FIRE OCCURRENCE PATTERNS AT LANDSCAPE LEVEL: BEYOND POSITIONAL ACCURACY OF IGNITION POINTS WITH KERNEL DENSITY ESTIMATION METHODS

ABSTRACT. Based on kernel density estimation methods, this paper introduces an alternative approach of fire occurrence modeling that addresses the inherent positional inaccuracies of recorded wildland fire ignition points. These observations, recorded in longitude and latitude using only degrees and first minutes, contain positional inaccuracies of about ± 700 to ± 925 meters in x and y axes. Kernel density estimation was applied to these historical fire observations recorded between 1985 and 1995 in Halkidiki peninsula, Greece, as well as, to simulated inaccurate points into which positional inaccuracies of the same magnitude were randomly introduced. Substantial differences were observed when a regular grid of quadrants was superimposed over the two point distributions. Although, at higher grid resolution these mismatches were minimized, the problem of generalization appeared. Contrar‐ily, the concept of “moving window” assisted to retain high grid resolution and minimize the effect of inaccurate point observations. In addition, the kernel approach, which considers also the relative position of points within the “moving window,” produced more realistic estimates.     

Dielectric behaviour of α-cyclodextrin,heptakis (2,3,6-tri-Omethyl)-β-cyclodextrin,randomly methylated β-cyclodextrin and low frequency Raman spectra of α- and β-cyclodextrins

The frequency and temperature dependence of the real (?′) and imaginary (?″)parts of the dielectric constant of α-cyclodrextrin (form 1; α-CD. 5.9H₂O) and α-cyclodextrin (form III; α-CD.7.6H₂O) and of the corresponding dried forms (α-CD.1.1H₂O, α-CD.2.9H₂O, respectively) has been investigated over the frequency range 0–100 k Hz and temperature range 130–350 K. In addition the dielectric behaviour has been investigated of heptakis-(2,3,6-tri-O-methyl)-β-cyclodextrin (β-CD.TRIME. 0.3H₂O) and randomly methylated β-cyclodextrin (β-CD.RAME.0.8H₂O). The dielectric behaviour is described well by Debyetype relaxation (α-disperson). All α-CD systems exhibit an additional ω-dispersion at low frequencies, which is attributed to proton transport. The fact that the ?′ values of α-CD form III are larger than those of α-CD form I is attributed to the different numbers and different strengths of the intramolecular hydrogen bonds. Form III has a stable conformation which is shown by the constant values of ?′ in the temperature range 125–250 K. By contrast, in form I the ?′ values increased linearly with temperature, indicating that the system passed through succesive conformations. The temperature dependence of ?″ and phase shift ∞ in all the specimens of α-CD (forms I, III) and fully methylated β-CD do not reveal any orderdisorder transition, because the developed hydrogen bonds ae not of the flip-flop type according to their crystal structures. The partially methylated β-CD reveals the characteristics of the order-disorder transition, which was observed before in the systems dried β-CD.2H₂O and non-dried β-CD.9.8H₂O. There is a direct relation between the hydroxyl groups of β-CD and the order-disorder transition. The order-disorder transition could also be shown in dried β-CD.2.4H₂O and non-dried β-CD.9.8H₂O samples but not in dried α-CD.1.1H₂O and non-dried a-CD.5.9H₂O samples, by low frequency Raman spectroscopy (< 180 cm^?1). The step-like temperature dependence of the band at 33.7cm^?1 reveals a transition at about 223K for both β-CD samples. In the case of α-CD samples the almost linear temperature dependence of the band at 49.1 cm^?1 does not reveal any transition.     

THE PARALLEL BLOCK ADAPTIVE MULTIGRID METHOD FOR THE IMPLICIT SOLUTION OF THE EULER EQUATIONS

A method capable of solving very fast and robust complex non-linear systems of equations is presented. The block adaptive multigrid (BAM) method combines mesh adaptive techniques with multigrid and domain decomposition methods. The overall method is based on the FAS multigrid, but instead of using global grids, locally enriched subgrids are also employed in regions where excessive solution errors are encountered. The final mesh is a composite grid with uniform rectangular subgrids of various mesh densities. The regions where finer grid resolution is necessary are detected using an estimation of the solution error by comparing solutions between grid levels. Furthermore, an alternative domain decomposition strategy has been developed to take advantage of parallel computing machines. The proposed method has been applied to an implicit upwind Euler code (EuFlex) for the solution of complex transonic flows around aerofoils. The efficiency and robustness of the BAM method are demonstrated for two popular inviscid test cases. Up to 19-fold acceleration with respect to the single-grid solution has been achieved, but a further twofold speed-up is possible on four-processor parallel computers.