Effect of boundary conditions on diffusion in two-dimensional granular gases

We analyze the influence of boundary conditions on numerical simulations of the diffusive properties of a two dimensional granular gas. We show in particular that periodic boundary conditions introduce unphysical correlations in time which cause the coefficient of diffusion to be strongly dependent on the system size. On the other hand, in large enough systems with hard walls at the boundaries, diffusion is found to be independent of the system size. We compare the results obtained in this case with Langevin theory for an elastic gas. Good agreement is found. We then calculate the relaxation time and the influence of the mass for a particle of radius $R_s$ in a sea of particles of radius $R_b$. As granular gases are dissipative, we also study the influence of an external random force on the diffusion process in a forced dissipative system. In particular, we analyze differences in the mean square velocity and displacement between the elastic and inelastic cases.Comment: 15 figures eps figures, include

Localized and Cellular Patterns in a Vibrated Granular Layer

We propose a phenomenological model for pattern formation in a vertically vibrated layer of granular material. This model exhibits a variety of stable cellular patterns including standing rolls and squares as well as localized objects (oscillons and worms), similar to recent experimental observations(Umbanhowar et al., 1996). The model is an amplitude equation for the parametrical instability coupled to the mass conservation law. The structure and dynamics of the solutions resemble closely the properties of localized and cellular patterns observed in the experiments.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Let

A model for the atomic-scale structure of a dense, nonequilibrium fluid: the homogeneous cooling state of granular fluids

It is shown that the equilibrium Generalized Mean Spherical Model of fluid structure may be extended to nonequilibrium states with equation of state information used in equilibrium replaced by an exact condition on the two-body distribution function. The model is applied to the homogeneous cooling state of granular fluids and upon comparison to molecular dynamics simulations is found to provide an accurate picture of the pair distribution function.Comment: 29 pages, 11 figures Revision corrects formatting of the figure

Localized behavior in the Lyapunov vectors for quasi-one-dimensional many-hard-disk systems

We introduce a definition of a "localization width" whose logarithm is given by the entropy of the distribution of particle component amplitudes in the Lyapunov vector. Different types of localization widths are observed, for example, a minimum localization width where the components of only two particles are dominant. We can distinguish a delocalization associated with a random distribution of particle contributions, a delocalization associated with a uniform distribution and a delocalization associated with a wave-like structure in the Lyapunov vector. Using the localization width we show that in quasi-one-dimensional systems of many hard disks there are two kinds of dependence of the localization width on the Lyapunov exponent index for the larger exponents: one is exponential, and the other is linear. Differences, due to these kinds of localizations also appear in the shapes of the localized peaks of the Lyapunov vectors, the Lyapunov spectra and the angle between the spatial and momentum parts of the Lyapunov vectors. We show that the Krylov relation for the largest Lyapunov exponent $\lambda\sim-\rho\ln\rho$ as a function of the density $\rho$ is satisfied (apart from a factor) in the same density region as the linear dependence of the localization widths is observed. It is also shown that there are asymmetries in the spatial and momentum parts of the Lyapunov vectors, as well as in their $x$ and $y$-components.Comment: 41 pages, 21 figures, Manuscript including the figures of better quality is available from http://www.phys.unsw.edu.au/~gary/Research.htm

Real-time RT–PCR detection of disseminated tumour cells in bone marrow has superior prognostic significance in comparison with circulating tumour cells in patients with breast cancer

