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

B-Spline potential function for maximum a-posteriori image reconstruction in fluorescence microscopy

An iterative image reconstruction technique employing B-Spline potential function in a Bayesian framework is proposed for fluorescence microscopy images. B-splines are piecewise polynomials with smooth transition, compact support and are the shortest polynomial splines. Incorporation of the B-spline potential function in the maximum-a-posteriori reconstruction technique resulted in improved contrast, enhanced resolution and substantial background reduction. The proposed technique is validated on simulated data as well as on the images acquired from fluorescence microscopes (widefield, confocal laser scanning fluorescence and super-resolution 4Pi microscopy). A comparative study of the proposed technique with the state-of-art maximum likelihood (ML) and maximum-a-posteriori (MAP) with quadratic potential function shows its superiority over the others. B-Spline MAP technique can find applications in several imaging modalities of fluorescence microscopy like selective plane illumination microscopy, localization microscopy and STED. (C) 2015 Author(s).

Mesh-free approximations via the error reproducing kernel method and applications to nonlinear systems developing shocks

Error estimates for the error reproducing kernel method (ERKM) are provided. The ERKM is a mesh-free functional approximation scheme [A. Shaw, D. Roy, A NURBS-based error reproducing kernel method with applications in solid mechanics, Computational Mechanics (2006), to appear (available online)], wherein a targeted function and its derivatives are first approximated via non-uniform rational B-splines (NURBS) basis function. Errors in the NURBS approximation are then reproduced via a family of non-NURBS basis functions, constructed using a polynomial reproduction condition, and added to the NURBS approximation of the function obtained in the first step. In addition to the derivation of error estimates, convergence studies are undertaken for a couple of test boundary value problems with known exact solutions. The ERKM is next applied to a one-dimensional Burgers equation where, time evolution leads to a breakdown of the continuous solution and the appearance of a shock. Many available mesh-free schemes appear to be unable to capture this shock without numerical instability. However, given that any desired order of continuity is achievable through NURBS approximations, the ERKM can even accurately approximate functions with discontinuous derivatives. Moreover, due to the variation diminishing property of NURBS, it has advantages in representing sharp changes in gradients. This paper is focused on demonstrating this ability of ERKM via some numerical examples. Comparisons of some of the results with those via the standard form of the reproducing kernel particle method (RKPM) demonstrate the relative numerical advantages and accuracy of the ERKM.

The Reproducing Kernel DMS-FEM: 3D Shape Functions and Applications to Linear Solid Mechanics

We propose a family of 3D versions of a smooth finite element method (Sunilkumar and Roy 2010), wherein the globally smooth shape functions are derivable through the condition of polynomial reproduction with the tetrahedral B-splines (DMS-splines) or tensor-product forms of triangular B-splines and ID NURBS bases acting as the kernel functions. While the domain decomposition is accomplished through tetrahedral or triangular prism elements, an additional requirement here is an appropriate generation of knotclouds around the element vertices or corners. The possibility of sensitive dependence of numerical solutions to the placements of knotclouds is largely arrested by enforcing the condition of polynomial reproduction whilst deriving the shape functions. Nevertheless, given the higher complexity in forming the knotclouds for tetrahedral elements especially when higher demand is placed on the order of continuity of the shape functions across inter-element boundaries, we presently emphasize an exploration of the triangular prism based formulation in the context of several benchmark problems of interest in linear solid mechanics. In the absence of a more rigorous study on the convergence analyses, the numerical exercise, reported herein, helps establish the method as one of remarkable accuracy and robust performance against numerical ill-conditioning (such as locking of different kinds) vis-a-vis the conventional FEM.

Online character recognition using regression techniques

This paper introduces a scheme for classification of online handwritten characters based on polynomial regression of the sampled points of the sub-strokes in a character. The segmentation is done based on the velocity profile of the written character and this requires a smoothening of the velocity profile. We propose a novel scheme for smoothening the velocity profile curve and identification of the critical points to segment the character. We also porpose another method for segmentation based on the human eye perception. We then extract two sets of features for recognition of handwritten characters. Each sub-stroke is a simple curve, a part of the character, and is represented by the distance measure of each point from the first point. This forms the first set of feature vector for each character. The second feature vector are the coeficients obtained from the B-splines fitted to the control knots obtained from the segmentation algorithm. The feature vector is fed to the SVM classifier and it indicates an efficiency of 68% using the polynomial regression technique and 74% using the spline fitting method.

Size-dependent free flexural vibration behavior of functionally graded nanoplates

In this paper, size dependent linear free flexural vibration behavior of functionally graded (FG) nanoplates are investigated using the iso-geometric based finite element method. The field variables are approximated by non-uniform rational B-splines. The nonlocal constitutive relation is based on Eringen's differential form of nonlocal elasticity theory. The material properties are assumed to vary only in the thickness direction and the effective properties for the FG plate are computed using Mori-Tanaka homogenization scheme. The accuracy of the present formulation is demonstrated considering the problems for which solutions are available. A detailed numerical study is carried out to examine the effect of material gradient index, the characteristic internal length, the plate thickness, the plate aspect ratio and the boundary conditions on the global response of the FG nanoplate. From the detailed numerical study it is seen that the fundamental frequency decreases with increasing gradient index and characteristic internal length. (c) 2012 Elsevier B.V. All rights reserved.

