2,549 research outputs found
The stress transmission universality classes of periodic granular arrays
The transmission of stress is analysed for static periodic arrays of rigid grains, with perfect and zero friction. For minimal coordination number (which is sensitive to friction, sphericity and dimensionality), the stress distribution is soluble without reference to the corresponding displacement fields. In non-degenerate cases, the constitutive equations are found to be simple linear in the stress components. The corresponding coefficients depend crucially upon geometrical disorder of the grain contacts
Critical Dynamical Exponent of the Two-Dimensional Scalar Model with Local Moves
We study the scalar one-component two-dimensional (2D) model by
computer simulations, with local Metropolis moves. The equilibrium exponents of
this model are well-established, e.g. for the 2D model
and . The model has also been conjectured to belong to the Ising
universality class. However, the value of the critical dynamical exponent
is not settled. In this paper, we obtain for the 2D model using
two independent methods: (a) by calculating the relative terminal exponential
decay time for the correlation function ,
and thereafter fitting the data as , where is the system
size, and (b) by measuring the anomalous diffusion exponent for the order
parameter, viz., the mean-square displacement (MSD) as , and from the numerically
obtained value , we calculate . For different values of the
coupling constant , we report that and
for the two methods respectively. Our results indicate that
is independent of , and is likely identical to that for the 2D
Ising model. Additionally, we demonstrate that the Generalised Langevin
Equation (GLE) formulation with a memory kernel, identical to those applicable
for the Ising model and polymeric systems, consistently capture the observed
anomalous diffusion behavior.Comment: 14 pages, 4 figures, 6 figure files, to appear in Phys. Rev.
Anisotropic diffusion limited aggregation in three dimensions : universality and nonuniversality
We explore the macroscopic consequences of lattice anisotropy for diffusion limited aggregation (DLA) in three dimensions. Simple cubic and bcc lattice growths are shown to approach universal asymptotic states in a coherent fashion, and the approach is accelerated by the use of noise reduction. These states are strikingly anisotropic dendrites with a rich hierarchy of structure. For growth on an fcc lattice, our data suggest at least two stable fixed points of anisotropy, one matching the bcc case. Hexagonal growths, favoring six planar and two polar directions, appear to approach a line of asymptotic states with continuously tunable polar anisotropy. The more planar of these growths visually resembles real snowflake morphologies. Our simulations use a new and dimension-independent implementation of the DLA model. The algorithm maintains a hierarchy of sphere coverings of the growth, supporting efficient random walks onto the growth by spherical moves. Anisotropy was introduced by restricting growth to certain preferred directions
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