1,267 research outputs found
Structural transformations in porous glasses under mechanical loading. I. Tension
The evolution of porous structure and mechanical properties of binary glasses
under tensile loading were examined using molecular dynamics simulations. We
consider vitreous systems obtained in the process of phase separation after a
rapid isochoric quench of a glass-forming liquid to a temperature below the
glass transition. The porous structure in undeformed samples varies from a
connected porous network to a random distribution of isolated pores upon
increasing average glass density. We find that at small strain, the elastic
modulus follows a power-law dependence on the average glass density and the
pore size distribution remains nearly the same as in quiescent samples. Upon
further loading, the pores become significantly deformed and coalesce into
larger voids that leads to formation of system-spanning empty regions
associated with breaking of the material.Comment: 27 pages, 13 figure
Distributions of pore sizes and atomic densities in binary glasses revealed by molecular dynamics simulations
We report on the results of a molecular dynamics simulation study of binodal
glassy systems, formed in the process of isochoric rapid quenching from a
high-temperature fluid phase. The transition to vitreous state occurs due to
concurrent spinodal decomposition and solidification of the matter. The study
is focused on topographies of the porous solid structures and their dependence
on temperature and average density. To quantify the pore-size distributions, we
put forth a scaling relation that provides a robust data collapse in systems
with high porosity. We also find that the local density of glassy phases is
broadly distributed, and, with increasing average glass density, a distinct
peak in the local density distribution is displaced toward higher values.Comment: 22 pages, 6 figure
Structural transformations in porous glasses under mechanical loading. II. Compression
The role of porous structure and glass density in response to compressive
deformation of amorphous materials is investigated via molecular dynamics
simulations. The disordered, porous structures were prepared by quenching a
high-temperature binary mixture below the glass transition into the phase
coexistence region. With decreasing average glass density, the pore morphology
in quiescent samples varies from a random distribution of compact voids to a
porous network embedded in a continuous glass phase. We find that during
compressive loading at constant volume, the porous structure is linearly
transformed in the elastic regime and the elastic modulus follows a power-law
increase as a function of the average glass density. Upon further compression,
pores deform significantly and coalesce into large voids leading to formation
of domains with nearly homogeneous glass phase, which provides an enhanced
resistance to deformation at high strain.Comment: 25 pages, 12 figure
A note on Makeev's conjectures
A counterexample is given for the Knaster-like conjecture of Makeev for
functions on . Some particular cases of another conjecture of Makeev, on
inscribing a quadrangle into a smooth simple closed curve, are solved
positively
Evolution of the pore size distribution in sheared binary glasses
Molecular dynamics simulations are carried out to investigate mechanical
properties and porous structure of binary glasses subjected to steady shear.
The model vitreous systems were prepared via thermal quench at constant volume
to a temperature well below the glass transition. The quiescent samples are
characterized by a relatively narrow pore size distribution whose mean size is
larger at lower glass densities. We find that in the linear regime of
deformation, the shear modulus is a strong function of porosity, and the
individual pores become slightly stretched while their structural topology
remains unaffected. By contrast, with further increasing strain, the shear
stress saturates to a density-dependent plateau value, which is accompanied by
pore coalescence and a gradual development of a broader pore size distribution
with a discrete set of peaks at large length scales.Comment: 30 pages, 16 figure
Coarse Stability and Bifurcation Analysis Using Stochastic Simulators: Kinetic Monte Carlo Examples
We implement a computer-assisted approach that, under appropriate conditions,
allows the bifurcation analysis of the coarse dynamic behavior of microscopic
simulators without requiring the explicit derivation of closed macroscopic
equations for this behavior. The approach is inspired by the so-called
time-step per based numerical bifurcation theory. We illustrate the approach
through the computation of both stable and unstable coarsely invariant states
for Kinetic Monte Carlo models of three simple surface reaction schemes. We
quantify the linearized stability of these coarsely invariant states, perform
pseudo-arclength continuation, detect coarse limit point and coarse Hopf
bifurcations and construct two-parameter bifurcation diagrams.Comment: 26 pages, 5 figure
Multiscale analysis of re-entrant production lines: An equation-free approach
The computer-assisted modeling of re-entrant production lines, and, in
particular, simulation scalability, is attracting a lot of attention due to the
importance of such lines in semiconductor manufacturing. Re-entrant flows lead
to competition for processing capacity among the items produced, which
significantly impacts their throughput time (TPT). Such production models
naturally exhibit two time scales: a short one, characteristic of single items
processed through individual machines, and a longer one, characteristic of the
response time of the entire factory. Coarse-grained partial differential
equations for the spatio-temporal evolution of a "phase density" were obtained
through a kinetic theory approach in Armbruster et al. [2]. We take advantage
of the time scale separation to directly solve such coarse-grained equations,
even when we cannot derive them explicitly, through an equation-free
computational approach. Short bursts of appropriately initialized stochastic
fine-scale simulation are used to perform coarse projective integration on the
phase density. The key step in this process is lifting: the construction of
fine-scale, discrete realizations consistent with a given coarse-grained phase
density field. We achieve this through computational evaluation of conditional
distributions of a "phase velocity" at the limit of large item influxes.Comment: 14 pages, 17 figure
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