This study assessed the ability of real-time reverse transcription–polymerase chain reaction (RT–PCR) analysis to detect disseminated epithelial cells (DEC) in peripheral blood (PB) and bone marrow (BM) of patients with breast cancer (BC). Detection of DEC in BM is an obvious choice in BC, but blood sampling is more convenient. The aim of this study was to evaluate whether the detection of DEC in either PB or BM predicts overall survival (OS). Peripheral blood and BM samples were collected from 148 patients with primary (stage M0, n=116/78%) and metastatic (stage M+, n=32/21%) BC before the initiation of any local or systemic treatment. Peripheral blood of healthy volunteers and BM of patients with a nonmalignant breast lesion or a haematological malignancy served as the control group. Disseminated epithelial cells was detected by measuring relative gene expression (RGE) for cytokeratin-19 (CK-19) and mammaglobin (MAM), using a quantitative RT–PCR detection method. The mean follow-up time was 786 days (+/− 487). Kaplan–Meier analysis was used for predicting OS. By taking the 95 percentile of the RGE of CK-19 (BM: 26.3 and PB: 58.7) of the control group as cutoff, elevated CK-19 expression was detected in 42 (28%) BM samples and in 22 (15%) PB samples. Mammaglobin expression was elevated in 20% (both PB and BM) of the patients with BC. There was a 68% (CK-19) and 75% (MAM) concordance between PB and BM samples when classifying the results as either positive or negative. Patients with an elevated CK-19 or MAM expression in the BM had a worse prognosis than patients without elevated expression levels (OS: log-rank test, P=0.0045 (CK-19) and P=0.025 (MAM)). For PB survival analysis, no statistical significant difference was observed between patients with or without elevated CK-19 or MAM expression (OS: log-rank test, P=0.551 (CK-19) and P=0.329 (MAM)). Separate analyses of the M0 and M+ patients revealed a marked difference in OS according to the BM CK-19 or MAM status in the M+ patient group, but in the M0 group, only MAM expression was a prognostic marker for OS. Disseminated epithelial cells, measured as elevated CK-19 or MAM mRNA expression, could be detected in both PB and BM of patients with BC. Only the presence of DEC in BM was highly predictive for OS. The occurrence of DEC in the BM is probably less time-dependent and may act as a filter for circulating BC cells. The use of either larger volumes of PB or performing an enrichment step for circulating tumour in blood cells might improve these results

Establishment of a constructed wetland in extreme dryland.

The project was set to construct an extensive wetland in the southernmost region of Israel at Kibbutz Neot Smadar (30A degrees 02'45aEuro(3) N and 35A degrees 01'19aEuro(3) E). The results of the first period of monitoring, summary, and perspectives are presented. The constructed wetland (CW) was built and the subsequent monitoring performed in the framework of the Southern Arava Sustainable Waste Management Plan, funded by the EU LIFE Fund. The specific aims were: (1) To end current sewage disposal and pollution of the ground, the aquifer, and the dry river bed (wadi) paths by biologically treating the sewage as part of the creation of a sustainable wetland ecosystem. (2) Serve as an example of CW in the Negev highlands and the Arava Valley climates for neighboring communities and as a test ground for plants and building methods appropriate to hyper arid climate. (3) Serve as an educational resource and tourist attraction for groups to learn about water reuse, recycling, local wildlife and migrating birds, including serving the heart of a planned Ecological-Educational Bird Park. This report is intended to allow others who are planning similar systems in hyper arid climates to learn from our experience. The project is located in an extreme arid desert with less than 40 mm of rain annually and temperature ranges of -5A degrees C to +42A degrees C. The site receives 165-185 m(3) of municipal and agricultural wastes daily, including cowshed and goat wastes and winery outflow. The CW establishment at Neot Smadar was completed in October 2006. For 8 months, clean water flowed through the system while the plants were taking root. In June 2007, the wetland was connected to the oxidation pond and full operation began. Because of seepage and evaporation, during the first several months, the water level was not high enough to allow free flow from one bed to the next. To bed A, the water was pumped periodically from the oxidation pond (Fig. 1) and from there flowed by gravitation through the rest of the system. The initial results of the monitoring are promising. In nearly all measurements, the system succeeded as expected to reduce levels of contaminants at least to the level acceptable for irrigating fruit trees and often to the level of unlimited irrigation. The introduction of the plants in the system and their physiological performance were evaluated and were found to correlate well to the quality of water in the various beds. It should be said at the outset that evaluation of the performance of a CW system is a long-term process. Thus, the main aim of this report is to present the problems, difficulties, preliminary results, and concepts concerned with the first stage of establishment of CW in an extremely dry region. The CW system was designed to dispose of municipal and agricultural wastes in a way that not merely reduces pollution, but adds to environmental quality by creating accessible parkland for local residents and tourists. Several factors affected the performance of the system at the initial stages of operation: ecological balance between microbes and plants, big seasonal variations, seepage and evaporation reduced the flow in the initial operation of the system. Despite the initial difficulties, the quality of water coming out the system is acceptable for irrigation. The CW can function well under extreme dryland conditions. The oxidation pond was the major source of evaporation and bad odors. Therefore, alternatives to the oxidation pond are needed. Cost effectiveness of the system still has to be evaluated systematically