Analytical and numerical treatment of oscillatory mixed differential equations with differentiable delays and advances

NOTICE: this is the author’s version of a work that was accepted for publication in Journal of computational and applied mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of computational and applied mathematics, 235(2011), doi: 10.1016/j.cam.2011.04.041This article discusses the oscillatory behaviour of the differential equation of mixed type

Optical properties of intermetallic compounds from first principles calculations: A search for the ideal plasmonic material

First principles calculations have been used to predict the optical properties for a range of intermetallic compounds for which little or no experimental optical data are currently available. Density functional theory combined with the random phase approximation is used to calculate the dielectric functions for these compounds. The aim of this work is to investigate how the band edge and plasma frequency vary with composition in order to identify materials with promising plasmonic properties. Towards this end the intermetallic compounds chosen are composed of elements which on their own have reasonable optical properties for plasmonic applications. The position of the band edge relative to the plasma frequency is most favourable in the simple binary compounds formed from the alkali plus noble metals NaAu, KAu and KAg. In particular, for KAu the band edge and plasma frequency occur at almost the same frequency, and hence the imaginary part of the dielectric function is practically zero for frequencies below the plasma frequency. In addition, the plasma frequency in this compound is at relatively low frequency, promising a material with strong plasmon response in the infrared. © 2009 IOP Publishing Ltd

Search for the ideal lasmonic nanoshell: the effects of surface scattering and alternatives to gold and silver

The optical absorption efficiency of nanospheres and nanoshells of the elements Na, K, Al, Ag, and Au are compared, and the effects of surface scattering, as introduced by the billiard model [Moroz, A. J. Phys. Chem. C 2008, 112 (29), 10641-10652] are discussed. We find that the introduction of surface scattering has comparatively little effect on the optimized absorption efficiency of nanospheres, with the maximum absorption efficiency of K nanospheres falling from 14.7 to 13.3. Conversely, the reduction in absorption efficiency in nanoshells is substantial. This effect is compounded in metals with higher plasma frequency. We show that the high comparative plasma frequencies in silver and gold result in a greatly reduced optimized absorption efficiency when compared to nanoshells in the absence of surface scattering. Whereas sodium and potassium, with low plasma frequencies, are not affected as much. © 2009 American Chemical Society

Universal scaling of local plasmons in chains of metal spheres

The position, width, extinction, and electric field of localized plasmon modes in closely-coupled linear chains of small spheres are investigated. A dipole-like model is presented that separates the universal geometric factors from the specific metal permittivity. An electrostatic surface integral method is used to deduce universal parameters that are confirmed against results for different metals (bulk experimental Ag, Au, Al, K) calculated using retarded vector spherical harmonics and finite elements. The mode permittivity change decays to an asymptote with the number of particles in the chain, and changes dramatically from 1/f3to 1/f 1/2 as the gap fraction (ratio of gap between spheres to their diameter), f, gets smaller. Scattering increases significantly with closer coupling. The mode sharpness, strength and electric field for weakly retarded calculations are consistent with electrostatic predictions once the effect of radiative damping is accounted for. ©2010 Optical Society of America

Damping of plasmons of closely coupled sphere chains due to disordered gaps

The damping of plasmons due to structural disorder may have important practical consequences. Here, we use spherical harmonic expansions to quantify the damping of plasmons of ensembles of closely coupled sphere chains with moderately disordered gaps. We show that the quadratic shift of average resonance position due to disorder is maintained in the transition from weak to close coupling, but the sensitivity to disorder increases. Further, we find that although the main peak is most often damped and broadened by disorder, it is possible for the optical extinction of disordered gold chains to increase slightly due to red-skew into a region with more favorable metal properties. © 2011 American Chemical Society

Plasmonic resonances of closely coupled gold nanosphere chains

The optical properties of an ordered array of gold nanospheres have been calculated using the T-matrix method in the regime where the near-fields of the particles are strongly coupled. The array consists of a one-dimensional chain of spheres of 15 nm diameter where the number of spheres in the chain and interparticle spacing is varied. Calculations have been performed with chains up to 150 particles in length and with an interparticle spacing between 0.5 and 30 nm. Incident light polarized along the axis of the chain (longitudinal) and perpendicular (transverse) to it are considered, and in the latter case for wavevectors along and perpendicular to the chain axis. For fixed chain length the longitudinal plasmon resonance red shifts, relative to the resonance of an isolated sphere, as the interparticle spacing is reduced. The shift in the plasmon resonance does not appear to follow an exponential dependence upon gap size for these extended arrays of particles. The peak shift is inversely proportional to the distance, a result that is consistent with the van der Waals attraction between two spheres at short range, which also varies as 1/d. The transverse plasmon resonance shifts in the opposite direction as the interparticle gap is reduced; this shift is considerably smaller and approaches 500 nm as the gap tends to zero. Increasing the number of particles in the chain for a fixed gap has a similar effect on the longitudinal and transverse plasmon. In this case, however, the longitudinal plasmon tends toward an asymptotic value with increasing chain length, with the asymptotic value determined by the interparticle spacing. Here, the approach to the asymptote is exponential with a characteristic length of approximately two particles, at small interparticle spacings. This approach to an asymptote as the chain length becomes infinite has been verified in a finite element calculation with periodic boundary conditions. © 2009 American Chemical Society

