Numerical methods and analysis for a class of fractional advection-dispersion models

In this paper, a class of fractional advection–dispersion models (FADMs) is considered. These models include five fractional advection–dispersion models, i.e., the time FADM, the mobile/immobile time FADM with a time Caputo fractional derivative 0 < γ < 1, the space FADM with two sides Riemann–Liouville derivatives, the time–space FADM and the time fractional advection–diffusion-wave model with damping with index 1 < γ < 2. These equations can be used to simulate the regional-scale anomalous dispersion with heavy tails. We propose computationally effective implicit numerical methods for these FADMs. The stability and convergence of the implicit numerical methods are analysed and compared systematically. Finally, some results are given to demonstrate the effectiveness of theoretical analysis.

Gene duplication is an evolutionary mechanism for expanding spectral diversity in the long-wavelength photopigments of butterflies

Butterfly long-wavelength (L) photopigments are interesting for comparative studies of adaptive evolution because of the tremendous phenotypic variation that exists in their wavelength of peak absorbance (lambda(max) value). Here we present a comprehensive survey of L photopigment variation by measuring lambda(max) in 12 nymphalid and 1 riodinid species using epi-microspectrophotometry. Together with previous data, we find that L photopigment lambda(max) varies from 510-565 nm in 22 nymphalids, with an even broader 505- to 600-nm range in riodinids. We then surveyed the L opsin genes for which lambda(max) values are available as well as from related taxa and found 2 instances of L opsin gene duplication within nymphalids, in Hermeuptychia hermes and Amathusia phidippus, and 1 instance within riodinids, in the metalmark butterfly Apodemia mormo. Using maximum parsimony and maximum likelihood ancestral state reconstructions to map the evolution of spectral shifts within the L photopigments of nymphalids, we estimate the ancestral pigment had a lambda(max) = 540 nm +/- 10 nm standard error and that blueshifts in wavelength have occurred at least 4 times within the family. We used ancestral state reconstructions to investigate the importance of several amino acid substitutions (Ile17Met, Ala64Ser, Asn70Ser, and Ser137Ala) previously shown to have evolved under positive selection that are correlated with blue spectral shifts. These reconstructions suggest that the Ala64Ser substitution has indeed occurred along the newly identified blueshifted L photopigment lineages. Substitutions at the other 3 sites may also be involved in the functional diversification of L photopigments. Our data strongly suggest that there are limits to the evolution of L photopigment spectral shifts among species with only one L opsin gene and that opsin gene duplication broadens the potential range of lambda(max) values.

Stability and convergence of a finite volume method for the space fractional advection-dispersion equation

We consider the space fractional advection–dispersion equation, which is obtained from the classical advection–diffusion equation by replacing the spatial derivatives with a generalised derivative of fractional order. We derive a finite volume method that utilises fractionally-shifted Grünwald formulae for the discretisation of the fractional derivative, to numerically solve the equation on a finite domain with homogeneous Dirichlet boundary conditions. We prove that the method is stable and convergent when coupled with an implicit timestepping strategy. Results of numerical experiments are presented that support the theoretical analysis.

Dry powder inhaler formulations : effect of carrier size on the drug dispersion

Background: The size of the carrier influences drug aerosolization from a dry powder inhaler (DPI) formulation. Lactose particles with irregular shape and rough surface in a variety of sizes are additionally used as carriers; however, contradictory reports exist regarding the effect of carrier size on the dispersion of drug. We examined the influence of the spherical particle size of the biodegradable polylactide-co-glycolide (PLGA) carrier on the aerosolization of a model drug, salbutamol sulphate (SS). Methods: Four different sizes (20-150 µm) of polymer carriers were fabricated using solvent evaporation technique and the dispersion of SS from these carriers was measured by a Twin Stage Impinger (TSI). The size and morphological properties of polymer carriers were determined by laser diffraction and SEM, respectively. Results: The FPF was found to increase from 5.6% to 21.3% with increasing carrier sizeup to150 µm. Conclusions: The aerosolization of drug increased linearly with the size of polymer carriers. For a fixed mass of drug particles in a formulation, the mass of drug particles per unit area of carriers is higher in formulations containing the larger carriers, which leads to an increase in the dispersion of drug due to the increased mechanical forces occurred between the carriers and the device walls.

