Nonuniversality and Breakdown of Scaling in Aggregation Process with Removal Term

We study the kinetics of an irreversible aggregation model with removal term. We solve the mean-field rate equation to obtain the general solution of the cluster-mass distribution for the case with arbitrary time-dependent remora/probability P(t). In particular, we analyze the scaling properties of the cluster distribution in the case with P(t)=u(t+t0)^v and find that the cluster-mass distribution always obeys a scaling law. We also investigate the kinetic behavior of another simple system, in which the removal probability of a cluster is proportional to its mass, and the results indicate that for this system the scaring description of the cluster-mass distribution breaks down completely.

Insight into fouling behavior of poly(vinylidene fluoride)(PVDF)hollow fiber membranes caused by dextran with different pore size distributions

Membrane fouling is the key problem that occurs in membrane process for water treatment. However, how membrane microstructure influences the fouling behavior is still not clear. In this study, fouling behavior caused by dextran was deeply and systematically investigated by employing four poly（vinylidene fluoride） （PVDF） membranes with different pore sizes, ranging from 24 to 94 nm. The extent of fouling by dextran was accurately characterized by pore reduction, flux decline, and the change of critical flux. The result shows that membrane with the smallest pore size of 24 nm experienced the smallest fouling rate and the lowest fouling extent. As the membrane pore size increased, the critical flux ranges were 105-114, 63-73, 38-44 and 34- 43 L. m 2. h t, respectively. The critical flux and fouling resistances indicated that the fouling propensity in- creases with the increase of membrane pore size. Two pilot membrane modules with mean pore size of 25 nm and 60 nm were applied in membrane filtration of surface water treatment. The results showed that serious ir- reversible membrane fouling occurred on the membrane with pore size of 60 nm at the permeate flux of 40.5 L.m 2.h 1. On the other hand, membrane with pore size of 25 nm exhibited much better anti-fouling per- formance when permeate flux was set to 40.5, 48 and 60 L-m 2-h- 1.

Nonlinear conductive properties and scaling behavior of conductive particle filled high-density polyethylene composites

The blends prepared by incorporation of carbon black (CB) or graphite powder (GP) inHto high-density polyethylene (HDPE) matrix have been novel and extensively applied polymeric positive temperature coefficient (PTC) composites. A phenomenological model was proposed on the basis of the GEM equation and the dilution effect of filler volume fraction due to the thermal volume expansion of the polymer matrix. Accordingly, the contribution of the thermal expansion of the matrix to the jump-like PTC transition of the composites was quantitatively estimated and a mechanical explanation was given. It was proved that the contribution of the volume expansion to PTC effect decreased for HDPE/CB composites crosslinked through electron-beam irradiation. Furthermore, the influences of the filler content, temperature and crosslinking on the self-heating behavior as well as the nonlinear conduction characteristics at electrical-thermal equilibrium state were examined. Based on the electric-field and initial resistivity dependence of the self-heating temperature and resistance dependence of the critical field, the mechanisms of the self-heating of the polymeric PTC materials were evaluated. The intrinsic relations between macroscopic electrical properties and microscopic percolation network at electrical-thermal equilibrium state were discussed according to the scaling relationship between the self-heating critical parameter and the conductivity of materials.

Scaling behavior of magnitude clusters in aftershock sequence:An example of the Wenchuan Earthquake,China

The Gutenberg-Richter and Omori Laws, which are generally used to characterize the temporal distribution of aftershock, failed to reflect the statistic properties of climatic outbreak of aftershock energy. Based on a new concept of magnitude clusters describing the fluctuation of aftershock energy release of the Wenchuan Earthquake, we discovered that the pattern of the continuous high-magnitude aftershock follows a power-law rather than a non-Poisson distribution. This suggests that the after-shocks with high magnitudes are statistically clustered. We then divided the aftershock sequences into three sections and demonstrated that though the probability of strong outbreaks decreased with time, there exists a high possibility of the occurrence of isolated high-magnitude aftershocks in the future. Based on self-organized criticality theory, the mechanisms of the power-law pattern of magnitude clusters are discussed. This discovery may be used to guide future aftershock predication and the associated post-disaster reconstruction.