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

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.

Smooth DMS-FEM: A new approach to solving nearly incompressible nonlinear elasto-static problems

The DMS-FEM, which enables functional approximations with C(1) or still higher inter-element continuity within an FEM-based meshing of the domain, has recently been proposed by Sunilkumar and Roy [39,40]. Through numerical explorations on linear elasto-static problems, the method was found to have conspicuously superior convergence characteristics as well as higher numerical stability against locking. These observations motivate the present study, which aims at extending and exploring the DMS-FEM to (geometrically) nonlinear elasto-static problems of interest in solid mechanics and assessing its numerical performance vis-a-vis the FEM. In particular, the DMS-FEM is shown to vastly outperform the FEM (presently implemented through the commercial software ANSYS (R)) as the former requires fewer linearization and load steps to achieve convergence. In addition, in the context of nearly incompressible nonlinear systems prone to volumetric locking and with no special numerical artefacts (e.g. stabilized or mixed weak forms) employed to arrest locking, the DMS-FEM is shown to approach the incompressibility limit much more closely and with significantly fewer iterations than the FEM. The numerical findings are suggestive of the important role that higher order (uniform) continuity of the approximated field variables play in overcoming volumetric locking and the great promise that the method holds for a range of other numerically ill-conditioned problems of interest in computational structural mechanics. (C) 2011 Elsevier Ltd. All rights reserved.

Wrinkled and slack membranes: nonlinear 3D elasticity solutions via smooth DMS-FEM and experiment

The smooth DMS-FEM, recently proposed by the authors, is extended and applied to the geometrically nonlinear and ill-posed problem of a deformed and wrinkled/slack membrane. A key feature of this work is that three-dimensional nonlinear elasticity equations corresponding to linear momentum balance, without any dimensional reduction and the associated approximations, directly serve as the membrane governing equations. Domain discretization is performed with triangular prism elements and the higher order (C1 or more) interelement continuity of the shape functions ensures that the errors arising from possible jumps in the first derivatives of the conventional C0 shape functions do not propagate because the ill-conditioned tangent stiffness matrices are iteratively inverted. The present scheme employs no regularization and exhibits little sensitivity to h-refinement. Although the numerically computed deformed membrane profiles do show some sensitivity to initial imperfections (nonplanarity) in the membrane profile needed to initiate transverse deformations, the overall patterns of the wrinkles and the deformed shapes appear to be less so. Finally, the deformed profiles, computed through the DMS FEM-based weak formulation, are compared with those obtained through an experiment on an ultrathin Kapton membrane, wherein wrinkles form because of the applied boundary displacement conditions. Comparisons with a reported experiment on a rectangular membrane are also provided. These exercises lend credence to the feasibility of the DMS FEM-based numerical route to computing post-wrinkled membrane shapes. Copyright (c) 2012 John Wiley & Sons, Ltd.

Formation of a G-quadruplex at the BCL2 major breakpoint region of the t(14;18) translocation in follicular lymphoma

The t(14;18) translocation in follicular lymphoma is one of the most common chromosomal translocations. Most breaks on chromosome 18 are located at the 3'-UTR of the BCL2 gene and are mainly clustered in the major breakpoint region (MBR). Recently, we found that the BCL2 MBR has a non-B DNA character in genomic DNA. Here, we show that single-stranded DNA modeled from the template strand of the BCL2 MBR, forms secondary structures that migrate faster on native PAGE in the presence of potassium, due to the formation of intramolecular G-quadruplexes. Circular dichroism shows evidence for a parallel orientation for G-quadruplex structures in the template strand of the BCL2 MBR. Mutagenesis and the DMS modification assay confirm the presence of three guanine tetrads in the structure. 1H nuclear magnetic resonance studies further confirm the formation of an intramolecular G-quadruplex and a representative model has been built based on all of the experimental evidence. We also provide data consistent with the possible formation of a G-quadruplex structure at the BCL2 MBR within mammalian cells. In summary, these important features could contribute to the single-stranded character at the BCL2 MBR, thereby contributing to chromosomal fragility.

Formation of a G-quadruplex at the BCL2 major breakpoint region of the t(14;18) translocation in follicular lymphoma

The t(14;18) translocation in follicular lymphoma is one of the most common chromosomal translocations. Most breaks on chromosome 18 are located at the 3'-UTR of the BCL2 gene and are mainly clustered in the major breakpoint region (MBR). Recently, we found that the BCL2 MBR has a non-B DNA character in genomic DNA. Here, we show that single-stranded DNA modeled from the template strand of the BCL2 MBR, forms secondary structures that migrate faster on native PAGE in the presence of potassium, due to the formation of intramolecular G-quadruplexes. Circular dichroism shows evidence for a parallel orientation for G-quadruplex structures in the template strand of the BCL2 MBR. Mutagenesis and the DMS modification assay confirm the presence of three guanine tetrads in the structure. 1H nuclear magnetic resonance studies further confirm the formation of an intramolecular G-quadruplex and a representative model has been built based on all of the experimental evidence. We also provide data consistent with the possible formation of a G-quadruplex structure at the BCL2 MBR within mammalian cells. In summary, these important features could contribute to the single-stranded character at the BCL2 MBR, thereby contributing to chromosomal fragility.

