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

Branched Growth with η≈4\eta \approx 4 Walkers

Diffusion-limited aggregation has a natural generalization to the "$\eta$-models", in which $\eta$ random walkers must arrive at a point on the cluster surface in order for growth to occur. It has recently been proposed that in spatial dimensionality $d=2$, there is an upper critical $\eta_c=4$ above which the fractal dimensionality of the clusters is D=1. I compute the first order correction to $D$ for $\eta <4$, obtaining $D=1+{1/2}(4-\eta)$. The methods used can also determine multifractal dimensions to first order in $4-\eta$.Comment: 6 pages, 1 figur

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

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

Model-based solutions for structural coupling in flight control systems

Structural Coupling is the interaction between an aircraft's Flight Control System (FCS) and its structural and aero-dynamics. These interactions have the potential to cause significant problems to the aircraft, possibly through structural fatigue failure, or by corruption of sensor readings leading to degradation of the FCS loop. Presently notch filters are used to attenuate the sensor signals at the structural mode frequencies which cause significant problems. However, each of these notch filters adds a small amount of phase lag to the control loop which limits the performance of the FCS. This research has looked at using Kalman filters to provide an alternative approach to overcoming the structural coupling problem. [Continues.

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

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

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

Analysis for biotechnology innovations using Strategic Environmental Assessment (SEA):

" Meeting the food needs of the world's growing population while reducing poverty and protecting the environment is a major global challenge. Genetically modified crops appear to provide a promising option to deal with this challenge. However there is a need to make strategic decisions on how to spend limited agricultural research funds in order to achieve a maximum impact with regard to finding sustainable solutions to end hunger and poverty. In international development institutions, there is growing interest in the potential use of Strategic Environmental Assessment (SEA) as part of a research based Environmental Management System (EMS) to promote mainstreaming of environmental considerations in policy development. SEA was developed as an approach to integrate environmental considerations at a policy level, where alternatives environmental policies can be evaluated. In this paper, we propose using SEA in a policy research and priority setting process regarding new technologies, taking the development of Genetically Modified Organisms (GMOs) as an example. We propose that this method would be a useful tool for the international agricultural research centers of the Consultative Group for International Agricultural Research (CGIAR), streamlining business processes, strengthening accountability, sharpening the research agenda it supports, fostering broader partnerships, and increasing the relevance and impact of CGIAR research in achieving international development goals. Currently international law requires only Environmental Impact Assessments (EIAs) of specific biotechnology projects. The incorporation of environmental considerations only at the level of specific projects precludes the adoption of alternative environmental policies. In this review, we outline an SEA approach currently being considered at the International Food Policy Research Institute (IFPRI) for use in evaluating biotechnology policies. SEA may be a useful tool to inform the evaluation of biotechnology policies and priorities by taking account of information on the economic, social, and environmental benefits, cost and risks of adopting those policies." Authors' AbstractRisk, Strategic Environmental Assessment, Genetically modified organisms, Living modified organisms,

Strategic environmental assessment: assessing the environmental impact of biotechnology

Poverty reduction, Agricultural research, Environmental protection, Genetically modified organisms, Crops, Agricultural biotechnology Research, Investments, Strategic Environmental Assessment,