共查询到20条相似文献,搜索用时 0 毫秒
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Sarkar SK 《Physical review letters》1990,65(21):2680-2683
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Bogoyavlenskiy VA Chernova NA 《Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics》2000,61(2):1629-1633
We have combined the original diffusion-limited aggregation model introduced by Witten and Sander with the surface thermodynamics of the growing solid aggregate. The theory is based on the consideration of the surface chemical potential as a thermodynamic function of the temperature and nearest-neighbor configuration. The Monte Carlo simulations on a two-dimensional square lattice produce the broad range of shapes such as fractal dendritic structures, densely branching patterns, and compact aggregates. The morphology diagram illustrating the relationship between the model parameters and cluster geometry is presented and discussed. 相似文献
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Maher JV 《Physical review letters》1985,55(14):1498-1501
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We have measured the coarsening due to surface tension of radially grown fractal viscous fingering patterns. The patterns at late times depend on the structural form at the onset of coarsening, providing information on the age of the fractal. The coarsening process is not dynamically scale invariant, exhibiting two dynamic length scales that grow as L1(t) approximately t(0.22+/-0.02) and L2(t) approximately t(0.31+/-0.02). The measured exponents are in agreement with the results of recent numerical studies of diffusion-controlled coarsening of a diffusion-limited aggregation fractal [Phys. Rev. E 65, 050501 (2002)]]. 相似文献
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A. B. Ryabov E. B. Postnikov A. Yu. Loskutov 《Journal of Experimental and Theoretical Physics》2005,101(2):253-258
Mean field theory is used as a basis for a new approach to analyzing fractal pattern formation by diffusion-limited aggregation. A coarse time scale is introduced to take into account the discrete nature of DLA clusters. A system of equations is derived and solved numerically to determine the fractal dimension and density of a cluster as a function of distance from its center. The results obtained are in good agreement with direct numerical simulations. 相似文献
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Leonard M. Sander 《Contemporary Physics》2013,54(4):203-218
Diffusion-limited aggregation (DLA) is a model which represents noisy growth limited by diffusion. This process is quite common in nature and the simple algorithm gives a good representation of the large-scale structure of many natural objects. The clusters grown in the computer and the real objects in question are tenuous and approximately self-similar. A good deal is known about the algorithm, but a complete theory is not yet available. I review the current state of knowledge about the model, its applications and theoretical analysis of the results. 相似文献
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B. Widom 《Journal of statistical physics》1988,53(1-2):523-529
The tension of the interface between the equilibrium phases of a phase-separated polymer solution is obtained in the simplest mean-field approximation from the functional equation for the composition profile of the interface. For temperaturesT near the critical solution temperatureT
c, i.e., for Flory parameter near
c, and for high degrees of polymerizationN, the profile and tension scale with=N
1/2(–
c), just as do the compositions of the coexisting phases in mean-field approximation. The surface tension in the asymptotic limitN,
c at fixedx, is found to be given bya
2/kT
c
(2c'/c)1/2
N
-5/4(x), wherea is the lattice spacing of an underlying lattice (or, roughly, the length of a monomer),c andc are the vertical and total coordination numbers of the lattice, and(x) is a scaling function, known for allx, with the asymptotic behavior
asx0 and
asx. The latter implies that becomes independent ofN asN at fixedT nearT
c; the former implies that becomes proportional toN
–1/2(1–T/T
c)3/2 asTT
c at fixedN1, as found previously. 相似文献
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In this paper we undertake a numerical investigation of the dynamics of the interface in the problem of immiscible radial
viscous fingering in a Hele-Shaw cell when the areal flow rate is maintained constant. Comparison is made with experimental
results to check if there is a need to introduce velocity-dependent boundary conditions and to incorporate the effect of thickness
of the film left behind by the moving interface. Some new scaling results are suggested by the numerical data. These data,
along with those available from laboratory experiments, provide support for a mean field theory for radial immiscible viscous
fingering published recently [Phys. Rev. Lett.
65, 2680 (1990)]. 相似文献
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Miscible viscous fingering classically occurs when a less viscous fluid displaces a miscible more viscous one in a porous medium. We analyze here how double diffusive effects between a slow diffusing S and a fast diffusing F component, both influencing the viscosity of the fluids at hand, affect such fingering, and, most importantly, can destabilize the classically stable situation of a more viscous fluid displacing a less viscous one. Various instability scenarios are classified in a parameter space spanned by the log-mobility ratios R(s) and R(f) of the slow and fast component, respectively, and parametrized by the ratio of diffusion coefficients δ. Numerical simulations of the full nonlinear problem confirm the existence of the predicted instability scenarios and highlight the influence of differential diffusion effects on the nonlinear fingering dynamics. 相似文献
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We simulate viscous fingering generated by separating two plates with a constant force, in a lifting Hele-Shaw cell. Variation in the patterns for different fluid viscosity and lifting force is studied. Viscous fingering is strongly affected by anisotropy. We report a computer simulation study of fingering patterns, where circular or square grooves are etched on to the lower plate. Results are compared with experiments. 相似文献
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