Spatial B-jump at sudden channel enlargements with abrupt drop

An analytical and experimental study of the hydraulic jump in stilling basins with abrupt drop and sudden enlargement, called the spatial B-jump here, is carried out for finding the sequent depth ratio and resulting energy dissipation. The spatial B-jump studied has its toe downstream of the expansion section, and the stream lines at the toe are characterized by downward curvature. An expression is obtained for the sequent depth ratio based on the momentum equation with suitable assumptions for the extra pressure force term because of the abrupt drop in the bed and sudden enlargement in the basin width. Predictions compare favorably with experiments. It is shown that the spatial B-jump needs less tailwater depth, thereby enhancing the stability of the jump when compared either with spatial jump, which forms in sudden expanding channels, or with B-jump, which forms in a channel with an abrupt drop in bed. It is also shown that there is a significant increase in relative energy loss for the spatial B-jump compared to either the spatial jump or B-jump alone.

B- and T-cell epitopes of tropomyosin, the major shrimp allergen

Seafood allergy is often encountered on ingestion of crustaceans such as shrimp, lobster, crab, and crayfish (1). On eating cooked shrimp, sensitive individuals experience a wide spectrum of reactions ranging from abdominal discomfort to anaphylaxis. The presence of cross-reacting heat-stable allergens in crustacean food was first recognized by Hoffman et al. (2) and Lehrer et al. (3). Subsequently, the major allergen was isolated and characterized from the shrimp species Paneaus indicus (Pen i 1) (4) and I? aztecm (Pen a 1) (5). Pen i 1 (originally designated Sa-TI) and Pen a 1, with mol. mass of 34 and 36 kDa, respectively, contain 301 and 312 amino-acid residues with a predominance of gluta- mate/glutamine and asparatate/asparagine.

Effect of microstructure on the mechanical behavior of b-modified ti-6al-4v alloys

Small additions of B to Titanium alloys refine the as-cast microstructure significantly and hence improve their mechanical performance. In this work, tensile, fracture and fatigue properties of the as-cast and HIPed Ti-6Al-4V alloy with hypoeutectic wt.% of B additions have been examined, with particular emphasis on identifying the microstructural length scale that controls the mechanical properties of these alloys.

Polymorphism in B-DNA - X-ray-Diffraction Studies on Li-DNA Fibers

From X-ray diffraction studies it is generally believed that B-DNA has the structural parameters n = 10 and h = 3.4 Å. However, for the first time we report that polymorphism in the B-form can be observed in DNA fibres. This was achieved by the precise control of salt and humidity in fibres and by the application of the precession method of X-ray diffraction to DNA fibres. The significant result obtained is that n = 10 is not observed for crystalline fibre patterns. In fact, n = 10 and h = 3.4 Å are not found to occur simultaneously. Instead, a range of values, n = 9.6–10.0 and h = 3.35 Å–3.41 Å is observed.

Critical Cation Balance In B-]Z Transition - Role Of Li+

The sodium salt of poly(dG-dC) is known to exhibit a B + Z transition in the presence of various cations and 60% alcohol. We here show that the lithium salt of poly(dG-dC) does not undergo B 4 Z transition in the presence of 60% alcohol since Li’ with its large hydration shell cannot stabilize the Z-form. On the other hand, high concentrations of Mg2* or micromolar concentrations of the cobalt hexamine complex which are known to stabilize the Z-form can compete with Li+ for charge neutraIization and hence bring about a B--t Z transition in the same polymer. From the model building studies the mode of action of the cobalt-hexamine complex in stabilizing the Z-form is postulated.

Fibre diffraction of lithium DNA shows structural variability and deviation from a regular helical structure for the B-form

Recently, reports have appeared which show structural variations in B-DNA and indicate deviations from a uniform helical structure. We report for the first time that these indications are also present in the B-form fibre diffraction patterns for the lithium salt of natural DNA. We have used an improved method of controlling the salt concentration in the fibres. Our results are based on the appearance and disappearance of meridional reflections on different layer lines depending upon the salt.

Competing A-site and B-site driven ferroelectric instabilities in the (1-x)PbTiO3-(x)BiAlO3 system

The system (1-x)PbTiO3-(x)BiAlO3 has been investigated with regard to its solid solubility, crystal structure, microstructure, and ferroelectric transition. The unit cell volume and the tetragonality exhibit anomalous behavior near x=0.10. The Curie point (T-C) of PbTiO3 was however found to be nearly unchanged. The study seems to suggest that the decrease in the stability of the ferroelectric state due to dilution of the Ti-sublattice by smaller sized Al+3 ions is compensated by the increase in the ferroelectric stability by the Bi+3 ions.

Beta-Ketoacyl-ACP Synthase I/II from Plasmodium falciparum (PfFabB/F)-Is it B or F?

Condensing enzymes play an important and decisive role in terms of fatty acid composition of any organism. They can be classified as condensing enzymes involved in initiating the cycle and enzymes involved in elongating the initiated fatty acyl chain. In E. coli, two isoforms for the elongation condensing enzymes (FabB and FabF) exists whereas Plasmodium genome contains only one isoform. By in vitro complementation studies in E. coli CY244 cells, we show that PfFabB/ functions like E. coli FabF as the growth of the mutant cells could rescued only in the presence of oleic acid. But unlike bacterial enzyme, PfFabB/F does not increase the cis-vaccenic acid content in the mutant cells upon lowering the growth temperature. This study thus highlights the distinct properties of P. falciparum FabF which sets it apart from E. coli and most other enzymes of this family, described so far.

Small local variations in B-form DNA lead to a large variety of global geometries which can accommodate most DNA-binding protein motifs

An important question of biological relevance is the polymorphism of the double-helical DNA structure in its free form, and the changes that it undergoes upon protein-binding. We have analysed a database of free DNA crystal structures to assess the inherent variability of the free DNA structure and have compared it with a database of protein-bound DNA crystal structures to ascertain the protein-induced variations.