A novel numerical approximation for the space fractional advection-dispersion equation

In this paper, we consider a space fractional advection–dispersion equation. The equation is obtained from the standard advection–diffusion equation by replacing the first- and second-order space derivatives by the Riesz fractional derivatives of order β1 ∈ (0, 1) and β2 ∈ (1, 2], respectively. The fractional advection and dispersion terms are approximated by using two fractional centred difference schemes. A new weighted Riesz fractional finite-difference approximation scheme is proposed. When the weighting factor θ equals 12, a second-order accuracy scheme is obtained. The stability, consistency and convergence of the numerical approximation scheme are discussed. A numerical example is given to show that the numerical results are in good agreement with our theoretical analysis.

A comparison of finite difference and finite volume methods for solving the space fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non-classical diffusion or dispersion; that is, not adequately described by the classical theory of Brownian motion and Fick's law. We consider a space fractional advection-dispersion equation based on a fractional Fick's law. The equation involves the Riemann-Liouville fractional derivative which arises from assuming that particles may make large jumps. Finite difference methods for solving this equation have been proposed by Meerschaert and Tadjeran. In the variable coefficient case, the product rule is first applied, and then the Riemann-Liouville fractional derivatives are discretised using standard and shifted Grunwald formulas, depending on the fractional order. In this work, we consider a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Grunwald formulas are used to discretise the fractional derivatives at control volume faces. We compare the two methods for several case studies from the literature, highlighting the convenience of the finite volume approach.

The effect of Fe doping on adsorption of CO2/N2within carbon nanotubes : a density functional theory study with dispersion corrections

An ab initio density functional theory (DFT) study with correction for dispersive interactions was performed to study the adsorption of N2 and CO2 inside an (8, 8) single-walled carbon nanotube. We find that the approach of combining DFT and van der Waals correction is very effective for describing the long-range interaction between N2/CO2 and the carbon nanotube (CNT). Surprisingly, exohedral doping of an Fe atom onto the CNT surface will only affect the adsorption energy of the quadrupolar CO2 molecule inside the CNT (20–30%), and not that of molecular N2. Our results suggest the feasibility of enhancement of CO2/N2 separation in CNT-based membranes by using exohedral doping of metal atoms.

Mixing and dispersion of pollutants emitted from an outboard motor

This paper quantifies the mixing and dispersion from an outboard motor by field experiments in a small subtropical waterway. Organic dye was used as a surrogate for exhaust emissions and was mixed with uncontaminated creek water before being dispersed into the creek. Dye concentrations were measured with an array of concentration probes stationed in the creek. The data were then processed and fitted with a power law function. The corresponding dispersion constants agreed well with the literature. However, the amplitude was lower than the IMO equation but higher than the correlation from laboratory tests. Results for dye concentration intermittency (presence of dye) are presented for the first time from such field measurements and show significant mixing in-homogeneity.

Are consumers fooled by discounts? An experimental test in a consumer search environment

In this article, we investigate experimentally whether people search optimally and how price promotions influence search behaviour. We implement a sequential search task with exogenous price dispersion in a baseline treatment and introduce discounts in two experimental treatments. We find that search behaviour is roughly consistent with optimal search but also observe some discount biases. If subjects do not know in advance where discounts are offered, the purchase probability is increased by 19 percentage points in shops with discounts, even after controlling for the benefit of the discount and for risk preferences. If consumers know in advance where discounts are given, then the bias is only weakly significant and much smaller (7 percentage points).

