Exact Multifractal Spectra for Arbitrary Laplacian Random Walks

Iterated conformal mappings are used to obtain exact multifractal spectra of the harmonic measure for arbitrary Laplacian random walks in two dimensions. Separate spectra are found to describe scaling of the growth measure in time, of the measure near the growth tip, and of the measure away from the growth tip. The spectra away from the tip coincide with those of conformally invariant equilibrium systems with arbitrary central charge $c\leq 1$, with $c$ related to the particular walk chosen, while the scaling in time and near the tip cannot be obtained from the equilibrium properties.Comment: 4 pages, 3 figures; references added, minor correction

Diffusion-limited aggregation as branched growth

I present a first-principles theory of diffusion-limited aggregation in two dimensions. A renormalized mean-field approximation gives the form of the unstable manifold for branch competition, following the method of Halsey and Leibig [Phys. Rev. A {\bf 46}, 7793 (1992)]. This leads to a result for the cluster dimensionality, D \approx 1.66, which is close to numerically obtained values. In addition, the multifractal exponent \tau(3) = D in this theory, in agreement with a proposed `electrostatic' scaling law.Comment: 13 pages, one figure not included (available by request, by ordinary mail), Plain Te

The branching structure of diffusion-limited aggregates

I analyze the topological structures generated by diffusion-limited aggregation (DLA), using the recently developed "branched growth model". The computed bifurcation number B for DLA in two dimensions is B ~ 4.9, in good agreement with the numerically obtained result of B ~ 5.2. In high dimensions, B -> 3.12; the bifurcation ratio is thus a decreasing function of dimensionality. This analysis also determines the scaling properties of the ramification matrix, which describes the hierarchy of branches.Comment: 6 pages, 1 figure, Euro-LaTeX styl

Exploring trends and challenges in sociological research

This is the first e-special issue for the journal Sociology and its chosen focus is the article ‘The coming crisis of empirical sociology’ by Savage and Burrows (2007). This article challenged sociologists with a variety of questions about the role, relevance and methodological opportunities for sociological research in the 21st century. On publication it stoked the already charged debates on a public sociology (Burawoy, 2004), the role of publicly funded research (ESRC, 2009) and relevance of sociological research in an age of burgeoning social media (Brewer and Hunter, 2006). This e-special provides a reprise of these debates and explores relevant papers in Sociology, as well as alerting readers to recurring themes and new directions on the topic of methods and social research

Maximum Angle of Stability of a Wet Granular Pile

Anyone who has built a sandcastle recognizes that the addition of liquid to granular materials increases their stability. However, measurements of this increased stability often conflict with theory and with each other [1-7]. A friction-based Mohr-Coulomb model has been developed [3,8]. However, it distinguishes between granular friction and inter-particle friction, and uses the former without providing a physical mechanism. Albert, {\em et al.} [2] analyzed the geometric stability of grains on a pile's surface. The frictionless model for dry particles is in excellent agreement with experiment. But, their model for wet grains overestimates stability and predicts no dependence on system size. Using the frictionless model and performing stability analysis within the pile, we reproduce the dependence of the stability angle on system size, particle size, and surface tension observed in our experiments. Additionally, we account for past discrepancies in experimental reports by showing that sidewalls can significantly increase the stability of granular material.Comment: 4 pages, 4 figure

Energy level statistics of electrons in a 2D quasicrystal

A numerical study is made of the spectra of a tight-binding hamiltonian on square approximants of the quasiperiodic octagonal tiling. Tilings may be pure or random, with different degrees of phason disorder considered. The level statistics for the randomized tilings follow the predictions of random matrix theory, while for the perfect tilings a new type of level statistics is found. In this case, the first-, second- level spacing distributions are well described by lognormal laws with power law tails for large spacing. In addition, level spacing properties being related to properties of the density of states, the latter quantity is studied and the multifractal character of the spectral measure is exhibited.Comment: 9 pages including references and figure captions, 6 figures available upon request, LATEX, report-number els

Dynamics of electrostatically-driven granular media. Effects of Humidity

We performed experimental studies of the effect of humidity on the dynamics of electrostatically-driven granular materials. Both conducting and dielectric particles undergo a phase transition from an immobile state (granular solid) to a fluidized state (granular gas) with increasing applied field. Spontaneous precipitation of solid clusters from the gas phase occurs as the external driving is decreased. The clustering dynamics in conducting particles is primarily controlled by screening of the electric field but is aided by cohesion due to humidity. It is shown that humidity effects dominate the clustering process with dielectric particles.Comment: 4 pages, 4 fig

Analytical results for random walks in the presence of disorder and traps

In this paper, we study the dynamics of a random walker diffusing on a disordered one-dimensional lattice with random trappings. The distribution of escape probabilities is computed exactly for any strength of the disorder. These probabilities do not display any multifractal properties contrary to previous numerical claims. The explanation for this apparent multifractal behavior is given, and our conclusion are supported by numerical calculations. These exact results are exploited to compute the large time asymptotics of the survival probability (or the density) which is found to decay as $\exp [-Ct^{1/3}\log^{2/3}(t)]$. An exact lower bound for the density is found to decay in a similar way.Comment: 21 pages including 3 PS figures. Submitted to Phys. Rev.

The GATA1s isoform is normally down-regulated during terminal haematopoietic differentiation and over-expression leads to failure to repress MYB, CCND2 and SKI during erythroid differentiation of K562 cells

Background: Although GATA1 is one of the most extensively studied haematopoietic transcription factors little is currently known about the physiological functions of its naturally occurring isoforms GATA1s and GATA1FL in humans—particularly whether the isoforms have distinct roles in different lineages and whether they have non-redundant roles in haematopoietic differentiation. As well as being of general interest to understanding of haematopoiesis, GATA1 isoform biology is important for children with Down syndrome associated acute megakaryoblastic leukaemia (DS-AMKL) where GATA1FL mutations are an essential driver for disease pathogenesis. <p/>Methods: Human primary cells and cell lines were analyzed using GATA1 isoform specific PCR. K562 cells expressing GATA1s or GATA1FL transgenes were used to model the effects of the two isoforms on in vitro haematopoietic differentiation. <p/>Results: We found no evidence for lineage specific use of GATA1 isoforms; however GATA1s transcripts, but not GATA1FL transcripts, are down-regulated during in vitro induction of terminal megakaryocytic and erythroid differentiation in the cell line K562. In addition, transgenic K562-GATA1s and K562-GATA1FL cells have distinct gene expression profiles both in steady state and during terminal erythroid differentiation, with GATA1s expression characterised by lack of repression of MYB, CCND2 and SKI. <p/>Conclusions: These findings support the theory that the GATA1s isoform plays a role in the maintenance of proliferative multipotent megakaryocyte-erythroid precursor cells and must be down-regulated prior to terminal differentiation. In addition our data suggest that SKI may be a potential therapeutic target for the treatment of children with DS-AMKL

Two-Dimensional Copolymers and Exact Conformal Multifractality

We consider in two dimensions the most general star-shaped copolymer, mixing random (RW) or self-avoiding walks (SAW) with specific interactions thereof. Its exact bulk or boundary conformal scaling dimensions in the plane are all derived from an algebraic structure existing on a random lattice (2D quantum gravity). The multifractal dimensions of the harmonic measure of a 2D RW or SAW are conformal dimensions of certain star copolymers, here calculated exactly as non rational algebraic numbers. The associated multifractal function f(alpha) are found to be identical for a random walk or a SAW in 2D. These are the first examples of exact conformal multifractality in two dimensions.Comment: 4 pages, 2 figures, revtex, to appear in Phys. Rev. Lett., January 199