245 research outputs found
Trapping of Vibrational Energy in Crumpled Sheets
We investigate the propagation of transverse elastic waves in crumpled media.
We set up the wave equation for transverse waves on a generic curved, strained
surface via a Langrangian formalism and use this to study the scaling behaviour
of the dispersion curves near the ridges and on the flat facets. This analysis
suggests that ridges act as barriers to wave propagation and that modes in a
certain frequency regime could be trapped in the facets. A simulation study of
the wave propagation qualitatively supported our analysis and showed
interesting effects of the ridges on wave propagation.Comment: RevTex 12 pages, 7 figures, Submitted to PR
Anomalous strength of membranes with elastic ridges
We report on a simulational study of the compression and buckling of elastic
ridges formed by joining the boundary of a flat sheet to itself. Such ridges
store energy anomalously: their resting energy scales as the linear size of the
sheet to the 1/3 power. We find that the energy required to buckle such a ridge
is a fixed multiple of the resting energy. Thus thin sheets with elastic ridges
such as crumpled sheets are qualitatively stronger than smoothly bent sheets.Comment: 4 pages, REVTEX, 3 figure
The effects of forcing and dissipation on phase transitions in thin granular layers
Recent experimental and computational studies of vibrated thin layers of
identical spheres have shown transitions to ordered phases similar to those
seen in equilibrium systems. Motivated by these results, we carry out
simulations of hard inelastic spheres forced by homogenous white noise. We find
a transition to an ordered state of the same symmetry as that seen in the
experiments, but the clear phase separation observed in the vibrated system is
absent. Simulations of purely elastic spheres also show no evidence for phase
separation. We show that the energy injection in the vibrated system is
dramatically different in the different phases, and suggest that this creates
an effective surface tension not present in the equilibrium or randomly forced
systems. We do find, however, that inelasticity suppresses the onset of the
ordered phase with random forcing, as is observed in the vibrating system, and
that the amount of the suppression is proportional to the degree of
inelasticity. The suppression depends on the details of the energy injection
mechanism, but is completely eliminated when inelastic collisions are replaced
by uniform system-wide energy dissipation.Comment: 10 pages, 5 figure
Phase field model of premelting of grain boundaries
We present a phase field model of solidification which includes the effects
of the crystalline orientation in the solid phase. This model describes grain
boundaries as well as solid-liquid boundaries within a unified framework. With
an appropriate choice of coupling of the phase field variable to the gradient
of the crystalline orientation variable in the free energy, we find that high
angle boundaries undergo a premelting transition. As the melting temperature is
approached from below, low angle grain boundaries remain narrow. The width of
the liquid layer at high angle grain boundaries diverges logarithmically. In
addition, for some choices of model coupling, there may be a discontinuous jump
in the width of the fluid layer as function of temperature.Comment: 6 pages, 9 figures, RevTeX
Unsteady Crack Motion and Branching in a Phase-Field Model of Brittle Fracture
Crack propagation is studied numerically using a continuum phase-field
approach to mode III brittle fracture. The results shed light on the physics
that controls the speed of accelerating cracks and the characteristic branching
instability at a fraction of the wave speed.Comment: 11 pages, 4 figure
Properties of Ridges in Elastic Membranes
When a thin elastic sheet is confined to a region much smaller than its size
the morphology of the resulting crumpled membrane is a network of straight
ridges or folds that meet at sharp vertices. A virial theorem predicts the
ratio of the total bending and stretching energies of a ridge. Small strains
and curvatures persist far away from the ridge. We discuss several kinds of
perturbations that distinguish a ridge in a crumpled sheet from an isolated
ridge studied earlier (A. E. Lobkovsky, Phys. Rev. E. 53 3750 (1996)). Linear
response as well as buckling properties are investigated. We find that quite
generally, the energy of a ridge can change by no more than a finite fraction
before it buckles.Comment: 13 pages, RevTeX, acknowledgement adde
Geometry of Valley Growth
Although amphitheater-shaped valley heads can be cut by groundwater flows
