A new type of high-order elements based on the mesh-free interpolations

We propose a new type of high-order elements that incorporates the mesh-free Galerkin formulations into the framework of finite element method. Traditional polynomial interpolation is replaced by mesh-free interpolations in the present high-order elements, and the strain smoothing technique is used for integration of the governing equations based on smoothing cells. The properties of high-order elements, which are influenced by the basis function of mesh-free interpolations and boundary nodes, are discussed through numerical examples. It can be found that the basis function has significant influence on the computational accuracy and upper-lower bounds of energy norm, when the strain smoothing technique retains the softening phenomenon. This new type of high-order elements shows good performance when quadratic basis functions are used in the mesh-free interpolations and present elements prove advantageous in adaptive mesh and nodes refinement schemes. Furthermore, it shows less sensitive to the quality of element because it uses the mesh-free interpolations and obeys the Weakened Weak (W2) formulation as introduced in [3, 5].

A sub‒domain smoothed Galerkin method for solid mechanics problems

A sub‒domain smoothed Galerkin method is proposed to integrate the advantages of mesh‒free Galerkin method and FEM. Arbitrarily shaped sub‒domains are predefined in problems domain with mesh‒free nodes. In each sub‒domain, based on mesh‒free Galerkin weak formulation, the local discrete equation can be obtained by using the moving Kriging interpolation, which is similar to the discretization of the high‒order finite elements. Strain smoothing technique is subsequently applied to the nodal integration of sub‒domain by dividing the sub‒domain into several smoothing cells. Moreover, condensation of DOF can also be introduced into the local discrete equations to improve the computational efficiency. The global governing equations of present method are obtained on the basis of the scheme of FEM by assembling all local discrete equations of the sub‒domains. The mesh‒free properties of Galerkin method are retained in each sub‒domain. Several 2D elastic problems have been solved on the basis of this newly proposed method to validate its computational performance. These numerical examples proved that the newly proposed sub‒domain smoothed Galerkin method is a robust technique to solve solid mechanics problems based on its characteristics of high computational efficiency, good accuracy, and convergence.

A coupled SPH-DEM model for fluid and solid mechanics of apple parenchyma cells during drying

A coupled SPH-DEM based two-dimensional (2-D) micro-scale single cell model is developed to predict basic cell-level shrinkage effects of apple parenchyma cells during air drying. In this newly developed drying model, Smoothed Particle Hydrodynamics (SPH) is used to model the low Reynolds Number fluid motions of the cell protoplasm, and a Discrete Element Method (DEM) is employed to simulate the polymer-like cell wall. Simulations results reasonably agree with published experimental drying results on cellular shrinkage properties such as cellular area, diameter and perimeter. These preliminary results indicate that the model is effective for the modelling and simulation of apple parenchyma cells during air drying.

A particle-based micromechanics approach to simulate structural changes of plant cells during drying

This paper is concerned with applying a particle-based approach to simulate the micro-level cellular structural changes of plant cells during drying. The objective of the investigation was to relate the micro-level structural properties such as cell area, diameter and perimeter to the change of moisture content of the cell. Model assumes a simplified cell which consists of two basic components, cell wall and cell fluid. The cell fluid is assumed to be a Newtonian fluid with higher viscosity compared to water and cell wall is assumed to be a visco-elastic solid boundary located around the cell fluid. Cell fluid is modelled with Smoothed Particle Hydrodynamics (SPH) technique and for the cell wall; a Discrete Element Method (DEM) is used. The developed model is two-dimensional, but accounts for three-dimensional physical properties of real plant cells. Drying phenomena is simulated as fluid mass reductions and the model is used to predict the above mentioned structural properties as a function of cell fluid mass. Model predictions are found to be in fairly good agreement with experimental data in literature and the particle-based approach is demonstrated to be suitable for numerical studies of drying related structural deformations. Also a sensitivity analysis is included to demonstrate the influence of key model parameters to model predictions.

