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

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

Geomorphology, Sedimentary Structures, and Genesis of Dome Dunes in Western Canada

Dome dunes in four stabilized, inland dune fields in western Canada are predominantly composed of horizontal to low-angle cross-strata, indicating that slip face development was rare. Dip angles of lee side deposits decrease upward in the dome dunes. The spread of dip directions increases with elevation in the dunes, spanning 360° for topset deposits. Sedimentary structures indicative of moisture (adhesion laminae) and vegetation (scour surfaces) occur in the dunes and denivation features are also present. Sediment adhesion is responsible for the maintenance of the dome morphology. Sediment sorting within the dome dunes is poorer than in other local dune types in the vicinity, suggesting that less reworking/ineffective selective transport occurred and that the dome dunes are more efficient in retaining sediment. The rarity of slip face and grainfall deposits and the abundance of low angle deposits indicate that preferential accumulation of sediment at the top of the lee side did not occur. Development of domal morphology is a consequence of the inhibition of slip face development. In inland, relatively moist boreal environments, the primary factor limiting or precluding sediment accumulation at the crest of the dunes is a low rate of sedimentation.Les dunes en dôme situées dans des champs de dunes stabilisés à l'intérieur des terres sont en grande partie constituées de stratifications entrecroisées subhorizontales, indiquant ainsi un faible développement de la face sous le vent. L'angle de pendage du versant sous le vent tend à diminuer vers la partie supérieure des dunes. Les directions de pendage s'étalent avec l'altitude, jusqu'à 360° dans les dépôts sommitaux. On trouve dans ces dunes des structures sédimentaires indicatrices de la présence d'humidité (feuillets adhérents) et de végétation (surface d'affouillement) ainsi que des formes de dénivation. La préservation de la morphologie des dunes est attribuable à l'adhésivité des sédiments. La granulométrie des dunes en dôme n'est pas aussi complète que dans les autres types de dunes de la région, indiquant ainsi que le remaniement des sédiments et leur transport sélectif ont été moins efficaces et qu'il y a eu meilleure rétention des sédiments. La faible accumulation par écoulement granulaire et sur la face sous le vent et la forte accumulation par strates subhorizontales montrent qu'il n'y a pas eu de mise en place préférentielle de sédiments au sommet du versant sous le vent. L'élaboration de la morphologie en dôme est attribuable au faible développement de la face sous le vent. À l'intérieur des terres, en milieu boréal relativement humide, l'accumulation des sédiments est minime-au sommet des dunes, surtout en raison du faible taux de sédimentation.Kuppeldunen in vier stabilisierten Inlanddûnenfeldern in West-Kanada bestehen vor allem aus hori-zontalen bis gering geneigten Kreuzschichtungen, was darauf hinweist, dass abrutschende Entwicklung selten war. Die Neigungswinkel der Ablagerungen auf der Leeseite nehmen in den Kuppeldunen nach oben hin ab. Die Ausdehnung der Neigungsrichtungen nimmt mit der Hôhe der Dûnen zu, bis zu 360° in den hôchsten Ablagerungen. Es gibt in den Dùnen Sedimentstrukturen, die auf Feuchtigkeit (haftende Blatter) und Vegetation (Schleifoberflàchen) hinweisen, und auch Denivationserscheinungen sind vorhanden. Der Sedimentadhâsion wird die Erhaltung der Kuppelmorphologie zugeschrieben. Die Sedimentsortierung innerhalb der Kuppeldunen ist geringer als in anderen lokalen Dùnen-typen in der Nàhe, so dass man annimmt, dass weniger Umarbeitung/ ineffektiver selektiver Transport geschah und dass die Kuppeldunen erfolgreicher Sediment zurùckhalten. Das seltene Vorkommen abrutschender und kôrniger Ablagerungen und die Fùlle von gering geneigten Ablagerungen zeigen, dass bevorzugte Sedimentakkumulation an der Spitze der Leeseite nicht vorkam. Die Entwicklung der Kuppelmorphologie ergibt sich aus der Verhinderung abrutschender Entwicklung. Im Inland, in relativ feuchter nôrdlicher Umwelt ist der hauptsachliche Faktor der Begren-zung oder Verhinderung der Sedimentakkumulation an der Spitze der Dùnen eine niedrige Sedimentierungsrate

A different angle: comparative analyses of whole-animal transport costs running uphill

