correction algorithm removes spurious high frequency oscillations in the computed response whilst retaining the stabilizing characteristics of the artificial viscosity in the presence of shocks and layers with sharp gradients. In this paper, we aim at gathering further insights into the acceleration correction algorithm by further exploring its application to problems related to impact dynamics. The numerical evidence in this work thus establishes that, together with the acceleration correction algorithm, SPH can be used as an accurate and efficient tool in dynamic, inelastic structural mechanics. (C) 2011 Elsevier Ltd. All rights reserved.

Prior image-constrained l(1)-norm-based reconstruction method for effective usage of structural information in diffuse optical tomography

A novel approach that can more effectively use the structural information provided by the traditional imaging modalities in multimodal diffuse optical tomographic imaging is introduced. This approach is based on a prior image-constrained-l(1) minimization scheme and has been motivated by the recent progress in the sparse image reconstruction techniques. It is shown that the proposed framework is more effective in terms of localizing the tumor region and recovering the optical property values both in numerical and gelatin phantom cases compared to the traditional methods that use structural information. (C) 2012 Optical Society of America

Effective contrast recovery in rapid dynamic near-infrared diffuse optical tomography using l(1)-norm-based linear image reconstruction method

Traditional image reconstruction methods in rapid dynamic diffuse optical tomography employ l(2)-norm-based regularization, which is known to remove the high-frequency components in the reconstructed images and make them appear smooth. The contrast recovery in these type of methods is typically dependent on the iterative nature of method employed, where the nonlinear iterative technique is known to perform better in comparison to linear techniques (noniterative) with a caveat that nonlinear techniques are computationally complex. Assuming that there is a linear dependency of solution between successive frames resulted in a linear inverse problem. This new framework with the combination of l(1)-norm based regularization can provide better robustness to noise and provide better contrast recovery compared to conventional l(2)-based techniques. Moreover, it is shown that the proposed l(1)-based technique is computationally efficient compared to its counterpart (l(2)-based one). The proposed framework requires a reasonably close estimate of the actual solution for the initial frame, and any suboptimal estimate leads to erroneous reconstruction results for the subsequent frames.

Least squares QR-based decomposition provides an efficient way of computing optimal regularization parameter in photoacoustic tomography

A computationally efficient approach that computes the optimal regularization parameter for the Tikhonov-minimization scheme is developed for photoacoustic imaging. This approach is based on the least squares-QR decomposition which is a well-known dimensionality reduction technique for a large system of equations. It is shown that the proposed framework is effective in terms of quantitative and qualitative reconstructions of initial pressure distribution enabled via finding an optimal regularization parameter. The computational efficiency and performance of the proposed method are shown using a test case of numerical blood vessel phantom, where the initial pressure is exactly known for quantitative comparison. (C) 2013 Society of Photo-Optical Instrumentation Engineers (SPIE)

Sparse Recovery Methods Hold Promise for Diffuse Optical Tomographic Image Reconstruction

The sparse recovery methods utilize the l(p)-normbased regularization in the estimation problem with 0 <= p <= 1. These methods have a better utility when the number of independent measurements are limited in nature, which is a typical case for diffuse optical tomographic image reconstruction problem. These sparse recovery methods, along with an approximation to utilize the l(0)-norm, have been deployed for the reconstruction of diffuse optical images. Their performancewas compared systematically using both numerical and gelatin phantom cases to show that these methods hold promise in improving the reconstructed image quality.

Performance evaluation of typical approximation algorithms for nonconvex l(p)-minimization in diffuse optical tomography

The sparse estimation methods that utilize the l(p)-norm, with p being between 0 and 1, have shown better utility in providing optimal solutions to the inverse problem in diffuse optical tomography. These l(p)-norm-based regularizations make the optimization function nonconvex, and algorithms that implement l(p)-norm minimization utilize approximations to the original l(p)-norm function. In this work, three such typical methods for implementing the l(p)-norm were considered, namely, iteratively reweighted l(1)-minimization (IRL1), iteratively reweighted least squares (IRLS), and the iteratively thresholding method (ITM). These methods were deployed for performing diffuse optical tomographic image reconstruction, and a systematic comparison with the help of three numerical and gelatin phantom cases was executed. The results indicate that these three methods in the implementation of l(p)-minimization yields similar results, with IRL1 fairing marginally in cases considered here in terms of shape recovery and quantitative accuracy of the reconstructed diffuse optical tomographic images. (C) 2014 Optical Society of America