Analytical modelling of bacterial migration and accumulation with rate-limited sorption in discrete fractures

An analytical model for bacterial accumulation in a discrete fractllre has been developed. The transport and accumlllation processes incorporate into the model include advection, dispersion, rate-limited adsorption, rate-limited desorption, irreversible adsorption, attachment, detachment, growth and first order decay botl1 in sorbed and aqueous phases. An analytical solution in Laplace space is derived and nlln1erically inverted. The model is implemented in the code BIOFRAC vvhich is written in Fortran 99. The model is derived for two phases, Phase I, where adsorption-desorption are dominant, and Phase II, where attachment-detachment are dominant. Phase I ends yvhen enollgh bacteria to fully cover the substratllm have accllillulated. The model for Phase I vvas verified by comparing to the Ogata-Banks solution and the model for Phase II was verified by comparing to a nonHomogenous version of the Ogata-Banks solution. After verification, a sensitiv"ity analysis on the inpllt parameters was performed. The sensitivity analysis was condllcted by varying one inpllt parameter vvhile all others were fixed and observing the impact on the shape of the clirve describing bacterial concentration verSllS time. Increasing fracture apertllre allovvs more transport and thus more accllffilliation, "Vvhich diminishes the dllration of Phase I. The larger the bacteria size, the faster the sllbstratum will be covered. Increasing adsorption rate, was observed to increase the dllration of Phase I. Contrary to the aSSllmption ofllniform biofilm thickness, the accllffilliation starts frOll1 the inlet, and the bacterial concentration in aqlleous phase moving towards the olitiet declines, sloyving the accumulation at the outlet. Increasing the desorption rate, redllces the dliration of Phase I, speeding IIp the accllmlilation. It was also observed that Phase II is of longer duration than Phase I. Increasing the attachment rate lengthens the accliffililation period. High rates of detachment speeds up the transport. The grovvth and decay rates have no significant effect on transport, althollgh increases the concentrations in both aqueous and sorbed phases are observed. Irreversible adsorption can stop accllillulation completely if the vallIes are high.

On the equation of state and atomic mean square displacement of crystals

We have presented a Green's function method for the calculation of the atomic mean square displacement (MSD) for an anharmonic Hamil toni an . This method effectively sums a whole class of anharmonic contributions to MSD in the perturbation expansion in the high temperature limit. Using this formalism we have calculated the MSD for a nearest neighbour fcc Lennard Jones solid. The results show an improvement over the lowest order perturbation theory results, the difference with Monte Carlo calculations at temperatures close to melting is reduced from 11% to 3%. We also calculated the MSD for the Alkali metals Nat K/ Cs where a sixth neighbour interaction potential derived from the pseudopotential theory was employed in the calculations. The MSD by this method increases by 2.5% to 3.5% over the respective perturbation theory results. The MSD was calculated for Aluminum where different pseudopotential functions and a phenomenological Morse potential were used. The results show that the pseudopotentials provide better agreement with experimental data than the Morse potential. An excellent agreement with experiment over the whole temperature range is achieved with the Harrison modified point-ion pseudopotential with Hubbard-Sham screening function. We have calculated the thermodynamic properties of solid Kr by minimizing the total energy consisting of static and vibrational components, employing different schemes: The quasiharmonic theory (QH), ).2 and).4 perturbation theory, all terms up to 0 ().4) of the improved self consistent phonon theory (ISC), the ring diagrams up to o ().4) (RING), the iteration scheme (ITER) derived from the Greens's function method and a scheme consisting of ITER plus the remaining contributions of 0 ().4) which are not included in ITER which we call E(FULL). We have calculated the lattice constant, the volume expansion, the isothermal and adiabatic bulk modulus, the specific heat at constant volume and at constant pressure, and the Gruneisen parameter from two different potential functions: Lennard-Jones and Aziz. The Aziz potential gives generally a better agreement with experimental data than the LJ potential for the QH, ).2, ).4 and E(FULL) schemes. When only a partial sum of the).4 diagrams is used in the calculations (e.g. RING and ISC) the LJ results are in better agreement with experiment. The iteration scheme brings a definitive improvement over the).2 PT for both potentials.

Sex chromosome translocation and speciation : a Drosophila genetic model

Although exceptions may be readily identified, two generalizations concerning genetic differences among species may be drawn from the available allozyme and chromosome data. First, structural gene differences among species vary widely. In many cases, species pairs do not differ more than intraspecific populations. This suggests that either very few or no gene substitutions are required to produce barriers to reproduction (Avise 1976). Second, chromosome form and/or number differs among even closely related species (White 1963; 1978; Fredga 1977; Wright 1970). Many of the observed chromosomal differences involve translocational rearrangements; these produce severe fitness depression in heterozygotes and were, thus, long considered unlikely candidates for the fixation required of genetic changes leading to speciation (Wright 1977). Nonetheless, the fact that species differences are frequently translocational argues convincingly for their fixation despite prejudices to the contrary. Haldane's rule states that in the F of interspecific crosses, the heterogametic sex is absent or sterile in the preponderance of cases (Haldane 1932). This rule definitely applies in the genus Dr°sophila (Ehrman 1962). Sex chromosome translocations do not impose a fitness depression as severe as that imposed by autosomal translocations, and X-Y translocations may account for Haldane's rule (Haldane 1932). Consequently a study of the fit ness parameters of an X·yL and a yS chromosome in Drosophila melanogaster populations was initiated by Tracey (1972). Preliminary results suggested that x.yL//YSmales enjoyed a mating advantage with X·yL//X·yL females, that this advantage was frequency dependent, that the translocation produced sexual isolation and that interactions between the yL, yS and a yellow marker contributed to the observed isolation (Tracey and Espinet 1976; Espinet and Tracey 1976). Encouraged by the results of these prelimimary studies, further experiments were performed to clarify the genetic nature of the observed sexual isolation, S the reality of the y frequency dependent fitness .and the behavioural changes, if any, produced by the translocation. The results of this work are reported herein. Although the marker genes used in earlier studies, sparkling poliert an d yellow have both been found to affect activity,but only yellow effects asymmetric sexual isolation. In addition yellow effects isolation through an interaction with the T(X-y) chromosomes, yS also effects isolation, and translocational strains are isolated from those of normal karyotype in the absence of marker gene differences. When yS chromosomes are in competition with y chromosomes on an X.yL background, yS males are at a distinct advantage only when their frequency is less than 97%. The sex chromosome translocation alters the normal courtship pattern by the incorporation of circling between vibration and licking in the male repertoire. Finally a model of speciation base on the fixation of this sex chromosome translocation in a geographically isolated gene pool is proposed.