Effects of Par1a Deletion on Tubulointerstitial Fibrosis in Folic Acid Mouse Models of Renal Injury

Chronic Kidney Disease (CKD) affects 1 out of 7 adults in the United States and causes significant morbidity and mortality. Development of tubulointerstitial fibrosis, and the accompanying loss of functional tubular cells, leads to CKD progression. The Notch signaling pathway is required for renal development, however, sustained Notch activation in adult mice induces tubulointerstitial fibrosis. Dual deletion of Par1a and Par1b, serine threonine kinases, in developing mouse kidneys impaired Notch activation and resulted in the formation of abnormal glomeruli and proximal tubules. Deletion of either Par1a or 1b does not affect kidney development.We hypothesize that Par1a or 1b deletion in mice would protect against folic acid (FA) induced tubulointerstitial fibrosis. FA models of renal fibrosis were induced in Par1a WT and Par1a KO mice with intraperitoneal injections of 250 mg/kg FA dissolved in 300 nM NaHCO3. Mice were examined 7 days after injection—the time of earliest fibrosis and peak Notch expression. Sirius red collagen staining was used to quantify the severity of fibrosis. Immunohistochemical staining for Notch signaling components and Par1a were performed. It was observed that Par1a expression was increased after FA injection. Par1a colocalized in tubules with increased Jag1 expression. Sirius red staining demonstrated less fibrosis in Par1a KO vs. WT mice. Together, our results suggest Par1a deletion may be protective against renal fibrosis. Par1-Notch interactions may be mediated by effects on Jag1. Par1-Notch signaling could be a novel target for therapeutic intervention and potentially attenuate CKD progression

Numerical treatment of oscillary functional differential equations

NOTICE: this is the author’s version of a work that was accepted for publication in Journal of computational and applied mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of computational and applied mathematics, 234(2010), doi: 10.1016/j.cam.2010.01.035This preprint is concerned with oscillatory functional differential equations (that is, those equations where all the solutions oscillate) under a numerical approximation. Our interest is in the preservation of qualitative properties of solutions under a numerical discretisation. We give conditions under which an equation is oscillatory, and consider whether the discrete schemes derived using linear v-methods will also be oscillatory. We conclude with some general theor

Cost of Salmonella infections in Australia, 2015

Copyright Ó, International Association for Food Protection Gastroenteritis caused from infections with Salmonella enterica (salmonellosis) causes significant morbidity in Australia. In addition to acute gastroenteritis, approximately 8.8% of people develop irritable bowel syndrome (IBS) and 8.5% of people develop reactive arthritis (ReA). We estimated the economic cost of salmonellosis and associated sequel illnesses in Australia in a typical year circa 2015. We estimated incidence, hospitalizations, other health care usage, absenteeism, and premature mortality for four age groups using a variety of complementary data sets. We calculated direct costs (health care) and indirect costs (lost productivity and premature mortality) by using Monte Carlo simulation to estimate 90% credible intervals (CrI) around our point estimates. We estimated that 90,833 cases, 4,312 hospitalizations, and 19 deaths occurred from salmonellosis in Australia circa 2015 at a direct cost of AUD 23.8 million (90% CrI, 19.3 to 28.9 million) and a total cost of AUD 124.4 million (90% CrI, 107.4 to 143.1 million). When IBS and ReA were included, the estimated direct cost was 35.7 million (90% CrI, 29.9 to 42.7 million) and the total cost was AUD 146.8 million (90% CrI, 127.8 to 167.9 million). Foodborne infections were responsible for AUD 88.9 million (90% CrI, 63.9 to 112.4 million) from acute salmonellosis and AUD 104.8 million (90% CrI, 75.5 to 132.3 million) when IBS and ReA were included. Targeted interventions to prevent illness could considerably reduce costs and societal impact from Salmonella infections and sequel illnesses in Australia

Disseminated Histoplasmosis in a Patient with Advanced HIV Disease—Lessons Learnt from Bangladesh

Histoplasmosis is a systemic fungal disease, also known as Darling's disease, caused by the dimorphic fungus Histoplasma capsulatum. It is usually self-limiting or localized in immunecompetent individuals whereas in patients with acquired immune deficiency syndrome (AIDS), it occurs in the disseminated form in 95% of cases. Although histoplasmosis predominates in the Americas (United States and Latin America, including Brazil) as an important infection among AIDS patients, it is not common in Bangladesh. In contrast, tuberculosis is extremely common in Bangladesh, with an estimated prevalence of 387 per 100,000 people. Here, a confirmed case of disseminated histoplasmosis is reported in Bangladesh in a known HIV-positive patient, which was initially suspected to be extrapulmonary tuberculosis