Dissimilarities in alignment-free methods for phylogenetic analysis based on genomes

Whole genome sequences are generally accepted as excellent tools for studying evolutionary relationships. Due to the problems caused by the uncertainty in alignment, existing tools for phylogenetic analysis based on multiple alignments could not be directly applied to the whole-genome comparison and phylogenomic studies. There has been a growing interest in alignment-free methods for phylogenetic analysis using complete genome data. The “distances” used in these alignment-free methods are not proper distance metrics in the strict mathematical sense. In this study, we first review them in a more general frame — dissimilarity. Then we propose some new dissimilarities for phylogenetic analysis. Last three genome datasets are employed to evaluate these dissimilarities from a biological point of view.

Silylation of layered double hydroxides via a calcination−rehydration route

Silylated layered double hydroxides (LDHs) were synthesized through a surfactant-free method involving an in situ condensation of silane with the surface hydroxyl group of LDHs during its reconstruction in carbonate solution. X-ray diffraction (XRD) patterns showed the silylation reaction occurred on the external surfaces of LDHs layers. The successful silylation was evidenced by 29Si cross-polarization magic-angle spinning nuclear magnetic resonance (29Si CP/MAS NMR) spectroscopy, attenuated total reflection Fourier transform infrared (ATR FTIR) spectroscopy, and infrared emission spectroscopy (IES). The ribbon shaped crystallites with a “rodlike” aggregation were observed through transmission electron microscopy (TEM) images. The aggregation was explained by the T2 and T3 types of linkage between adjacent silane molecules as indicated in the 29Si NMR spectrum. In addition, the silylated products show high thermal stability by maintained Si related bands even when the temperature was increased to 1000 °C as observed in IES spectra.

Promise and pitfalls of the Immunochip

Genomewide association studies (GWAS) have proven a powerful hypothesis-free method to identify common disease-associated variants. Even quite large GWAS, however, have only at best identified moderate proportions of the genetic variants contributing to disease heritability. To provide cost-effective genotyping of common and rare variants to map the remaining heritability and to fine-map established loci, the Immunochip Consortium has developed a 200,000 SNP chip that has been produced in very large numbers for a fraction of the cost of GWAS chips. This chip provides a powerful tool for immunogenetics gene mapping.

Genome-wide association studies and musculoskeletal diseases

Bone and joint diseases are major causes of morbidity and mortality worldwide, and their prevalence is increasing as the average population age increases. Most common musculoskeletal diseases show significant heritability, and few have treatments that prevent disease or can induce true treatment-free, disease-free remission. Furthermore, despite valiant efforts of hypothesis-driven research, our understanding of the etiopathogenesis of these conditions is, with few exceptions, at best moderate. Therefore, there has been a long-standing interest in genetics research in musculoskeletal disease as a hypothesis-free method for investigating disease etiopathogenesis. Important contributions have been made through the identification of monogenic causes of disease, but the holy grail of human genetics research has been the identification of the genes responsible for common diseases. The development of genome-wide association (GWA) studies has revolutionized this field, and led to an explosion in the number of genes identified that are definitely involved in musculoskeletal disease pathogenesis. However, this approach will not identify all common disease genes, and although the current progress is exciting and proves the potential of this research discipline, other approaches will be required to identify many of the types of genetic variation likely to be involved.

Robust estimating functions and bias correction for longitudinal data analysis

Robust methods are useful in making reliable statistical inferences when there are small deviations from the model assumptions. The widely used method of the generalized estimating equations can be "robustified" by replacing the standardized residuals with the M-residuals. If the Pearson residuals are assumed to be unbiased from zero, parameter estimators from the robust approach are asymptotically biased when error distributions are not symmetric. We propose a distribution-free method for correcting this bias. Our extensive numerical studies show that the proposed method can reduce the bias substantially. Examples are given for illustration.

