Time-dependent fractional advection–diffusion equations by an implicit MLS meshless method

Recently, many new applications in engineering and science are governed by a series of fractional partial differential equations (FPDEs). Unlike the normal partial differential equations (PDEs), the differential order in a FPDE is with a fractional order, which will lead to new challenges for numerical simulation, because most existing numerical simulation techniques are developed for the PDE with an integer differential order. The current dominant numerical method for FPDEs is Finite Difference Method (FDM), which is usually difficult to handle a complex problem domain, and also hard to use irregular nodal distribution. This paper aims to develop an implicit meshless approach based on the moving least squares (MLS) approximation for numerical simulation of fractional advection-diffusion equations (FADE), which is a typical FPDE. The discrete system of equations is obtained by using the MLS meshless shape functions and the meshless strong-forms. The stability and convergence related to the time discretization of this approach are then discussed and theoretically proven. Several numerical examples with different problem domains and different nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the FADE.

An implicit RBF meshless approach for time fractional diffusion equations

This paper aims to develop an implicit meshless approach based on the radial basis function (RBF) for numerical simulation of time fractional diffusion equations. The meshless RBF interpolation is firstly briefed. The discrete equations for two-dimensional time fractional diffusion equation (FDE) are obtained by using the meshless RBF shape functions and the strong-forms of the time FDE. The stability and convergence of this meshless approach are discussed and theoretically proven. Numerical examples with different problem domains and different nodal distributions are studied to validate and investigate accuracy and efficiency of the newly developed meshless approach. It has proven that the present meshless formulation is very effective for modeling and simulation of fractional differential equations.

Cloning and characterization of a novel human gene related to vascular endothelial growth factor

This paper describes the cloning and characterization of a new member of the vascular endothelial growth factor (VEGF) gene family, which we have designated VRF for VEGF-related-factor. Sequencing of cDNAs from a human fetal brain library and RT-PCR products from normal and tumor tissue cDNA pools indicate two alternatively spliced messages with open reading frames of 621 and 564 bp, respectively. The predicted proteins differ at their carboxyl ends resulting from a shift in the open reading frame. Both isoforms show strong homology to VEGF at their amino termini, but only the shorter isoform maintains homology to VEGF at its carboxyl terminus and conserves all 16 cysteine residues of VEGF165. Similarity comparisons of this isoform revealed overall protein identity of 48% and conservative substitution of 69% with VEGF189. VRF is predicted to contain a signal peptide, suggesting that it may be a secreted factor. The VRF gene maps to the D11S750 locus at chromosome band 11q13, and the protein coding region, spanning approximately 5 kb, is comprised of 8 exons that range in size from 36 to 431 bp. Exons 6 and 7 are contiguous and the two isoforms of VRF arise through alternate splicing of exon 6. VRF appears to be ubiquitously expressed as two transcripts of 2.0 and 5.5 kb; the level of expression is similar among normal and malignant tissues.

Targeting mutant fibroblast growth factor receptors in cancer

Fibroblast growth factor receptors (FGFRs) play diverse roles in the control of cell proliferation, cell differentiation, angiogenesis and development. Activating the mutations of FGFRs in the germline has long been known to cause a variety of skeletal developmental disorders, but it is only recently that a similar spectrum of somatic FGFR mutations has been associated with human cancers. Many of these somatic mutations are gain-of-function and oncogenic and create dependencies in tumor cell lines harboring such mutations. A combination of knockdown studies and pharmaceutical inhibition in preclinical models has further substantiated genomically altered FGFR as a therapeutic target in cancer, and the oncology community is responding with clinical trials evaluating multikinase inhibitors with anti-FGFR activity and a new generation of specific pan-FGFR inhibitors.

Vertical growth and resonator properties of hexagonally shaped zinc oxide nanonails

We synthesized vertically aligned nail-shaped ZnO nanocrystal arrays on silicon substrates via a combination of a carbothermal reduction method and textured ZnO seeding layers that were precoated on silicon substrates by thermally decomposing zinc acetate, and studied their optical properties using cathodoluminescence (CL) and photoluminescence techniques. The ZnO nanonails show a sharp band-gap edge UV emission and a defect-related broad green emission. Monochromatic CL images of an individual ZnO nanonail show variations in spatial distributions of respective CL bands that had different origins. We attribute the spatial variation of CL images to an uneven distribution of luminescent defects and/or a structure-related light out-coupling from hexagonal ZnO nanostructures. The most distinct CL feature from the hexagonal head of an individual ZnO nanonail was the occurrence of a series of distinct resonant peaks within the visible wavelength range. It appeared that the head of a nanonail played the role of a hexagonal cavity so that polarizationdependent whispering gallery modes were stimulated by electron beam excitation.

Catalyst-free growth and optical properties of vertically aligned ZnO Nanorod Arrays on Si substrates covered with thin buffer layers

Vertically aligned ZnO nanorods have been grown on silicon substrates pre-coated with thin, less than 10 nm, textured ZnO seeding layers via a vapor-solid mechanism. The ZnO seeding layers, which were essential for vertical alignment of ZnO nanorods without using any metal catalyst, were prepared by decomposing zinc acetate. The structure and the luminescence properties of the ZnO nanorods synthesized onto ZnO seeding layers were investigated and their morphologies were compared with those of single-crystalline GaN substrates and silicon substrates covered with sputtered ZnO flms. Patterning of ZnO seed layers using photolithography allowed the fabrication of patterned ZnO-nanorod arrays.

