91 research outputs found
Nonaffine Correlations in Random Elastic Media
Materials characterized by spatially homogeneous elastic moduli undergo
affine distortions when subjected to external stress at their boundaries, i.e.,
their displacements \uv (\xv) from a uniform reference state grow linearly
with position \xv, and their strains are spatially constant. Many materials,
including all macroscopically isotropic amorphous ones, have elastic moduli
that vary randomly with position, and they necessarily undergo nonaffine
distortions in response to external stress. We study general aspects of
nonaffine response and correlation using analytic calculations and numerical
simulations. We define nonaffine displacements \uv' (\xv) as the difference
between \uv (\xv) and affine displacements, and we investigate the
nonaffinity correlation function
and related functions. We introduce four model random systems with random
elastic moduli induced by locally random spring constants, by random
coordination number, by random stress, or by any combination of these. We show
analytically and numerically that scales as A |\xv|^{-(d-2)}
where the amplitude is proportional to the variance of local elastic moduli
regardless of the origin of their randomness. We show that the driving force
for nonaffine displacements is a spatial derivative of the random elastic
constant tensor times the constant affine strain. Random stress by itself does
not drive nonaffine response, though the randomness in elastic moduli it may
generate does. We study models with both short and long-range correlations in
random elastic moduli.Comment: 22 Pages, 18 figures, RevTeX
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
Qualcuno volò dal nido familiare: convivenza o matrimonio? Spagna e Portogallo a confronto
In Spagna e Portogallo il matrimonio continua ad essere la forma prevalente di unione (88% di
entrata in matrimonio per la Spagna e 95% per il Portogallo); anche se le generazioni di donne più
giovani manifestano una maggior propensione alla convivenza rispetto alle coorti precedenti. I nati tra il 1978 e il 1985 presentano una maggiore tendenza a convivere
rispetto a coloro che sono nati nella prima metà del XX secolo, più in Spagna che in Portogallo
(23,9% vs 20,2%).Si noti che la convivenza, confrontata con il matrimonio quale prima unione,
differisce significativamente tra i due Paesi, con una più ampia e anticipata diffusione in Spagna. La fonte di dati utilizzata permette di
confrontare le differenze tra convivenza e matrimonio attraverso la loro relazione con altri eventi del
corso di vita quali: l’età media all’unione, l’attività lavorativa, l’emancipazione dal nucleo familiare e
la presenza di figli
Scaling of the buckling transition of ridges in thin sheets
When a thin elastic sheet crumples, the elastic energy condenses into a
network of folding lines and point vertices. These folds and vertices have
elastic energy densities much greater than the surrounding areas, and most of
the work required to crumple the sheet is consumed in breaking the folding
lines or ``ridges''. To understand crumpling it is then necessary to understand
the strength of ridges. In this work, we consider the buckling of a single
ridge under the action of inward forcing applied at its ends. We demonstrate a
simple scaling relation for the response of the ridge to the force prior to
buckling. We also show that the buckling instability depends only on the ratio
of strain along the ridge to curvature across it. Numerically, we find for a
wide range of boundary conditions that ridges buckle when our forcing has
increased their elastic energy by 20% over their resting state value. We also
observe a correlation between neighbor interactions and the location of initial
buckling. Analytic arguments and numerical simulations are employed to prove
these results. Implications for the strength of ridges as structural elements
are discussed.Comment: 42 pages, latex, doctoral dissertation, to be submitted to Phys Rev
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
A Gradient-Based Approach for Breast DCE-MRI Analysis
Breast cancer is the main cause of female malignancy worldwide. Effective early detection by imaging studies remains critical to decrease mortality rates, particularly in women at high risk for developing breast cancer. Breast Magnetic Resonance Imaging (MRI) is a common diagnostic tool in the management of breast diseases, especially for high-risk women. However, during this examination, both normal and abnormal breast tissues enhance after contrast material administration. Specifically, the normal breast tissue enhancement is known as background parenchymal enhancement: it may represent breast activity and depends on several factors, varying in degree and distribution in different patients as well as in the same patient over time. While a light degree of normal breast tissue enhancement generally causes no interpretative difficulties, a higher degree may cause difficulty to detect and classify breast lesions at Magnetic Resonance Imaging even for experienced radiologists. In this work, we intend to investigate the exploitation of some statistical measurements to automatically characterize the enhancement trend of the whole breast area in both normal and abnormal tissues independently from the presence of a background parenchymal enhancement thus to provide a diagnostic support tool for radiologists in the MRI analysis
Sonoluminescence as a QED vacuum effect. I: The Physical Scenario
Several years ago Schwinger proposed a physical mechanism for
sonoluminescence in terms of changes in the properties of the
quantum-electrodynamic (QED) vacuum state. This mechanism is most often phrased
in terms of changes in the Casimir Energy: changes in the distribution of
zero-point energies and has recently been the subject of considerable
controversy. The present paper further develops this quantum-vacuum approach to
sonoluminescence: We calculate Bogolubov coefficients relating the QED vacuum
states in the presence of a homogeneous medium of changing dielectric constant.
In this way we derive an estimate for the spectrum, number of photons, and
total energy emitted. We emphasize the importance of rapid spatio-temporal
changes in refractive indices, and the delicate sensitivity of the emitted
radiation to the precise dependence of the refractive index as a function of
wavenumber, pressure, temperature, and noble gas admixture. Although the
physics of the dynamical Casimir effect is a universal phenomenon of QED,
specific experimental features are encoded in the condensed matter physics
controlling the details of the refractive index. This calculation places rather
tight constraints on the possibility of using the dynamical Casimir effect as
an explanation for sonoluminescence, and we are hopeful that this scenario will
soon be amenable to direct experimental probes. In a companion paper we discuss
the technical complications due to finite-size effects, but for reasons of
clarity in this paper we confine attention to bulk effects.Comment: 25 pages, LaTeX 209, ReV-TeX 3.2, eight figures. Minor revisions:
Typos fixed, references updated, minor changes in numerical estimates, minor
changes in some figure
Redundancy and cooperativity in the mechanics of compositely crosslinked filamentous networks
The actin cytoskeleton in living cells has many types of crosslinkers. The
mechanical interplay between these different crosslinker types is an open issue
in cytoskeletal mechanics. We develop a framework to study the cooperativity
and redundancy in the mechanics of filamentous networks with two types of
crosslinkers: crosslinkers that allow free rotations of filaments and
crosslinkers that do not. The framework consists of numerical simulations and
an effective medium theory on a percolating triangular lattice. We find that
the introduction of angle-constraining crosslinkers significantly lowers the
filament concentrations required for these networks to attain mechanical
integrity. This cooperative effect also enhances the stiffness of the network
and suppresses non-affine deformations at a fixed filament concentration. We
further find that semiflexible networks with only freely-rotating crosslinks
are mechanically very similar to compositely crosslinked flexible networks with
both networks exhibiting the same scaling behavior. We show that the network
mechanics can either be redundant or cooperative depending on the relative
energy scale of filament bending to the energy stored in the angle-constraining
crosslinkers, and the relative concentration of crosslinkers. Our results may
have implications for understanding the role of multiple crosslinkers even in a
system without bundle formation or other structural motifs.Comment: 21 pages, 5 figure
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