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

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

Surface width scaling in noise reduced Eden clusters

The surface width scaling of Eden A clusters grown from a single aggregate site on the square lattice is investigated as a function of the noise reduction parameter. A two-exponent scaling ansatz is introduced and used to fit the results from simulations covering the range from fully stochastic to the zero-noise limit.Comment: 4 pages, RevTex, 3 figure

ELSA: An Integrated, Semi-Automated Nebular Abundance Package

We present ELSA, a new modular software package, written in C, to analyze and manage spectroscopic data from emission-line objects. In addition to calculating plasma diagnostics and abundances from nebular emission lines, the software provides a number of convenient features including the ability to ingest logs produced by IRAF's splot task, to semi-automatically merge spectra in different wavelength ranges, and to automatically generate various data tables in machine-readable or LaTeX format. ELSA features a highly sophisticated interstellar reddening correction scheme that takes into account temperature and density effects as well as He II contamination of the hydrogen Balmer lines. Abundance calculations are performed using a 5-level atom approximation with recent atomic data, based on R. Henry's ABUN program. Improvements planned in the near future include use of a three-region ionization model, similar to IRAF's nebular package, error propagation, and the addition of ultraviolet and infrared line analysis capability. Detailed documentation for all aspects of ELSA are available at http://www.williams.edu/Astronomy/research/PN .Comment: 2 pages, contributed paper, IAU Symp. 234, Planetary Nebulae in Our Galaxy and Beyon

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

Effect of Photobiomodulation on Vinblastine-Poisoned Murine HERS Cells

Objective: The aim of this study was to investigate the effect of near-infrared (NIR) photobiomodulation on the proliferation and glutathione levels in murine Hertwig\u27s epithelial root sheath (HERS) cells after poisoning with vinblastine. Background: Photobiomodulation has been shown to improve wound healing in a number of animal models. There have been no studies on the effect of photobiomodulation on cancer-related chemotherapy injury to the cells that initiate tooth root growth. Materials and Methods: Control groups consisted of murine HERS cells without vinblastine (VB−) and cells with vinblastine at 10, 20, and 30 ng/mL (VB10, VB20, and VB30). Experimental groups consisted of these same groups with light therapy (VB-L, VB10L, VB20L, and VB30L). The cells were exposed to vinblastine for 1 h. Photobiomodulation consisted of a 75-cm2 gallium-aluminum-arsenide light-emitting diode (LED) array at an energy density of 12.8 J/cm2, delivered with 50 mW/cm2 power over 256 s. Results: Vinblastine alone significantly decreased HERS cell proliferation and glutathione levels at all concentrations (VB10 [−55%, p \u3c 1.0 × 10−8]; VB20 [−72%, p \u3c 1.0 × 10−9]; VB30 [−80%, p \u3c 1.0 × 10−10]; and VB10 [−36%, p \u3c 0.0001]; VB20 [−49%, p \u3c 1.0 × 10−6]; VB30 [−53%, p \u3c 1.0 × 10−7] respectively). Photobiomodulation significantly increased cell proliferation at all levels of vinblastine exposure (VB10L [+50%, p \u3c 0.0001]; VB20L [+45%, p \u3c 0.05]; VB30 [+39%, p \u3c 0.05]) but not of the control (+22%, p  = 0.063). The photobiomodulation significantly increased glutathione production in all concentrations of vinblastine except 20 ng/mL (VB10L [+39%, p = 0.007]; VB20L [+19%, p = 0.087]; VB30 [+14%, p = 0.025]) and the control (+12%, p = 0.13). Conclusions: Photobiomodulation demonstrated an improvement in proliferation and glutathione levels in vinblastine-poisoned murine HERS cells