290 research outputs found
Elastic Moduli in Nano-Size Samples of Amorphous Solids: System Size Dependence
This Letter is motivated by some recent experiments on pan-cake shaped
nano-samples of metallic glass that indicate a decline in the measured shear
modulus upon decreasing the sample radius. Similar measurements on crystalline
samples of the same dimensions showed a much more modest change. In this Letter
we offer a theory of this phenomenon; we argue that such results are
generically expected for any amorphous solid, with the main effect being
related to the increased contribution of surfaces with respect to bulk when the
samples get smaller. We employ exact relations between the shear modulus and
the eigenvalues of the system's Hessian matrix to explore the role of surface
modes in affecting the elastic moduli
Conformal Theory of the Dimensions of Diffusion Limited Aggregates
We employ the recently introduced conformal iterative construction of
Diffusion Limited Aggregates (DLA) to study the multifractal properties of the
harmonic measure. The support of the harmonic measure is obtained from a
dynamical process which is complementary to the iterative cluster growth. We
use this method to establish the existence of a series of random scaling
functions that yield, via the thermodynamic formalism of multifractals, the
generalized dimensions D(q) of DLA for q >= 1. The scaling function is
determined just by the last stages of the iterative growth process which are
relevant to the complementary dynamics. Using the scaling relation D(3) =
D(0)/2 we estimate the fractal dimension of DLA to be D(0) = 1.69 +- 0.03.Comment: 5 pages, 3 figures, submitted to Phys. Rev. Let
Statistical Physics of the Yielding Transition in Amorphous Solids
The art of making structural, polymeric and metallic glasses is rapidly
developing with many applications. A limitation to their use is their
mechanical stability: under increasing external strain all amorphous solids
respond elastically to small strains but have a finite yield stress which
cannot be exceeded without effecting a plastic response which typically leads
to mechanical failure. Understanding this is crucial for assessing the risk of
failure of glassy materials under mechanical loads. Here we show that the
statistics of the energy barriers \Delta E that need to be surmounted changes
from a probability distribution function (pdf) that goes smoothly to zero to a
pdf which is finite at \Delta E=0. This fundamental change implies a dramatic
transition in the mechanical stability properties with respect to external
strain. We derive exact results for the scaling exponents that characterize the
magnitudes of average energy and stress drops in plastic events as a function
of system size.Comment: 4 pages, 5 figure
Disentangling Scaling Properties in Anisotropic Fracture
Structure functions of rough fracture surfaces in isotropic materials exhibit
complicated scaling properties due to the broken isotropy in the fracture plane
generated by a preferred propagation direction. Decomposing the structure
functions into the even order irreducible representations of the SO(2) symmetry
group (indexed by ) results in a lucid and quickly convergent
description. The scaling exponent of the isotropic sector () dominates at
small length scales. One can reconstruct the anisotropic structure functions
using only the isotropic and the first non vanishing anisotropic sector ()
(or at most the next one ()). The scaling exponent of the isotropic sector
should be observed in a proposed, yet unperformed, experiment.Comment: 5 pages, 8 figure
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