Novel Mn-doped chalcopyrites

Heavily Mn-doped II-VI-V-2 semiconductors, such as CdGeP2 and ZnGeP2 have been prepared by depositing Mn on single crystalline substrate at nearly 400 T in an ultra high vacuum chamber. Well-defined ferromagnetic hysteresis with a saturation behavior appears in the magnetization curve up to above room temperature. The chemical states of the ZDGeP(2):Mn interface has been clarified by a careful in situ photoemission spectroscopy. The as-prepared surface consists of Ge-rich, metallic Mn compound. In and below the sub-surface region, dilute divalent Mn species as precursors of the DMS phase exist. No MnP phase was observed at any stage of the depth profile. Theoretical band-calculation suggests that the system with vacancies (Cd, V-c, Mn)GeP2 or a non-stoichiometric (Cd, Ge, Mn)GeP2 are ferromagnetic and energetically stable although ferromagnetism is not stable in a stoichiometric compound (Cd, Mn)GeP2. (C) 2003 Elsevier Ltd. All rights reserved.

Structured Dispersion Matrices From Division Algebra Codes for Space-Time Shift Keying

We propose a novel method of constructing Dispersion Matrices (DM) for Coherent Space-Time Shift Keying (CSTSK) relying on arbitrary PSK signal sets by exploiting codes from division algebras. We show that classic codes from Cyclic Division Algebras (CDA) may be interpreted as DMs conceived for PSK signal sets. Hence various benefits of CDA codes such as their ability to achieve full diversity are inherited by CSTSK. We demonstrate that the proposed CDA based DMs are capable of achieving a lower symbol error ratio than the existing DMs generated using the capacity as their optimization objective function for both perfect and imperfect channel estimation.

Optical bio-sensing devices based on etched fiber Bragg gratings coated with carbon nanotubes and graphene oxide along with a specific dendrimer

We demonstrate that etched fiber Bragg gratings (eFBGs) coated with single walled carbon nanotubes (SWNTs) and graphene oxide (GO) are highly sensitive and accurate biochemical sensors. Here, for detecting protein concanavalin A (Con A), mannose-functionalized poly(propyl ether imine) (PETIM) dendrimers (DMs) have been attached to the SWNTs (or GO) coated on the surface modified eFBG. The dendrimers act as multivalent ligands, having specificity to detect lectin Con A. The specificity of the sensor is shown by a much weaker response (factor of similar to 2500 for the SWNT and similar to 2000 for the GO coated eFBG) to detect non specific lectin peanut agglutinin. DM molecules functionalized GO coated eFBG sensors showed excellent specificity to Con A even in the presence of excess amount of an interfering protein bovine serum albumin. The shift in the Bragg wavelength (Delta lambda(B)) with respect to the lambda(B) values of SWNT (or GO)-DM coated eFBG for various concentrations of lectin follows Langmuir type adsorption isotherm, giving an affinity constant of similar to 4 x 10(7) M-1 for SWNTs coated eFBG and similar to 3 x 10(8) M-1 for the GO coated eFBG. (C) 2014 Elsevier B.V. All rights reserved.

Exploring sand and bentonite - enhanced sand as filter media for nitrate removal

Increasing nitrate concentrations in ground water is deleterious to human health as ingestion of such water can cause methemoglobinemia in infants and even cancer in adults (desirable limit for nitrate as NO3 - 45 mg/L, IS code 10500-1991). Excess nitrate concentrations in ground water is contributed by reason being disposal of sewage and excessive use of fertilizers. Though numerous technologies such as reverse osmosis, ion exchange, electro-dialysis, permeable reactive barriers using zerovalent iron etc exists, nitrate removal continues to be one of challenging issue as nitrate ion is highly mobile within the soil strata. The tapping the denitrification potential of soil denitrifiers which are inherently available in the soil matrix is the most sustainable approach to mitigate accumulation of nitrate in ground water. The insitu denitrification of sand and bentonite enhanced sand (bentonite content = 5%) in presence of easily assimilable organic carbon such as ethanol was studied. Batch studies showed that nitrate reduction by sand follows first order kinetics with a rate constant 5.3x10(-2) hr(-1) and rate constant 4.3 x 10(-2) hr(-1) was obtained for bentonite-enhanced sand (BS) at 25 degrees C. Filter columns (height = 5 cm and diameter = 8.2 cm) were constructed using sand and bentonite-enhanced sand as filter media. The filtration rate through both the filter columns was maintained at average value of 2.60 cm/h. The nitrate removal rates through both the filter media was assessed for solution containing 22.6 mg NO3-N/L concentrations while keeping C/N mass ratio as 3. For sand filter column, the nitrate removal efficiency reached the average value of 97.6% after passing 50 pore volumes of the nitrate solution. For bentonite-enhanced sand filter column, the average nitrate removal efficiency was 83.5%. The time required for effective operation for sand filter bed was 100 hours, while bentonite-enhanced sand filter bed did not require any maturation period as that of sand filter bed for effective performance because the presence of micropores in bentonite increases the hydraulic retention time of the solution inside the filter bed.

A Smooth Discretization Bridging Finite Element and Mesh-free Methods Using Polynomial Reproducing Simplex Splines

This work sets forth a `hybrid' discretization scheme utilizing bivariate simplex splines as kernels in a polynomial reproducing scheme constructed over a conventional Finite Element Method (FEM)-like domain discretization based on Delaunay triangulation. Careful construction of the simplex spline knotset ensures the success of the polynomial reproduction procedure at all points in the domain of interest, a significant advancement over its precursor, the DMS-FEM. The shape functions in the proposed method inherit the global continuity (Cp-1) and local supports of the simplex splines of degree p. In the proposed scheme, the triangles comprising the domain discretization also serve as background cells for numerical integration which here are near-aligned to the supports of the shape functions (and their intersections), thus considerably ameliorating an oft-cited source of inaccuracy in the numerical integration of mesh-free (MF) schemes. Numerical experiments show the proposed method requires lower order quadrature rules for accurate evaluation of integrals in the Galerkin weak form. Numerical demonstrations of optimal convergence rates for a few test cases are given and the method is also implemented to compute crack-tip fields in a gradient-enhanced elasticity model.