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.

Identification of dispersion-dependent hexagonal cavity modes of an individual ZnO nanonail

The hexagonal resonator characteristics of an individual ZnO-nanonail’s head were investigated via spatially resolved cathodoluminescence (CL) at room temperature. The positions of most of distinct CL peaks in visible range were well matched to those of whispering gallery modes (WGMs) of a hexagonal dielectric cavity when we took birefringence and dispersion of refractive indices into account. The broad and weak peaks for TE polarization in long wavelength range were consistent with refractive-index values below the threshold for total internal inflection. CL peaks that were not matched to WGMs were identified as either triangular quasi-WGM or Fabry–Pérot resonance modes.

Instantaneous phase of the autocorrelation and robustness to signal-dependent noise

The phase of an analytic signal constructed from the autocorrelation function of a signal contains significant information about the shape of the signal. Using Bedrosian's (1963) theorem for the Hilbert transform it is proved that this phase is robust to multiplicative noise if the signal is baseband and the spectra of the signal and the noise do not overlap. Higher-order spectral features are interpreted in this context and shown to extract nonlinear phase information while retaining robustness. The significance of the result is that prior knowledge of the spectra is not required.

Investigation of the expression of the EphB4 receptor tyrosine kinase in prostate carcinoma

Background: The EphB4 receptor tyrosine kinase has been reported as increased in tumours originating from several different tissues and its expression in a prostate cancer xenograft model has been reported. Methods: RT-PCR, western blotting and immunohistochemical techniques were used to examine EphB4 expression and protein levels in human prostate cancer cell lines LNCaP, DU145 and PC3. Immunohistochemistry was also used to examine localisation of EphB4 in tissue samples from 15 patients with prostate carcinomas. Results: All three prostate cancer cell lines expressed the EphB4 gene and protein. EphB4 immunoreactivity in vivo was significantly greater in human prostate cancers as compared with matched normal prostate epithelium and there appeared to be a trend towards increased expression with higher grade disease. Conclusions: EphB4 is expressed in prostate cancer cell lines with increased expression in human prostate cancers when compared with matched normal tissue. EphB4 may therefore be a useful anti-prostate cancer target. © 2005 Lee et al., licensee BioMed Central Ltd.

MHD natural convection flow from an isothermal horizontal circular cylinder under consideration of temperature dependent viscosity

Magnetohydrodynamic (MHD) natural convection laminar flow from an iso-thermal horizontal circular cylinder immersed in a fluid with viscosity proportional to a linear function of temperature will be discussed with numerical simulations. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear system of partial differential equa-tions are reduced to convenient form, which are solved numerically by two very efficient methods, namely, (i) Implicit finite difference method together with Keller box scheme and (ii) Direct numerical scheme. Numerical results are presented by velocity and temperature distributions of the fluid as well as heat transfer characteristics, namely the shearing stress and the local heat transfer rate in terms of the local skin-friction coefficient and the local Nusselt number for a wide range of magnetohydrodynamic parameter, viscosity-variation parameter and viscous dissipation parameter. MHD flow in this geometry with temperature dependent viscosity is absent in the literature. The results obtained from the numerical simulations have been veri-fied by two methodologies.

Temperature dependent electrical resistivity in expoxy : multiwall carbon nanotube nanocomposites

Thin films of expoxy nanocomposites modified by multiwall carbon nanotubes (MWCNTs) were prepared by shear mixing and spin casting. The electrical behaviour and its dependence with temperature between 243 and 353 degrees Kelvin were characterized by measuring the direct current (DC) conductivity. Depending on the fabrication process, both linear and non-linear relationships between conductivity and temperature were observed. In addition, the thermal history also played a role in dictating the conductivity. The implications of these observations for potential application of these files as strain sensors are discussed.

Time-dependent rates of molecular evolution

For over half a century, it has been known that the rate of morphological evolution appears to vary with the time frame of measurement. Rates of microevolutionary change, measured between successive generations, were found to be far higher than rates of macroevolutionary change inferred from the fossil record. More recently, it has been suggested that rates of molecular evolution are also time dependent, with the estimated rate depending on the timescale of measurement. This followed surprising observations that estimates of mutation rates, obtained in studies of pedigrees and laboratory mutation-accumulation lines, exceeded long-term substitution rates by an order of magnitude or more. Although a range of studies have provided evidence for such a pattern, the hypothesis remains relatively contentious. Furthermore, there is ongoing discussion about the factors that can cause molecular rate estimates to be dependent on time. Here we present an overview of our current understanding of time-dependent rates. We provide a summary of the evidence for time-dependent rates in animals, bacteria and viruses. We review the various biological and methodological factors that can cause rates to be time dependent, including the effects of natural selection, calibration errors, model misspecification and other artefacts. We also describe the challenges in calibrating estimates of molecular rates, particularly on the intermediate timescales that are critical for an accurate characterization of time-dependent rates. This has important consequences for the use of molecular-clock methods to estimate timescales of recent evolutionary events.

Intensity dependent residual amplitude modulation in electro-optic phase modulators

Residual amplitude modulation (RAM) mechanisms in electro-optic phase modulators are detrimental in applications that require high purity phase modulation of the incident laser beam. While the origins of RAMare not fully understood, measurements have revealed that it depends on the beam properties of the laser as well as the properties of the medium. Here we present experimental and theoretical results that demonstrate, for the first time, the dependence of RAM production in electro-optic phase modulators on beam intensity. The results show an order of magnitude increase in the level of RAM, around 10 dB, with a fifteenfold enhancement in the input intensity from 12 to 190 mW/mm 2. We show that this intensity dependent RAM is photorefractive in origin. © 2012 Optical Society of America.

Polarization dependent photorefractive amplitude modulation production in MgO:LiNbO 3 phase modulators

We present experimental and theoretical results of the intensity dependence of residual amplitude modulation (RAM) production in electro-optic phase modulators. By utilizing the anisotropy of the medium, we show that RAM has a photorefractive origin.