A clarification of the Goodwin model of the growth cycle

We show that there is a difficulty in the original Goodwin model which isalso found in some more recent applications. In it both the labour share and theproportion employed can exceed unity, properties which are untenable. However, weshow that the underlying dynamic structure of the model can be reformulated toensure that these variables cannot exceed unity. An illustrative example extends theoriginal model, and we argue it is both plausible and satisfies the necessary unit boxrestrictions. We show that there is a difficulty in the original Goodwin model which isalso found in some more recent applications. In it both the labour share and theproportion employed can exceed unity, properties which are untenable. However, weshow that the underlying dynamic structure of the model can be reformulated toensure that these variables cannot exceed unity. An illustrative example extends theoriginal model, and we argue it is both plausible and satisfies the necessary unit boxrestrictions

Fractional Chemotaxis Diffusion Equations

We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modelling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macro-molecular crowding. The mesoscopic models are formulated using Continuous Time Random Walk master equations and the macroscopic models are formulated with fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to include linear reaction dynamics are also derived. Finally a Monte Carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations. The model equations developed here could be used to replace Keller-Segel type equations in biological systems with transport hindered by traps, macro-molecular crowding or other obstacles.Comment: 25page

Abundances of Disk Planetary Nebulae in M31 and the Radial Oxygen Gradient

We have obtained spectra of 16 planetary nebulae in the disk of M31 and determined the abundances of He, N, O, Ne, S and Ar. Here we present the median abundances and compare them with previous M31 PN disk measurements and with PNe in the Milky Way. We also derive the radial oxygen gradient in M31, which is shallower than that in the Milky Way, even accounting for M31's larger disk scale length.Comment: 2 pages, 1 figure, 1 table, to appear in the proceedings of IAU Symposium No. 283, Planetary Nebulae: An Eye to the Futur

Fractional chemotaxis diffusion equations

We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modeling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macromolecular crowding. The mesoscopic models are formulated using continuous time random walk equations and the macroscopic models are formulated with fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to include linear reaction dynamics are also derived. Finally a Monte Carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations. The model equations developed here could be used to replace Keller-Segel type equations in biological systems with transport hindered by traps, macromolecular crowding or other obstacles

Fractional Fokker-Planck Equations for Subdiffusion with Space-and-Time-Dependent Forces

We have derived a fractional Fokker-Planck equation for subdiffusion in a general space-and- time-dependent force field from power law waiting time continuous time random walks biased by Boltzmann weights. The governing equation is derived from a generalized master equation and is shown to be equivalent to a subordinated stochastic Langevin equation.Comment: 5 page

The effect of different module configurations on the radiation tolerance of multijunction solar cells

The effect of different module configurations on the performance of multijunction (MJ) solar cells in a radiation environment was investigated. Module configuration refers to the electrical circuit in which the subcells of the multijunction cell are wired. Experimental data for AlCaAs, GaAs, InGaAs, and silicon single-junction concentrator cells subjected to 1 MeV electron irradiation was used to calculate the expected performance of AlGaAs/InGaAs, AlGa/silicon, GaAs/InGaAs, and GaAs/silicon Mj concentrator cells. These calculations included independent, series, and voltage-matched configurations. The module configuration was found to have a significant impact on the radiation tolerance characteristic of the MJ cells

A comparison of the radiation tolerance characteristics of multijunction solar cells with series and voltage-matched configurations

The effect of series and voltage-matched configurations on the performance of multijunction solar cells in a radiation environment was investigated. It was found that the configuration of the multijunction solar cell can have a significant impact on its radiation tolerance characteristics

Ga^+ beam lithography for nanoscale silicon reactive ion etching

By using a dry etch chemistry which relies on the highly preferential etching of silicon, over that of gallium (Ga), we show resist-free fabrication of precision, high aspect ratio nanostructures and microstructures in silicon using a focused ion beam (FIB) and an inductively coupled plasma reactive ion etcher (ICP-RIE). Silicon etch masks are patterned via Ga^+ ion implantation in a FIB and then anisotropically etched in an ICP-RIE using fluorinated etch chemistries. We determine the critical areal density of the implanted Ga layer in silicon required to achieve a desired etch depth for both a Pseudo Bosch (SF_6/C_4F_8) and cryogenic fluorine (SF_6/O_2) silicon etching. High fidelity nanoscale structures down to 30 nm and high aspect ratio structures of 17:1 are demonstrated. Since etch masks may be patterned on uneven surfaces, we utilize this lithography to create multilayer structures in silicon. The linear selectivity versus implanted Ga density enables grayscale lithography. Limits on the ultimate resolution and selectivity of Ga lithography are also discussed

Abundances of PNe in the Outer Disk of M31

We present spectroscopic observations and chemical abundances of 16 planetary nebulae (PNe) in the outer disk of M31. The [O III] 4363 line is detected in all objects, allowing a direct measurement of the nebular temperature essential for accurate abundance determinations. Our results show that the abundances in these M31 PNe display the same correlations and general behaviors as Type II PNe in the Milky Way Galaxy. We also calculate photoionization models to derive estimates of central star properties. From these we infer that our sample PNe, all near the peak of the Planetary Nebula Luminosity Function, originated from stars near 2 M_sun. Finally, under the assumption that these PNe are located in M31's disk, we plot the oxygen abundance gradient, which appears shallower than the gradient in the Milky Way.Comment: 48 pages, including 12 figures and 8 tables, accepted by Astrophysical Journa