Degradation of simazine from aqueous solutions by diatomite-supported nanosized zero-valent iron composite materials

A novel composite material based on deposition of nanosized zero-valent iron (nZVI) particles on acid-leached diatomite was synthesised for the removal of a chlorinated contaminant in water. The nZVI /diatomite composites were characterized by X-ray diffraction, scanning electron microscopy, elemental analysis, transmission electron microscopy and X-ray photoelectron spectroscopy. Compared with the pure nZVI particles, better dispersion of nZVI particles on the surface or inside the pores of diatom shells was observed. The herbicide simazine was selected as the model chlorinated contaminant and the removal efficiency by nZVI /diatomite composite was compared with that of the pristine nZVI and commercial iron powder. It was found that the diatomite supported nZVI composite material prepared by centrifugation exhibits relatively better efficient activity in decomposition of simazine than commercial Fe, lab synthesized nZVI and composite material prepared via rotary evaporation, and the optimum experimental conditions were obtained based on a series of batch experiments. This study on immobilizing nZVI particles onto diatomite opens a new avenue for the practical application of nZVI and the diatomite-supported nanosized zero-valent iron composite materials have potential applications in environmental remediation.

Dry powder inhaler formulations-effect of polymer carrier size on the drug dispersion

Background The size of the carrier influences the aerosolization of drug from a dry powder inhaler (DPI) formulation. Currently, lactose monohydrate particles in a variety of sizes are preferably used in carrier based DPI formulations of various drugs; however, contradictory reports exist regarding the effect of the size of the carrier on the dispersion of drug. In this study we examined the influence of the intrinsic particle size of the polymeric carrier on the aerosolization of a model drug salbutamol sulphate (SS). Methods Four different sizes (20–150 lm) of polymer carriers were fabricated using solvent evaporation technique and the dispersion of SS particles from these carriers was measured by a Twin Stage Impinger (TSI). The size and morphological properties of polymer carriers were by laser diffraction and SEM, respectively. Results The FPF from these carriers was found to be increasing from 5.6% to 21.3% with increasing the carrier size. The FPF was found to be greater (21%) with the highest particle size of the carrier (150 lm). Conclusions The aerosolization of drug was dependent on the size of polymer carriers. The smaller size of the carrier resulted in lower FPF which was increased with increasing the carrier size. For a fixed mass of drug particles in a formulation, the mass of drug particles per unit area of carriers is higher in formulations containing the larger carriers, which leads to an increase in the dispersion of drug due to the increased mechanical forces occurred between the carriers and the device walls.

Bearing Fault Diagnostics Using the Spectral Pattern Recognition

In the field of diagnostics of rolling element bearings, the development of sophisticated techniques, such as Spectral Kurtosis and 2nd Order Cyclostationarity, extended the capability of expert users to identify not only the presence, but also the location of the damage in the bearing. Most of the signal-analysis methods, as the ones previously mentioned, result in a spectrum-like diagram that presents line frequencies or peaks in the neighbourhood of some theoretical characteristic frequencies, in case of damage. These frequencies depend only on damage position, bearing geometry and rotational speed. The major improvement in this field would be the development of algorithms with high degree of automation. This paper aims at this important objective, by discussing for the first time how these peaks can draw away from the theoretical expected frequencies as a function of different working conditions, i.e. speed, torque and lubrication. After providing a brief description of the peak-patterns associated with each type of damage, this paper shows the typical magnitudes of the deviations from the theoretical expected frequencies. The last part of the study presents some remarks about increasing the reliability of the automatic algorithm. The research is based on experimental data obtained by using artificially damaged bearings installed in a gearbox.

Hot spot detection and spatio-temporal dispersion of dengue fever in Hanoi, Vietnam

INTRODUCTION Dengue fever (DF) in Vietnam remains a serious emerging arboviral disease, which generates significant concerns among international health authorities. Incidence rates of DF have increased significantly during the last few years in many provinces and cities, especially Hanoi. The purpose of this study was to detect DF hot spots and identify the disease dynamics dispersion of DF over the period between 2004 and 2009 in Hanoi, Vietnam. METHODS Daily data on DF cases and population data for each postcode area of Hanoi between January 1998 and December 2009 were obtained from the Hanoi Center for Preventive Health and the General Statistic Office of Vietnam. Moran's I statistic was used to assess the spatial autocorrelation of reported DF. Spatial scan statistics and logistic regression were used to identify space-time clusters and dispersion of DF. RESULTS The study revealed a clear trend of geographic expansion of DF transmission in Hanoi through the study periods (OR 1.17, 95% CI 1.02-1.34). The spatial scan statistics showed that 6/14 (42.9%) districts in Hanoi had significant cluster patterns, which lasted 29 days and were limited to a radius of 1,000 m. The study also demonstrated that most DF cases occurred between June and November, during which the rainfall and temperatures are highest. CONCLUSIONS There is evidence for the existence of statistically significant clusters of DF in Hanoi, and that the geographical distribution of DF has expanded over recent years. This finding provides a foundation for further investigation into the social and environmental factors responsible for changing disease patterns, and provides data to inform program planning for DF control.

