A summary of AFCRL passive-sphere development efforts and experience

Falling spheres for meteorological rocket soundin

A High-Order Kernel Method for Diffusion and Reaction-Diffusion Equations on Surfaces

In this paper we present a high-order kernel method for numerically solving diffusion and reaction-diffusion partial differential equations (PDEs) on smooth, closed surfaces embedded in $\mathbb{R}^d$. For two-dimensional surfaces embedded in $\mathbb{R}^3$, these types of problems have received growing interest in biology, chemistry, and computer graphics to model such things as diffusion of chemicals on biological cells or membranes, pattern formations in biology, nonlinear chemical oscillators in excitable media, and texture mappings. Our kernel method is based on radial basis functions (RBFs) and uses a semi-discrete approach (or the method-of-lines) in which the surface derivative operators that appear in the PDEs are approximated using collocation. The method only requires nodes at "scattered" locations on the surface and the corresponding normal vectors to the surface. Additionally, it does not rely on any surface-based metrics and avoids any intrinsic coordinate systems, and thus does not suffer from any coordinate distortions or singularities. We provide error estimates for the kernel-based approximate surface derivative operators and numerically study the accuracy and stability of the method. Applications to different non-linear systems of PDEs that arise in biology and chemistry are also presented

Assessing the Effect of Photodynamic Therapy on Peripheral Nerve and Cancer Cells Using a Thin Tissue Engineered Collagen Culture Model

Abstract not available

Intracellular localisation of mTHPC and effect of photodynamic therapy in cells of the mammalian peripheral nervous system

Fewer nerve-related side effects have been noted after treating head and neck cancer with photodynamic therapy (PDT) compared to conventional cancer therapy. Our aim is to investigate the biological basis for any such nerve-sparing effect. In this study the intracellular localisation and effect on cell viability of the photosensitiser meta-tetrahydroxylphenylchlorin (mTHPC) was investigated in cell culture models using peripheral nerve cells. Primary cells from adult rat dorsal root ganglia (containing both neurons and glia) were used in these experiments. Localisation of mTHPC was detected using fluorescence and confocal microscopy. Levels of mTHPC fluorescence were quantified using digital image analysis. Immunocytochemistry with anti-?-III-tubulin and anti-S100 was used to distinguish neuronal and glial cell populations respectively. A cell-death assay using propidium iodide was used to evaluate neural cell susceptibility to PDT following incubation with mTHPC. The results showed that mTHPC was localised in cytoplasmic regions of neurons and glia, but was not detected in neuronal axons. Necrotic cell death was detected after PDT in these neural cell types. These results suggest that the cells of the peripheral nervous system are susceptible to PDT-mediated necrosis, but that the sparing of nerves observed during clinical PDT may be related to the heterogeneous distribution of mTHPC within neurons

Differences in sensitivity to mTHPC-mediated photodynamic therapy of neurons, glial cells and MCF7 cells in a 3-dimensional cell culture model

The effect of photodynamic therapy (PDT) on the cells of the nervous system is an important consideration in the treatment of tumours that are located within or adjacent to the brain, spinal cord and peripheral nerves. Previous studies have reported the sparing of nerves during PDT using meta-tetrahydroxyphenylchlorin (mTHPC, Foscan®) in patients and in animal models. The aim of this study was to investigate the effects of mTHPC on key nervous system cells using a 3-dimensional cell culture system for the accurate detection of differences in sensitivity

3D Photoionisation Modelling of NGC 6302

We present a three-dimensional photoionisation and dust radiative transfer model of NGC 6302, an extreme, high-excitation planetary nebula. We use the 3D photoionisation code Mocassin} to model the emission from the gas and dust. We have produced a good fit to the optical emission-line spectrum, from which we derived a density distribution for the nebula. A fit to the infrared coronal lines places strong constraints on the properties of the unseen ionising source. We find the best fit comes from using a 220,000 K hydrogen-deficient central star model atmosphere, indicating that the central star of this PN may have undergone a late thermal pulse. We have also fitted the overall shape of the ISO spectrum of NGC 6302 using a dust model with a shallow power-law size distribution and grains up to 1.0 micron in size. To obtain a good fit to the infrared SED the dust must be sufficiently recessed within the circumstellar disk to prevent large amounts of hot dust at short wavelengths, a region where the ISO spectrum is particularly lacking. These and other discoveries are helping to unveil many properties of this extreme object and trace it's evolutionary history.Comment: 8 pages, 4 figures; for the proceedings of "Asymmetric Planetary Nebuale IV," R. L. M. Corradi, A. Manchado, N. Soker ed

A High-Order Radial Basis Function (RBF) Leray Projection Method for the Solution of the Incompressible Unsteady Stokes Equations

A new projection method based on radial basis functions (RBFs) is presented for discretizing the incompressible unsteady Stokes equations in irregular geometries. The novelty of the method comes from the application of a new technique for computing the Leray-Helmholtz projection of a vector field using generalized interpolation with divergence-free and curl-free RBFs. Unlike traditional projection methods, this new method enables matching both tangential and normal components of divergence-free vector fields on the domain boundary. This allows incompressibility of the velocity field to be enforced without any time-splitting or pressure boundary conditions. Spatial derivatives are approximated using collocation with global RBFs so that the method only requires samples of the field at (possibly scattered) nodes over the domain. Numerical results are presented demonstrating high-order convergence in both space (between 5th and 6th order) and time (up to 4th order) for some model problems in two dimensional irregular geometries.Comment: 34 pages, 8 figure

Information, VARs and DSGE Models

How informative is a time series representation of a given vector of observables about the structural shocks and impulse response functions in a DSGE model? In this paper we refer to this econometrician’s problem as “E-invertibility” and consider the corresponding information problem of the agents in the assumed DGP, the DSGE model, which we refer to as “A-invertibility” We consider how the general nature of the agents’ signal extraction problem under imperfect information impacts on the econometrician’s problem of attempting to infer the nature of structural shocks and associated impulse responses from the data. We also examine a weaker condition of recoverability. A general conclusion is that validating a DSGE model by comparing its impulse response functions with those of a data VAR is more problematic when we drop the common assumption in the literature that agents have perfect information as an endowment. We develop measures of approximate fundamentalness for both perfect and imperfect information cases and illustrate our results using analytical and numerical examples