Transition density of diffusion on Sierpinski gasket and extension of Flory's formula

Some problems related to the transition density u(t,x) of the diffusion on the Sierpinski gasket are considerd, based on recent rigorous results and detailed numerical calculations. The main contents are an extension of Flory's formula for the end-to-end distance exponent of self-avoiding walks on the fractal spaces, and an evidence of the oscillatory behavior of u(t,x) on the Sierpinski gasket.Comment: 11 pages, REVTEX, 2 postscript figure

The association between general practitioner participation in joint teleconsultations and rates of referral: a discrete choice experiment.

Background: Joint consultations - such as teleconsultations - provide opportunities for continuing education of general practitioners (GPs). It has been reported this form of interactive case-based learning may lead to fewer GP referrals, yet these studies have relied on expert opinion and simple frequencies, without accounting for other factors known to influence referrals. We use a survey-based discrete choice experiment of GPs' referral preferences to estimate how referral rates are associated with participation in joint teleconsultations, explicitly controlling for a number of potentially confounding variables. Methods: We distributed questionnaires at two meetings of the Portuguese Association of General Practice. GPs were presented with descriptions of patients with dermatological lesions and asked whether they would refer based on the waiting time, the distance to appointment, and pressure from patients for a referral. We analysed GPs' responses to multiple combinations of these factors, coupled with information on GP and practice characteristics, using a binary logit model. We estimated the probabilities of referral of different lesions using marginal effects. Results: Questionnaires were returned by 44 GPs, giving a total of 721 referral choices. The average referral rate for the 11 GPs (25%) who had participated in teleconsultations was 68.1% (range 53-88%), compared to 74.4% (range 47-100%) for the remaining physicians. Participation in teleconsultations was associated with reductions in the probabilities of referral of 17.6% for patients presenting with keratosis (p = 0.02), 42.3% for psoriasis (p <0.001), 8.4% for melanoma (p = 0.14), and 5.4% for naevus (p = 0.19). Conclusions: The results indicate that GP participation in teleconsultations is associated with overall reductions in referral rates and in variation across GPs, and that these effects are robust to the inclusion of other factors known to influence referrals. The reduction in range, coupled with different effects for different clinical presentations, may suggest an educational effect. However, more research is needed to establish whether there are causal relationships between participation in teleconsultations, continuing education, and referral rates. © 2015 Cravo Oliveira et al.; licensee BioMed Central

Upper estimate of martingale dimension for self-similar fractals

We study upper estimates of the martingale dimension $d_m$ of diffusion processes associated with strong local Dirichlet forms. By applying a general strategy to self-similar Dirichlet forms on self-similar fractals, we prove that $d_m=1$ for natural diffusions on post-critically finite self-similar sets and that $d_m$ is dominated by the spectral dimension for the Brownian motion on Sierpinski carpets.Comment: 49 pages, 7 figures; minor revision with adding a referenc

3D-PDR: a new three-dimensional astrochemistry code for treating photodissociation regions

Photodissociation regions (PDRs) define the transition zone between an ionized and a dark molecular region. They consist of neutral gas which interacts with far-ultraviolet radiation and are characterized by strong infrared line emission. Various numerical codes treating one-dimensional PDRs have been developed in the past, simulating the complexity of chemical reactions occurring and providing a better understanding of the structure of a PDR. In this paper we present the three-dimensional code, 3D-PDR, which can treat PDRs of arbitrary density distribution. The code solves the chemistry and the thermal balance self-consistently within a given three-dimensional cloud. It calculates the total heating and cooling functions at any point in a given PDR by adopting an escape probability method. It uses a HEALPIx-based ray tracing scheme to evaluate the attenuation of the far-ultraviolet radiation in the PDR and the propagation of the far-infrared/submm line emission out of the PDR. We present benchmarking results and apply 3D-PDR to (i) a uniform-density spherical cloud interacting with a plane-parallel external radiation field, (ii) a uniform-density spherical cloud interacting with a two-component external radiation field and (iii) a cometary globule interacting with a plane-parallel external radiation field. We find that the code is able to reproduce the benchmarking results of various other one-dimensional numerical codes treating PDRs. We also find that the accurate treatment of the radiation field in the fully three-dimensional treatment of PDRs can in some cases leads to different results when compared to a standard one-dimensional treatment

The Alexander-Orbach conjecture holds in high dimensions

We examine the incipient infinite cluster (IIC) of critical percolation in regimes where mean-field behavior has been established, namely when the dimension d is large enough or when d>6 and the lattice is sufficiently spread out. We find that random walk on the IIC exhibits anomalous diffusion with the spectral dimension d_s=4/3, that is, p_t(x,x)= t^{-2/3+o(1)}. This establishes a conjecture of Alexander and Orbach. En route we calculate the one-arm exponent with respect to the intrinsic distance.Comment: 25 pages, 2 figures. To appear in Inventiones Mathematica

An optimal inverse method using Doppler lidar measurements to estimate the surface sensible heat flux

Inverse methods are widely used in various fields of atmospheric science. However, such methods are not commonly used within the boundary-layer community, where robust observations of surface fluxes are a particular concern. We present a new technique for deriving surface sensible heat fluxes from boundary-layer turbulence observations using an inverse method. Doppler lidar observations of vertical velocity variance are combined with two well-known mixed-layer scaling forward models for a convective boundary layer (CBL). The inverse method is validated using large-eddy simulations of a CBL with increasing wind speed. The majority of the estimated heat fluxes agree within error with the proscribed heat flux, across all wind speeds tested. The method is then applied to Doppler lidar data from the Chilbolton Observatory, UK. Heat fluxes are compared with those from a mast-mounted sonic anemometer. Errors in estimated heat fluxes are on average 18 %, an improvement on previous techniques. However, a significant negative bias is observed (on average −63%) that is more pronounced in the morning. Results are improved for the fully-developed CBL later in the day, which suggests that the bias is largely related to the choice of forward model, which is kept deliberately simple for this study. Overall, the inverse method provided reasonable flux estimates for the simple case of a CBL. Results shown here demonstrate that this method has promise in utilizing ground-based remote sensing to derive surface fluxes. Extension of the method is relatively straight-forward, and could include more complex forward models, or other measurements