A comparison of finite difference and finite volume methods for solving the space-fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non- classical diffusion or dispersion which is not adequately described by the classical theory of Brownian motion and Fick’s law. We consider a space-fractional advection-dispersion equation based on a fractional Fick’s law. Zhang et al. [Water Resources Research, 43(5)(2007)] considered such an equation with variable coefficients, which they dis- cretised using the finite difference method proposed by Meerschaert and Tadjeran [Journal of Computational and Applied Mathematics, 172(1):65-77 (2004)]. For this method the presence of variable coef- ficients necessitates applying the product rule before discretising the Riemann–Liouville fractional derivatives using standard and shifted Gru ̈nwald formulas, depending on the fractional order. As an alternative, we propose using a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Gru ̈nwald formulas are used to discretise the Riemann–Liouville fractional derivatives at control volume faces, eliminating the need for product rule expansions. We compare the two methods for several case studies, highlighting the convenience of the finite volume approach.

Elucidation of double bond position in unsaturated lipids by ozone electrospray ionization mass spectrometry

The position(s) of carbon-carbon double bonds within lipids can dramatically affect their structure and reactivity and thus has a direct bearing on biological function. Commonly employed mass spectrometric approaches to the characterization of complex lipids, however, fail to localize sites of unsaturation within the molecular structure and thus cannot distinguish naturally occurring regioisomers. In a recent communication \[Thomas, M. C.; Mitchell, T. W.; Blanksby, S. J. J. Am. Chem. Soc. 2006, 128, 58-59], we have presented a new technique for the elucidation of double bond position in glycerophospholipids using ozone-induced fragmentation within the source of a conventional electrospray ionization mass spectrometer. Here we report the on-line analysis, using ozone electrospray mass spectrometry (OzESI-MS), of a broad range of common unsaturated lipids including acidic and neutral glycerophospholipids, sphingomyelins, and triacylglycerols. All lipids analyzed are found to form a pair of chemically induced fragment ions diagnostic of the position of each double bond(s) regardless of the polarity, the number of charges, or the adduction (e.g., \[M - H](-), \[M - 2H](2-), \[M + H](+), \[M + Na](+), \[M + NH4](+)). The ability of OzESI-MS to distinguish lipids that differ only in the position of the double bonds is demonstrated using the glycerophosphocholine standards, GPCho(9Z-18:1/9Z-18:1) and GPCho(6Z-18:1/6Z-18:1). While these regioisomers cannot be differentiated by their conventional tandem mass spectra, the OzESI-MS spectra reveal abundant fragment ions of distinctive mass-to-charge ratio (m/z). The approach is found to be sufficiently robust to be used in conjunction with the m/z 184 precursor ion scans commonly employed for the identification of phosphocholine-containing lipids in shotgun lipidomic analyses. This tandem OzESI-MS approach was used, in conjunction with conventional tandem mass spectral analysis, for the structural characterization of an unknown sphingolipid in a crude lipid extract obtained from a human lens. The OzESI-MS data confirm the presence of two regioisomers, namely, SM(d18:0/15Z-24:1) and SM(d18:0/17Z-24:1), and suggest the possible presence of a third isomer, SM(d18:0/19Z-24:1), in lower abundance. The data presented herein demonstrate that OzESI-MS is a broadly applicable, on-line approach for structure determination and, when used in conjunction with established tandem mass spectrometric methods, can provide near complete structural characterization of a range of important lipid classes. As such, OzESI-MS may provide important new insight into the molecular diversity of naturally occurring lipids.