emerging from springs, recent geological evidence suggests that other processes
may also produce similar features, thus confounding the interpretations of such
valley heads on Earth and Mars. To better understand the origin of this
topographic form we combine field observations, laboratory experiments,
analysis of a high-resolution topographic map, and mathematical theory to
quantitatively characterize a class of physical phenomena that produce
amphitheater-shaped heads. The resulting geometric growth equation accurately
predicts the shape of decimeter-wide channels in laboratory experiments,
100-meter wide valleys in Florida and Idaho, and kilometer wide valleys on
Mars. We find that whenever the processes shaping a landscape favor the growth
of sharply protruding features, channels develop amphitheater-shaped heads with
an aspect ratio of pi
Estimation of prokaryotic supergenome size and composition from gene frequency distributions
BACKGROUND: Because prokaryotic genomes experience a rapid flux of genes, selection may act at a higher level than an individual genome. We explore a quantitative model of the distributed genome whereby groups of genomes evolve by acquiring genes from a fixed reservoir which we denote as supergenome. Previous attempts to understand the nature of the supergenome treated genomes as random, independent collections of genes and assumed that the supergenome consists of a small number of homogeneous sub-reservoirs. Here we explore the consequences of relaxing both assumptions. RESULTS: We surveyed several methods for estimating the size and composition of the supergenome. The methods assumed that genomes were either random, independent samples of the supergenome or that they evolved from a common ancestor along a known tree via stochastic sampling from the reservoir. The reservoir was assumed to be either a collection of homogeneous sub-reservoirs or alternatively composed of genes with Gamma distributed gain probabilities. Empirical gene frequencies were used to either compute the likelihood of the data directly or first to reconstruct the history of gene gains and then compute the likelihood of the reconstructed numbers of gains. CONCLUSIONS: Supergenome size estimates using the empirical gene frequencies directly are not robust with respect to the choice of the model. By contrast, using the gene frequencies and the phylogenetic tree to reconstruct multiple gene gains produces reliable estimates of the supergenome size and indicates that a homogeneous supergenome is more consistent with the data than a supergenome with Gamma distributed gain probabilities
Crumpling a Thin Sheet
Crumpled sheets have a surprisingly large resistance to further compression.
We have studied the crumpling of thin sheets of Mylar under different loading
conditions. When placed under a fixed compressive force, the size of a crumpled
material decreases logarithmically in time for periods up to three weeks. We
also find hysteretic behavior when measuring the compression as a function of
applied force. By using a pre-treating protocol, we control this hysteresis and
find reproducible scaling behavior for the size of the crumpled material as a
function of the applied force.Comment: revtex 4 pages, 6 eps figures submitted to Phys Rev. let
Critical examination of cohesive-zone models in the theory of dynamic fracture
We have examined a class of cohesive-zone models of dynamic mode-I fracture,
looking both at steady-state crack propagation and its stability against
out-of-plane perturbations. Our work is an extension of that of Ching, Langer,
and Nakanishi (CLN) (Phys. Rev. E, vol. 53, no. 3, p. 2864 (1996)), who studied
a non-dissipative version of this model and reported strong instability at all
non-zero crack speeds. We have reformulated the CLN theory and have discovered,
surprisingly, that their model is mathematically ill-posed. In an attempt to
correct this difficulty and to construct models that might exhibit realistic
behavior, we have extended the CLN analysis to include dissipative mechanisms
within the cohesive zone. We have succeeded to some extent in finding
mathematically well posed systems; and we even have found a class of models for
which a transition from stability to instability may occur at a nonzero crack
speed via a Hopf bifurcation at a finite wavelength of the applied
perturbation. However, our general conclusion is that these cohesive-zone
models are inherently unsatisfactory for use in dynamical studies. They are
extremely difficult mathematically, and they seem to be highly sensitive to
details that ought to be physically unimportant.Comment: 19 pages, REVTeX 3.1, epsf.sty, also available at
http://itp.ucsb.edu/~lobkovs
- …