Supplement : Efficient weak second-order stochastic Runge-Kutta methods for non-commutative Stratonvich stochastic differential equations

This paper gives a modification of a class of stochastic Runge–Kutta methods proposed in a paper by Komori (2007). The slight modification can reduce the computational costs of the methods significantly.

Novel numerical methods for time-space fractional reaction diffusion equations in two dimensions

We consider time-space fractional reaction diffusion equations in two dimensions. This equation is obtained from the standard reaction diffusion equation by replacing the first order time derivative with the Caputo fractional derivative, and the second order space derivatives with the fractional Laplacian. Using the matrix transfer technique proposed by Ilic, Liu, Turner and Anh [Fract. Calc. Appl. Anal., 9:333--349, 2006] and the numerical solution strategy used by Yang, Turner, Liu, and Ilic [SIAM J. Scientific Computing, 33:1159--1180, 2011], the solution of the time-space fractional reaction diffusion equations in two dimensions can be written in terms of a matrix function vector product $f(A)b$ at each time step, where $A$ is an approximate matrix representation of the standard Laplacian. We use the finite volume method over unstructured triangular meshes to generate the matrix $A$, which is therefore non-symmetric. However, the standard Lanczos method for approximating $f(A)b$ requires that $A$ is symmetric. We propose a simple and novel transformation in which the standard Lanczos method is still applicable to find $f(A)b$, despite the loss of symmetry. Numerical results are presented to verify the accuracy and efficiency of our newly proposed numerical solution strategy.

Hyaluronic acid : evaluation as a potential delivery vehicle for vitronectin:growth factor complexes in wound healing applications

We have previously reported that novel vitronectin:growth factor (VN:GF) complexes significantly increase re-epithelialization in a porcine deep dermal partial-thickness burn model. However, the potential exists to further enhance the healing response through combination with an appropriate delivery vehicle which facilitates sustained local release and reduced doses of VN:GF complexes. Hyaluronic acid (HA), an abundant constituent of the interstitium, is known to function as a reservoir for growth factors and other bioactive species. The physicochemical properties of HA confer it with an ability to sustain elevated pericellular concentrations of these species. This has been proposed to arise via HA prolonging interactions of the bioactive species with cell surface receptors and/or protecting them from degradation. In view of this, the potential of HA to facilitate the topical delivery of VN:GF complexes was evaluated. Two-dimensional (2D) monolayer cell cultures and 3D de-epidermised dermis (DED) human skin equivalent (HSE) models were used to test skin cell responses to HA and VN:GF complexes. Our 2D studies revealed that VN:GF complexes and HA stimulate the proliferation of human fibroblasts but not keratinocytes. Experiments in our 3D DED-HSE models showed that VN:GF complexes, both alone and in conjunction with HA, led to enhanced development of both the proliferative and differentiating layers in the DED-HSE models. However, there was no significant difference between the thicknesses of the epidermis treated with VN:GF complexes alone and VN:GF complexes together with HA. While the addition of HA did not enhance all the cellular responses to VN:GF complexes examined, it was not inhibitory, and may confer other advantages related to enhanced absorption and transport that could be beneficial in delivery of the VN:GF complexes to wounds.

Towards a controlled growth of self-assembled nanostructures: shaping, ordering and localization in Ge/Si heteroepitaxy.

The strain-induced self-assembly of suitable semiconductor pairs is an attractive natural route to nanofabrication. To bring to fruition their full potential for actual applications, individual nanostructures need to be combined into ordered patterns in which the location of each single unit is coupled with others and the surrounding environment. Within the Ge/Si model system, we analyze a number of examples of bottom-up strategies in which the shape, positioning, and actual growth mode of epitaxial nanostructures are tailored by manipulating the intrinsic physical processes of heteroepitaxy. The possibility of controlling elastic interactions and, hence, the configuration of self-assembled quantum dots by modulating surface orientation with the miscut angle is discussed. We focus on the use of atomic steps and step bunching as natural templates for nanodot clustering. Then, we consider several different patterning techniques which allow one to harness the natural self-organization dynamics of the system, such as: scanning tunneling nanolithography, focused ion beam and nanoindentation patterning. By analyzing the evolution of the dot assembly by scanning probe microscopy, we follow the pathway which leads to lateral ordering, discussing the thermodynamic and kinetic effects involved in selective nucleation on patterned substrates.

Relationship to the bereaved and perceptions of severity of trauma differentiate elements of posttraumatic growth

The field of bereavement and grief has been expanding to recognise the potential for growth following the loss of a loved one. This study sought to examine the effect of the relationship to the deceased and perceptions of the severity of the trauma on dimensions of posttraumatic growth. Participants were 146 people who had lost either: a) a first degree relative, b) a second degree relative, or c) a non-related friend. Results demonstrated that both severity and the relationship to the bereaved differentiate posttraumatic growth outcomes. For example, participants who had lost a first degree relative reported higher levels of growth than those who had lost a second degree relative. Consistent with previous research in general trauma populations, the more severe the loss was rated, the higher the levels of growth. Implications for practice are discussed.

Factors effecting motor vehicle growth in Dhaka

Dhaka’s traffic is heterogeneous, both motorized (MT) and non-motorized (NMT) transport are common. Traffic congestion has become a part of city dwellers’ lives. This paper explores the factors for motor vehicle growth in Dhaka. The scope of the paper will be limited to literature review...