Smoluchowski's equation for cluster exogenous growth

We introduce an extended Smoluchowski equation describing coagulation processes for which clusters of mass s grow between collisions with $ds/dt=As^\beta$. A physical example, dropwise condensation is provided, and its collision kernel K is derived. In the general case, the gelation criterion is determined. Exact solutions are found and scaling solutions are investigated. Finally we show how these results apply to nucleation of discs on a planeComment: Revtex, 4 pages (multicol.sty), 1 eps figures (uses epsfig

Undergraduate research in primary care: Is it sustainable?

To describe the research project component of the BSc in Primary Health Care and to discuss the issues faced by students and faculty in attempting to complete a student-led research project. Medical schools increasingly expect medical students to undertake research as part of intercalated BSc’s or in self-selected study modules. This research has historically been laboratory based, ‘piggybacking’ onto existing projects. Projects initiated by students themselves and studies in primary care or community settings are more unusual. A qualitative study, based on interviews with students and examiners, triangulated with data from the peer review process and personal observations on the running of the course. A London medical school, running an intercalated BSc in Primary Health Care. We interviewed 24 of 26 students and two external examiners during the interview period of the study. Students successfully undertook research, from initial question through to publication. Overall, 90 dissertations were completed since 1997, of which half used a qualitative methodology (45/90). Ten projects have subsequently been published; there were also 16 conference presentations and 6 research letters. Themes from the interview data include: the students’ strong sense of project ownership, the difficulties of being a novice researcher, the difficulties posed by the research governance hurdles, the beneficial and for some students adverse impact (stress and coping with unsuccessful projects) and finally, the impact on their careers. Students gain considerably from this learning process, not only by undertaking their own research, but they also gain in terms of acquisition of transferable skills such as critical appraisal and improved self-directedness. Project completion and publication rates suggest that programmes developing undergraduate initiated research projects can be as successful as those for other novice researchers. The student-led project is a fragile endeavour, but currently is sustainable. © 2008, Cambridge University Press. All rights reserved

Is it really possible to grow isotropic on-lattice diffusion-limited aggregates?

In a recent paper (Bogoyavlenskiy V A 2002 \JPA \textbf{35} 2533), an algorithm aiming to generate isotropic clusters of the on-lattice diffusion-limited aggregation (DLA) model was proposed. The procedure consists of aggregation probabilities proportional to the squared number of occupied sites ($k^2$). In the present work, we analyzed this algorithm using the noise reduced version of the DLA model and large scale simulations. In the noiseless limit, instead of isotropic patterns, a $45^\circ$ ($30^\circ$) rotation in the anisotropy directions of the clusters grown on square (triangular) lattices was observed. A generalized algorithm, in which the aggregation probability is proportional to $k^\nu$, was proposed. The exponent $\nu$ has a nonuniversal critical value $\nu_c$, for which the patterns generated in the noiseless limit exhibit the original (axial) anisotropy for $\nu<\nu_c$ and the rotated one (diagonal) for $\nu>\nu_c$. The values $\nu_c = 1.395\pm0.005$ and $\nu_c = 0.82\pm 0.01$ were found for square and triangular lattices, respectively. Moreover, large scale simulations show that there are a nontrivial relation between noise reduction and anisotropy direction. The case $\nu=2$ (\bogo's rule) is an example where the patterns exhibit the axial anisotropy for small and the diagonal one for large noise reduction.Comment: 12 pages, 8 figure

Aggregation in a mixture of Brownian and ballistic wandering particles

In this paper, we analyze the scaling properties of a model that has as limiting cases the diffusion-limited aggregation (DLA) and the ballistic aggregation (BA) models. This model allows us to control the radial and angular scaling of the patterns, as well as, their gap distributions. The particles added to the cluster can follow either ballistic trajectories, with probability $P_{ba}$, or random ones, with probability $P_{rw}=1-P_{ba}$. The patterns were characterized through several quantities, including those related to the radial and angular scaling. The fractal dimension as a function of $P_{ba}$ continuously increases from $d_f\approx 1.72$ (DLA dimensionality) for $P_{ba}=0$ to $d_f\approx 2$ (BA dimensionality) for $P_{ba}=1$. However, the lacunarity and the active zone width exhibt a distinct behavior: they are convex functions of $P_{ba}$ with a maximum at $P_{ba}\approx1/2$. Through the analysis of the angular correlation function, we found that the difference between the radial and angular exponents decreases continuously with increasing $P_{ba}$ and rapidly vanishes for $P_{ba}>1/2$, in agreement with recent results concerning the asymptotic scaling of DLA clusters.Comment: 7 pages, 6 figures. accepted for publication on PR

Young stars and dust in AFGL437: NICMOS/HST polarimetric imaging of an outflow source

