Numerical simulation of the Riesz fractional diffusion equation with a nonlinear source term

In this paper, A Riesz fractional diffusion equation with a nonlinear source term (RFDE-NST) is considered. This equation is commonly used to model the growth and spreading of biological species. According to the equivalent of the Riemann-Liouville(R-L) and Gr¨unwald-Letnikov(GL) fractional derivative definitions, an implicit difference approximation (IFDA) for the RFDE-NST is derived. We prove the IFDA is unconditionally stable and convergent. In order to evaluate the efficiency of the IFDA, a comparison with a fractional method of lines (FMOL) is used. Finally, two numerical examples are presented to show that the numerical results are in good agreement with our theoretical analysis.

Integrity determination of RTK solutions in precision farming applications

Integrity of Real Time Kinematic (RTK) positioning solutions relates to the confidential level that can be placed in the information provided by the RTK system. It includes the ability of the RTK system to provide timely valid warnings to users when the system must not be used for the intended operation. For instance, in the controlled traffic farming (CTF) system that controls traffic separates wheel beds and root beds, RTK positioning error causes overlap and increases the amount of soil compaction. The RTK system’s integrity capacity can inform users when the actual positional errors of the RTK solutions have exceeded Horizontal Protection Levels (HPL) within a certain Time-To-Alert (TTA) at a given Integrity Risk (IR). The later is defined as the probability that the system claims its normal operational status while actually being in an abnormal status, e.g., the ambiguities being incorrectly fixed and positional errors having exceeded the HPL. The paper studies the required positioning performance (RPP) of GPS positioning system for PA applications such as a CTF system, according to literature review and survey conducted among a number of farming companies. The HPL and IR are derived from these RPP parameters. A RTK-specific rover autonomous integrity monitoring (RAIM) algorithm is developed to determine the system integrity according to real time outputs, such as residual square sum (RSS), HDOP values. A two-station baseline data set is analyzed to demonstrate the concept of RTK integrity and assess the RTK solution continuity, missed detection probability and false alarm probability.

Can tissue engineering concepts advance tumor biology research?

Advances in tissue engineering have traditionally led to the design of scaffold- or matrix-based culture systems that better reflect the biological, physical and biochemical environment of the natural extracellular matrix. Although their clinical applications in regenerative medicine tend to receive most of the attention, it is obvious that other areas of biomedical research could be well served by the powerful tools that have already been developed in tissue engineering. In this article, we review the recent literature to demonstrate how tissue engineering platforms can enhance in vitro and in vivo models of tumorigenesis and thus hold great promise to contribute to future cancer research.

Effects of switching time on output voltages of a multilevel inverter used in high frequency applications

Employing multilevel inverters is a proper solution to reduce harmonic content of output voltage and electromagnetic interference in high power electronic applications. In this paper, a new pulse width modulation method for multilevel inverters is proposed in which power devices’ on-off switching times have been considered. This method can be surveyed in order to analyse the effect of switching time on harmonic contents of output voltage in high frequency applications when a switching time is not negligible compared to a switching cycle. Fast Fourier transform calculation and analysis of output voltage waveforms and harmonic contents with regard to switching time variation are presented in this paper for a single phase (3, 5)-level inverters used in high voltage and high frequency converters. Mathematical analysis and MATLAB simulation results have been carried out to validate the proposed method.

Structure–property relationships of silk-modified mesoporous bioglass scaffolds

Porous mesopore-bioglass (MBG) scaffolds have been proposed as a new class of bone regeneration materials due to their apatite-formation and drug-delivery properties; however, the material’s inherent brittleness and high degradation and surface instability are major disadvantages, which compromise its mechanical strength and cytocompatibility as a biological scaffold. Silk, on the other hand, is a native biomaterial and is well characterized with respect to biocompatibility and tensile strength. In this study we set out to investigate what effects blending silk with MBG had on the physiochemical, drug-delivery and biological properties of MBG scaffolds with a view to bone tissue engineering applications. Transmission electron microscopy (TEM), scanning electron microscopy (SEM) and Fourier transform infrared spectroscopy (FTIR) were the methods used to analyze the inner microstructure, pore size and morphology, and composition of MBG scaffolds, before and after addition of silk. The effect of silk modification on the mechanical property of MBG scaffolds was determined by testing the compressive strength of the scaffolds and also compressive strength after degradation over time. The drug-delivery potential was evaluated by the release of dexamethasone (DEX) from the scaffolds. Finally, the cytocompatibility of silk-modified scaffolds was investigated by the attachment, morphology, proliferation, differentiation and bone-relative gene expression of bone marrow stromal cells (BMSCs). The results showed that silk modification improved the uniformity and continuity of pore network of MBG scaffolds, and maintained high porosity (94%) and large-pore size (200–400 mm). There was a significant improvement in mechanical strength, mechanical stability, and control of burst release of DEX in silkmodified MBG scaffolds. Silk modification also appeared to provide a better environment for BMSC attachment, spreading, proliferation, and osteogenic differentiation on MBG scaffolds.