1,287 research outputs found
Jamming in finite systems: stability, anisotropy, fluctuations and scaling
Athermal packings of soft repulsive spheres exhibit a sharp jamming
transition in the thermodynamic limit. Upon further compression, various
structural and mechanical properties display clean power-law behavior over many
decades in pressure. As with any phase transition, the rounding of such
behavior in finite systems close to the transition plays an important role in
understanding the nature of the transition itself. The situation for jamming is
surprisingly rich: the assumption that jammed packings are isotropic is only
strictly true in the large-size limit, and finite-size has a profound effect on
the very meaning of jamming. Here, we provide a comprehensive numerical study
of finite-size effects in sphere packings above the jamming transition,
focusing on stability as well as the scaling of the contact number and the
elastic response.Comment: 20 pages, 12 figure
Glass and Jamming Transitions: From Exact Results to Finite-Dimensional Descriptions
Despite decades of work, gaining a first-principle understanding of amorphous
materials remains an extremely challenging problem. However, recent theoretical
breakthroughs have led to the formulation of an exact solution in the
mean-field limit of infinite spatial dimension, and numerical simulations have
remarkably confirmed the dimensional robustness of some of the predictions.
This review describes these latest advances. More specifically, we consider the
dynamical and thermodynamic descriptions of hard spheres around the dynamical,
Gardner and jamming transitions. Comparing mean-field predictions with the
finite-dimensional simulations, we identify robust aspects of the description
and uncover its more sensitive features. We conclude with a brief overview of
ongoing research.Comment: 5 figures, 26 page
Finite Element Simulation of Dense Wire Packings
A finite element program is presented to simulate the process of packing and
coiling elastic wires in two- and three-dimensional confining cavities. The
wire is represented by third order beam elements and embedded into a
corotational formulation to capture the geometric nonlinearity resulting from
large rotations and deformations. The hyperbolic equations of motion are
integrated in time using two different integration methods from the Newmark
family: an implicit iterative Newton-Raphson line search solver, and an
explicit predictor-corrector scheme, both with adaptive time stepping. These
two approaches reveal fundamentally different suitability for the problem of
strongly self-interacting bodies found in densely packed cavities. Generalizing
the spherical confinement symmetry investigated in recent studies, the packing
of a wire in hard ellipsoidal cavities is simulated in the frictionless elastic
limit. Evidence is given that packings in oblate spheroids and scalene
ellipsoids are energetically preferred to spheres.Comment: 17 pages, 7 figures, 1 tabl
Beyond icosahedral symmetry in packings of proteins in spherical shells
The formation of quasi-spherical cages from protein building blocks is a
remarkable self-assembly process in many natural systems, where a small number
of elementary building blocks are assembled to build a highly symmetric
icosahedral cage. In turn, this has inspired synthetic biologists to design de
novo protein cages. We use simple models, on multiple scales, to investigate
the self-assembly of a spherical cage, focusing on the regularity of the
packing of protein-like objects on the surface. Using building blocks, which
are able to pack with icosahedral symmetry, we examine how stable these highly
symmetric structures are to perturbations that may arise from the interplay
between flexibility of the interacting blocks and entropic effects. We find
that, in the presence of those perturbations, icosahedral packing is not the
most stable arrangement for a wide range of parameters; rather disordered
structures are found to be the most stable. Our results suggest that (i) many
designed, or even natural, protein cages may not be regular in the presence of
those perturbations, and (ii) that optimizing those flexibilities can be a
possible design strategy to obtain regular synthetic cages with full control
over their surface properties.Comment: 8 pages, 5 figure
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