Spatial distribution of persistent sites

We study the distribution of persistent sites (sites unvisited by particles $A$) in one dimensional $A+A\to\emptyset$ reaction-diffusion model. We define the {\it empty intervals} as the separations between adjacent persistent sites, and study their size distribution $n(k,t)$ as a function of interval length $k$ and time $t$. The decay of persistence is the process of irreversible coalescence of these empty intervals, which we study analytically under the Independent Interval Approximation (IIA). Physical considerations suggest that the asymptotic solution is given by the dynamic scaling form $n(k,t)=s^{-2}f(k/s)$ with the average interval size $s\sim t^{1/2}$. We show under the IIA that the scaling function $f(x)\sim x^{-\tau}$ as $x\to 0$ and decays exponentially at large $x$. The exponent $\tau$ is related to the persistence exponent $\theta$ through the scaling relation $\tau=2(1-\theta)$. We compare these predictions with the results of numerical simulations. We determine the two-point correlation function $C(r,t)$ under the IIA. We find that for $r\ll s$, $C(r,t)\sim r^{-\alpha}$ where $\alpha=2-\tau$, in agreement with our earlier numerical results.Comment: 15 pages in RevTeX, 5 postscript figure

Spatial Distribution of Planktonic Dinoflagellate in Makassar Waters, South Sulawesi

The objectives of this study were to determine the harmful species of dinoflagellates, to determine the concentration of nutriens in surface waters, and to analyze factors affecting the ecological aspects of the harmful dinoflagellates. The results showed that there were 7 genus of dinoflagellates found in this study i.e., Ceratium spp., Gymnodinium sp., Dinophysis sp., Gonyaulax sp., Noctiluca sp., Protoperi-dinium spp., and Peridinium sp. Protoperidinium spp. and Ceratium spp. were the predominant species, with their abundance ranged of 9-659 cells/L and 6-556 cells/L, respectively. In temporal scale, values of DO and water light penetration were not significantly different (α>0.05), while for the parameter of nutriens, salinity, and abundance were significantly different (α<0.05). Total abundance of dinoflagellates was significantly correlated with nitrate, nitrite, ammonia, phosphate, salinity, and DO. Harmful dinoflagellate species such as Dinophysis sp. (DSP), Gymnodinium spp. (NSP and PSP), Noctiluca sp. (anaerobic), and Gonyaulax sp. (anaerobic) were observed in the study area. The high concentration of ammonia (>1 mg/L) in the waters of Losari beach also indicated that the area was affected by anthropogenic activities. Minimizing nutrient inputs from the land was becoming the most priority measure to be done to avoid such effects related to dinoflagellate harmful algae bloms

Spatial Distribution of Thunnus.sp, Vertical and Horizontal Sub-surface Multilayer Temperature Profiles of In-situ Agro Float Data in Indian Ocean

The study was the first ever attempt in fisheries oceanography sciences to explore the empiric correlationbetween the spatial distribution of tuna (Thunnus.sp) and sub-surface in-situ temperature data. By means ofoptimalization and use of an in-situ data of both vertical and horizontal which will be processed into amultilayer subsurface seawater temperature of ARGO Float in Indian ocean. So far only sea surfacetemperature (with temperature around 29 °C) data were used to look for the correlation for tuna spatialdistribution, while the Thunnus.sp swimming layer as widely known is in about 80 – 250m depth withseawater temperature between 15 – 23 °C. The noble character of ARGO Float data is as in-situ datarecorded directly by the sensors, transmitted to the satellite, transmitted to the ground station and ready to beused by researcher all over the world.In the study, about 216 seawater temperature coordinates of ARGOFloat and actual tuna catch data in the same day were used to represent the dry season (April – November2007) analysis, and about 90 data were used for the rainy season (December – March 2007). The actualtuna catch and its coordinates data were collected with permission from PT. Perikanan Samudra Besar,(PT.PSB) Benoa – Bali Indonesia. Then both seawater temperature and tuna data were processed using aKrigging method or spatial interpolation method.Based on a monthly actual tuna production by fishing fleetof PT.PSB operated in Indian Ocean indicates that there were two cycles of low catch in March and July andhigh catch in May and December 2007. In general, seawater temperature in depth of 80m, 100m, 150m and200m of the dry season was 2 °C warmer than those of the rainy season. Range of seawater temperature willdecrease due to the water depth, range of seawater temperature at depth of 150m was between 14 – 22 °Cand at depth of 200m between 12 – 20 °C. Based on the regression and correlation between tuna catch andseawater temperature revealed that seawater temperature at depth 150m has the highest coefficient ofcorrelation than to the seawater temperature at depth 100m and 200m

Determinants of Spatial Distribution of Organic Farming in Germany

The share of organically managed land is spread unevenly throughout Germany and shows pronounced regional concentrations. The spatial distribution of organic farming is assumed to be influenced by several factors. Location factors of farms are regionally different and thus may influence the spatial distribution of organic farming. Agglomeration effects and therefore spatial dependence are also considered important in determining spatial distribution. These factors with a potential influence on the spatial distribution of organic farming can be divided into four categories: natural factors, farm-structure factors, socio-economic factors and political factors. Their possible influence on the spatial distribution of organic farming is analysed by several statistical methods: ordinary least square regression model, spatial autoregressive models, analysis of variance and Spearman correlation. Of the analysed factors, spatial contiguity has the strongest influence on the spatial distribution of organic farming (indicating relevant agglomeration effects)

Optimal design of spatial distribution networks

We consider the problem of constructing public facilities, such as hospitals, airports, or malls, in a country with a non-uniform population density, such that the average distance from a person's home to the nearest facility is minimized. Approximate analytic arguments suggest that the optimal distribution of facilities should have a density that increases with population density, but does so slower than linearly, as the two-thirds power. This result is confirmed numerically for the particular case of the United States with recent population data using two independent methods, one a straightforward regression analysis, the other based on density dependent map projections. We also consider strategies for linking the facilities to form a spatial network, such as a network of flights between airports, so that the combined cost of maintenance of and travel on the network is minimized. We show specific examples of such optimal networks for the case of the United States.Comment: 6 pages, 5 figure

Spatial distribution of mortality in Pacific oysters Crassostrea gigas: reflection on mechanisms of OsHV-1 transmission

The ostreid herpesvirus (OsHV-1) has the potential to devastate Crassostrea gigas culture in Australia as it has done in many other countries, highlighting the need for a better understanding of disease expression and transmission. The aim of this study was to assess the spatial distribution of OsHV-1 associated mortalities in one of only two infected areas in Australia, Woolooware Bay (Botany Bay New South Wales). In October 2011, healthy sentinel Pacific oysters were placed in three different locations at three different tidal levels and OsHV-1 associated mortalities were closely monitored over 7 months. The outbreak started in November 2011 and the disease remained active until April 2012. Three major mortality events were detected. Rather than being a propagating epizootic, it appeared that most oysters were infected from the same environmental source. The distribution of OsHV-1 associated mortalities was spatially clustered, highly variable and clearly dependent on the age of oysters and their position in the water column. Non-random distribution of mortalities at macro scale (sites several km apart) and micro scale (within rearing trays), and vertical clustering patterns in the water column are discussed in relation to mechanisms of transmission in water. We hypothesise that OsHV-1 may be carried through water by particles, possibly plankton. Key words: Crassostrea gigas, Ostreid herpesvirus 1, summer mortalities, spatial distribution, plankton, disease transmissionFunded by the Fisheries Research and Development Corporation, the University of Sydney and the Sydney Metropolitan Catchment Management Authorit