We present near infrared broad band and polarimetric images of the compact star forming cluster AFGL437 obtained with the NICMOS instrument aboard HST. Our high resolution images reveal a well collimated bipolar reflection nebulosity in the cluster and allow us to identify WK34 as the illuminating source. The scattered light in the bipolar nebulosity centered on this source is very highly polarized (up to 79%). Such high levels of polarization implies a distribution of dust grains lacking large grains, contrary to the usual dust models of dark clouds. We discuss the geometry of the dust distribution giving rise to the bipolar reflection nebulosity and make mass estimates for the underlying scattering material. We find that the most likely inclination of the bipolar nebulosity, south lobe inclined towards Earth, is consistent with the inclination of the large scale CO molecular outflow associated with the cluster, strengthening the identification of WK34 as the source powering it.Comment: 26 pages, 10 figues. Accepted for publication in the Astrophysical Journa

Analysis of patterns formed by two-component diffusion limited aggregation

We consider diffusion limited aggregation of particles of two different kinds. It is assumed that a particle of one kind may adhere only to another particle of the same kind. The particles aggregate on a linear substrate which consists of periodically or randomly placed particles of different kinds. We analyze the influence of initial patterns on the structure of growing clusters. It is shown that at small distances from the substrate, the cluster structures repeat initial patterns. However, starting from a critical distance the initial periodicity is abruptly lost, and the particle distribution tends to a random one. An approach describing the evolution of the number of branches is proposed. Our calculations show that the initial patter can be detected only at the distance which is not larger than approximately one and a half of the characteristic pattern size.Comment: Accepted for publication in Physical Review

Engineering geology of British rocks and soils : Lias Group

The report begins with an introduction and a detailed modern assessment of the geology of the Lias Group in terms of both stratigraphy and lithology. The modern lithostratigraphy is placed in the context of the old, and sometimes more familiar, usage. The next two chapters deal with the mineralogy of a suite of samples collected for the project, and an assessment of the nature and influence of weathering based on a detailed analysis of the Lias dataset held in the BGS National Geotechnical Properties Database. The following chapters cover geohazards associated with the Lias Group, and a brief overview of the wide variety of industrial applications for which the Lias is well known. The geotechnical database forms the basis of the penultimate chapter, geotechnical properties. The contents of the database are analysed, interpreted, presented in graphical form, and discussed in terms of statistical variation and in the light of likely engineering behaviour. The engineering geology of the Lias Group is discussed in the final chapter, borrowing from the preceding chapters. A comprehensive cited reference list and a bibliography are provided. In addition to the large number of technical data provided to BGS, a small data set has been generated by BGS laboratories, particularly in areas where the main database was deficient, and also in connection with associated BGS studies of the swelling and shrinkage properties of the Lias Group. The individual items of data making up the database are not attributed. However, the contribution of a wide range of consultancies, contractors, authorities, and individuals is acknowledged. It is hoped that this report will provide a source of useful information to a wide range of engineers, planners, scientists, and other interested parties concerned with Lias Group materials. It should be noted that whilst quantitative technical data are included in this report, these should not be used as a substitute for proper site investigation

Multifractal Dimensions for Branched Growth

A recently proposed theory for diffusion-limited aggregation (DLA), which models this system as a random branched growth process, is reviewed. Like DLA, this process is stochastic, and ensemble averaging is needed in order to define multifractal dimensions. In an earlier work [T. C. Halsey and M. Leibig, Phys. Rev. A46, 7793 (1992)], annealed average dimensions were computed for this model. In this paper, we compute the quenched average dimensions, which are expected to apply to typical members of the ensemble. We develop a perturbative expansion for the average of the logarithm of the multifractal partition function; the leading and sub-leading divergent terms in this expansion are then resummed to all orders. The result is that in the limit where the number of particles n -> \infty, the quenched and annealed dimensions are {\it identical}; however, the attainment of this limit requires enormous values of n. At smaller, more realistic values of n, the apparent quenched dimensions differ from the annealed dimensions. We interpret these results to mean that while multifractality as an ensemble property of random branched growth (and hence of DLA) is quite robust, it subtly fails for typical members of the ensemble.Comment: 82 pages, 24 included figures in 16 files, 1 included tabl

Hydrodynamic simulations of shell convection in stellar cores

Shell convection driven by nuclear burning in a stellar core is a common hydrodynamic event in the evolution of many types of stars. We encounter and simulate this convection (i) in the helium core of a low-mass red giant during core helium flash leading to a dredge-down of protons across an entropy barrier, (ii) in a carbon-oxygen core of an intermediate-mass star during core carbon flash, and (iii) in the oxygen and carbon burning shell above the silicon-sulfur rich core of a massive star prior to supernova explosion. Our results, which were obtained with the hydrodynamics code HERAKLES, suggest that both entropy gradients and entropy barriers are less important for stellar structure than commonly assumed. Our simulations further reveal a new dynamic mixing process operating below the base of shell convection zones.Comment: 8 pages, 3 figures .. submitted to a proceedings of conference about "Red Giants as Probes of the Structure and Evolution of the Milky Way" which has taken place between 15-17 November 2010 in Rom