Comparative work on animals' costs of terrestrial locomotion has focussed on the underpinning physiology and biomechanics. Often, much of an animal's energy budget is spent on moving around thus there is also value in interpreting such data from an ecological perspective. When animals move through their environment they encounter topographical variation, and this is a key factor that can dramatically affect their energy expenditure. We collated published data on the costs for birds and mammals to locomote terrestrially on inclines, and investigated the scaling relationships using a phylogenetically informed approach. We show that smaller animals have a greater mass-specific cost of transport on inclines across the body mass range analysed. We also demonstrate that the increase in cost for smaller animals to run up a slope relative to along a flat surface is comparatively low. Heavier animals show larger absolute and relative increases in energy cost to travel uphill. Consideration of all aspects of the cost of incline locomotion – absolute, relative, and mass-specific – provides a fuller understanding of the interactions between transport costs, body mass, incline gradient and phylogeny, and enables us to consider their ecological implications, which we couch within the context of the ‘energy landscape‘.</jats:p

Measuring Energetics and Behaviour Using Accelerometry in Cane Toads Bufo marinus

Cane toads Bufo marinus were introduced to Australia as a control agent but now have a rapidly progressing invasion front and damage new habitats they enter. Predictive models that can give expansion rates as functions of energy supply and feeding ground distribution could help to maximise control efficiency but to date no study has measured rates of field energy expenditure in an amphibian. In the present study we used the accelerometry technique to generate behavioural time budgets and, through the derivation of ODBA (overall dynamic body acceleration), to obtain estimates of energetics in free ranging cane toads. This represents the first time that accelerometers have been used to not only quantify the behaviour of animals but also assign to those behaviours rates of energy expenditure. Firstly, laboratory calibrations between ODBA and metabolic rate were obtained and used to generate a common prediction equation for the subject toads (R2 = 0.74). Furthermore, acceleration data recorded during different behaviours was studied to ascertain threshold values for objectively defining behaviour categories. Importantly, while subsequent accelerometer field deployments were relatively short they agreed with previous studies on the proportion of time that cane toads locomote yet suggest that the metabolic rate of cane toads in the wild may sometimes be considerably higher than might be assumed based on data for other species

Stability of Monomer-Dimer Piles

We measure how strong, localized contact adhesion between grains affects the maximum static critical angle, theta_c, of a dry sand pile. By mixing dimer grains, each consisting of two spheres that have been rigidly bonded together, with simple spherical monomer grains, we create sandpiles that contain strong localized adhesion between a given particle and at most one of its neighbors. We find that tan(theta_c) increases from 0.45 to 1.1 and the grain packing fraction, Phi, decreases from 0.58 to 0.52 as we increase the relative number fraction of dimer particles in the pile, nu_d, from 0 to 1. We attribute the increase in tan(theta_c(nu_d)) to the enhanced stability of dimers on the surface, which reduces the density of monomers that need to be accomodated in the most stable surface traps. A full characterization and geometrical stability analysis of surface traps provides a good quantitative agreement between experiment and theory over a wide range of nu_d, without any fitting parameters.Comment: 11 pages, 12 figures consisting of 21 eps files, submitted to PR

Diffusion-Reorganized Aggregates: Attractors in Diffusion Processes?

A process based on particle evaporation, diffusion and redeposition is applied iteratively to a two-dimensional object of arbitrary shape. The evolution spontaneously transforms the object morphology, converging to branched structures. Independently of initial geometry, the structures found after long time present fractal geometry with a fractal dimension around 1.75. The final morphology, which constantly evolves in time, can be considered as the dynamic attractor of this evaporation-diffusion-redeposition operator. The ensemble of these fractal shapes can be considered to be the {\em dynamical equilibrium} geometry of a diffusion controlled self-transformation process.Comment: 4 pages, 5 figure

Velocity Correlations in Dense Gravity Driven Granular Chute Flow

We report numerical results for velocity correlations in dense, gravity-driven granular flow down an inclined plane. For the grains on the surface layer, our results are consistent with experimental measurements reported by Pouliquen. We show that the correlation structure within planes parallel to the surface persists in the bulk. The two-point velocity correlation function exhibits exponential decay for small to intermediate values of the separation between spheres. The correlation lengths identified by exponential fits to the data show nontrivial dependence on the averaging time \dt used to determine grain velocities. We discuss the correlation length dependence on averaging time, incline angle, pile height, depth of the layer, system size and grain stiffness, and relate the results to other length scales associated with the rheology of the system. We find that correlation lengths are typically quite small, of the order of a particle diameter, and increase approximately logarithmically with a minimum pile height for which flow is possible, \hstop, contrary to the theoretical expectation of a proportional relationship between the two length scales.Comment: 21 pages, 16 figure

Investigation of the preparation of materials in space. Task 4 - Field management for weightless containerless processing Quarterly progress report, 22 Aug. - 31 Oct. 1969

Weightless containerless processing for space, electromagnetic position control, force measurements and techniques, and hydrodynamic