A point interpolation method with locally smoothed strain field (PIM-LS2) for mechanics problems using triangular mesh

A point interpolation method with locally smoothed strain field (PIM-LS2) is developed for mechanics problems using a triangular background mesh. In the PIM-LS2, the strain within each sub-cell of a nodal domain is assumed to be the average strain over the adjacent sub-cells of the neighboring element sharing the same field node. We prove theoretically that the energy norm of the smoothed strain field in PIM-LS2 is equivalent to that of the compatible strain field, and then prove that the solution of the PIM- LS2 converges to the exact solution of the original strong form. Furthermore, the softening effects of PIM-LS2 to system and the effects of the number of sub-cells that participated in the smoothing operation on the convergence of PIM-LS2 are investigated. Intensive numerical studies verify the convergence, softening effects and bound properties of the PIM-LS2, and show that the very ‘‘tight’’ lower and upper bound solutions can be obtained using PIM-LS2.

A mass-conservative control volume-finite element method for solving Richards’ equation in heterogeneous porous media

We present a mass-conservative vertex-centred finite volume method for efficiently solving the mixed form of Richards’ equation in heterogeneous porous media. The spatial discretisation is particularly well-suited to heterogeneous media because it produces consistent flux approximations at quadrature points where material properties are continuous. Combined with the method of lines, the spatial discretisation gives a set of differential algebraic equations amenable to solution using higher-order implicit solvers. We investigate the solution of the mixed form using a Jacobian-free inexact Newton solver, which requires the solution of an extra variable for each node in the mesh compared to the pressure-head form. By exploiting the structure of the Jacobian for the mixed form, the size of the preconditioner is reduced to that for the pressure-head form, and there is minimal computational overhead for solving the mixed form. The proposed formulation is tested on two challenging test problems. The solutions from the new formulation offer conservation of mass at least one order of magnitude more accurate than a pressure head formulation, and the higher-order temporal integration significantly improves both the mass balance and computational efficiency of the solution.

Jacobian-free Newton-Krylov methods with GPU acceleration for computing nonlinear ship wave patterns

The nonlinear problem of steady free-surface flow past a submerged source is considered as a case study for three-dimensional ship wave problems. Of particular interest is the distinctive wedge-shaped wave pattern that forms on the surface of the fluid. By reformulating the governing equations with a standard boundary-integral method, we derive a system of nonlinear algebraic equations that enforce a singular integro-differential equation at each midpoint on a two-dimensional mesh. Our contribution is to solve the system of equations with a Jacobian-free Newton-Krylov method together with a banded preconditioner that is carefully constructed with entries taken from the Jacobian of the linearised problem. Further, we are able to utilise graphics processing unit acceleration to significantly increase the grid refinement and decrease the run-time of our solutions in comparison to schemes that are presently employed in the literature. Our approach provides opportunities to explore the nonlinear features of three-dimensional ship wave patterns, such as the shape of steep waves close to their limiting configuration, in a manner that has been possible in the two-dimensional analogue for some time.

Ultra sensitive label free surface enhanced Raman spectroscopy method for the detection of biomolecules

We present a proof of concept for a novel nanosensor for the detection of ultra-trace amounts of bio-active molecules in complex matrices. The nanosensor is comprised of gold nanoparticles with an ultra-thin silica shell and antibody surface attachment, which allows for the immobilization and direct detection of bio-active molecules by surface enhanced Raman spectroscopy (SERS) without requiring a Raman label. The ultra-thin passive layer (~1.3 nm thickness) prevents competing molecules from binding non-selectively to the gold surface without compromising the signal enhancement. The antibodies attached on the surface of the nanoparticles selectively bind to the target molecule with high affinity. The interaction between the nanosensor and the target analyte result in conformational rearrangements of the antibody binding sites, leading to significant changes in the surface enhanced Raman spectra of the nanoparticles when compared to the spectra of the un-reacted nanoparticles. Nanosensors of this design targeting the bio-active compounds erythropoietin and caffeine were able to detect ultra-trace amounts the analyte to the lower quantification limits of 3.5×10−13 M and 1×10−9 M, respectively.