1,561 research outputs found

    Aerodynamic properties of fractal grains: Implications for the primordial solar nebula

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    Under conditions in the primordial solar nebula and dense interstellar clouds, small grains have low relative velocities. This is the condition for efficient sticking and formation of fractal aggregates. A calculation of the ratio of cross section, sigma, to number of primary particles, N, for fractal clusters yielded 1n sigma/N = 0.2635 + 0.5189N sup (-0.1748). This ratio decreases slowly with N and approaches a constant for large N. Under the usual assumption of collisions producing spherical compact, uniform density aggregates, sigma/N varies as N sup -1/3 and decreases rapidly. Fractal grains are therefore much more closely coupled to the gas than are compact aggregates. This has a significant effect on the aerodynamic behavior of aggregates and consequently on their evolution and that of the nebula

    Smoluchowski's equation for cluster exogenous growth

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    We introduce an extended Smoluchowski equation describing coagulation processes for which clusters of mass s grow between collisions with ds/dt=Asβds/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

    Conformal approach to cylindrical DLA

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    We extend the conformal mapping approach elaborated for the radial Diffusion Limited Aggregation model (DLA) to the cylindrical geometry. We introduce in particular a complex function which allows to grow a cylindrical cluster using as intermediate step a radial aggregate. The grown aggregate exhibits the same self-affine features of the original cylindrical DLA. The specific choice of the transformation allows us to study the relationship between the radial and the cylindrical geometry. In particular the cylindrical aggregate can be seen as a radial aggregate with particles of size increasing with the radius. On the other hand the radial aggregate can be seen as a cylindrical aggregate with particles of size decreasing with the height. This framework, which shifts the point of view from the geometry to the size of the particles, can open the way to more quantitative studies on the relationship between radial and cylindrical DLA.Comment: 16 pages, 8 figure

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

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    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 (k2k^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 4545^\circ (3030^\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 kνk^\nu, was proposed. The exponent ν\nu has a nonuniversal critical value νc\nu_c, for which the patterns generated in the noiseless limit exhibit the original (axial) anisotropy for ν<νc\nu<\nu_c and the rotated one (diagonal) for ν>νc\nu>\nu_c. The values νc=1.395±0.005\nu_c = 1.395\pm0.005 and νc=0.82±0.01\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 ν=2\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

    Amalgams of Inverse Semigroups and C*-algebras

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    An amalgam of inverse semigroups [S,T,U] is full if U contains all of the idempotents of S and T. We show that for a full amalgam [S,T,U], the C*-algebra of the inverse semigroup amaglam of S and T over U is the C*-algebraic amalgam of C*(S) and C*(T) over C*(U). Using this result, we describe certain amalgamated free products of C*-algebras, including finite-dimensional C*-algebras, the Toeplitz algebra, and the Toeplitz C*-algebras of graphs

    Spatial scaling in fracture propagation in dilute systems

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    The geometry of fracture patterns in a dilute elastic network is explored using molecular dynamics simulation. The network in two dimensions is subjected to a uniform strain which drives the fracture to develop by the growth and coalescence of the vacancy clusters in the network. For strong dilution, it has been shown earlier that there exists a characteristic time tct_c at which a dynamical transition occurs with a power law divergence (with the exponent zz) of the average cluster size. Close to tct_c, the growth of the clusters is scale-invariant in time and satisfies a dynamical scaling law. This paper shows that the cluster growth near tct_c also exhibits spatial scaling in addition to the temporal scaling. As fracture develops with time, the connectivity length ξ\xi of the clusters increses and diverges at tct_c as ξ(tct)ν\xi \sim (t_c-t)^{-\nu}, with ν=0.83±0.06\nu = 0.83 \pm 0.06. As a result of the scale-invariant growth, the vacancy clusters attain a fractal structure at tct_c with an effective dimensionality df1.85±0.05d_f \sim 1.85 \pm 0.05. These values are independent (within the limit of statistical error) of the concentration (provided it is sufficiently high) with which the network is diluted to begin with. Moreover, the values are very different from the corresponding values in qualitatively similar phenomena suggesting a different universality class of the problem. The values of ν\nu and dfd_f supports the scaling relation z=νdfz=\nu d_f with the value of zz obtained before.Comment: A single ps file (6 figures included), 12 pages, to appear in Physica

    Diffusion-limited deposition with dipolar interactions: fractal dimension and multifractal structure

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    Computer simulations are used to generate two-dimensional diffusion-limited deposits of dipoles. The structure of these deposits is analyzed by measuring some global quantities: the density of the deposit and the lateral correlation function at a given height, the mean height of the upper surface for a given number of deposited particles and the interfacial width at a given height. Evidences are given that the fractal dimension of the deposits remains constant as the deposition proceeds, independently of the dipolar strength. These same deposits are used to obtain the growth probability measure through Monte Carlo techniques. It is found that the distribution of growth probabilities obeys multifractal scaling, i.e. it can be analyzed in terms of its f(α)f(\alpha) multifractal spectrum. For low dipolar strengths, the f(α)f(\alpha) spectrum is similar to that of diffusion-limited aggregation. Our results suggest that for increasing dipolar strength both the minimal local growth exponent αmin\alpha_{min} and the information dimension D1D_1 decrease, while the fractal dimension remains the same.Comment: 10 pages, 7 figure

    Multifractal Dimensions for Branched Growth

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    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

    Diffusion-limited deposition of dipolar particles

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    Deposits of dipolar particles are investigated by means of extensive Monte Carlo simulations. We found that the effect of the interactions is described by an initial, non-universal, scaling regime characterized by orientationally ordered deposits. In the dipolar regime, the order and geometry of the clusters depend on the strength of the interactions and the magnetic properties are tunable by controlling the growth conditions. At later stages, the growth is dominated by thermal effects and the diffusion-limited universal regime obtains, at finite temperatures. At low temperatures the crossover size increases exponentially as T decreases and at T=0 only the dipolar regime is observed.Comment: 5 pages, 4 figure

    Aggregation in a mixture of Brownian and ballistic wandering particles

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    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 PbaP_{ba}, or random ones, with probability Prw=1PbaP_{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 PbaP_{ba} continuously increases from df1.72d_f\approx 1.72 (DLA dimensionality) for Pba=0P_{ba}=0 to df2d_f\approx 2 (BA dimensionality) for Pba=1P_{ba}=1. However, the lacunarity and the active zone width exhibt a distinct behavior: they are convex functions of PbaP_{ba} with a maximum at Pba1/2P_{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 PbaP_{ba} and rapidly vanishes for Pba>1/2P_{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
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