218 research outputs found
Nonparametric regression for multiple heterogeneous networks
We study nonparametric methods for the setting where multiple distinct networks are observed on the same set of nodes. Such samples may arise in the form of replicated networks drawn from a common distribution, or in the form of heterogeneous networks, with the network generating process varying from one network to another, e.g. dynamic and cross-sectional
networks. Nonparametric methods for undirected networks have focused on estimation of the graphon model. While the graphon model accounts for nodal heterogeneity, it does not account for network heterogeneity, a feature specific to applications where multiple networks are observed. To address this setting of multiple networks, we propose a multi-graphon model
which allows node-level as well as network-level heterogeneity. We show how information from multiple networks can be leveraged to enable estimation of the multi-graphon via standard nonparametric regression techniques, e.g. kernel regression, orthogonal series estimation. We study theoretical properties of the proposed estimator establishing recovery of the latent nodal positions up to negligible error, and convergence of the multi-graphon estimator to the normal distribution. Finite sample performance are investigated in a simulation study and application to two real-world networks--a dynamic contact network of ants and a collection of structural
brain networks from different subjects--illustrate the utility of our approach
Adhesive Contact to a Coated Elastic Substrate
We show how the quasi-analytic method developed to solve linear elastic
contacts to coated substrates (Perriot A. and Barthel E. {\em J. Mat. Res.},
{\bf 2004}, {\em 19}, 600) may be extended to adhesive contacts. Substrate
inhomogeneity lifts accidental degeneracies and highlights the general
structure of the adhesive contact theory. We explicit the variation of the
contact variables due to substrate inhomogeneity. The relation to other
approaches based on Finite Element analysis is discussed
Interplay of internal stresses, electric stresses and surface diffusion in polymer films
We investigate two destabilization mechanisms for elastic polymer films and
put them into a general framework: first, instabilities due to in-plane stress
and second due to an externally applied electric field normal to the film's
free surface. As shown recently, polymer films are often stressed due to
out-of-equilibrium fabrication processes as e.g. spin coating. Via an
Asaro-Tiller-Grinfeld mechanism as known from solids, the system can decrease
its energy by undulating its surface by surface diffusion of polymers and
thereby relaxing stresses. On the other hand, application of an electric field
is widely used experimentally to structure thin films: when the electric
Maxwell surface stress overcomes surface tension and elastic restoring forces,
the system undulates with a wavelength determined by the film thickness. We
develop a theory taking into account both mechanisms simultaneously and discuss
their interplay and the effects of the boundary conditions both at the
substrate and the free surface.Comment: 14 pages, 7 figures, 1 tabl
Dynamics of stick-slip in peeling of an adhesive tape
We investigate the dynamics of peeling of an adhesive tape subjected to a
constant pull speed. We derive the equations of motion for the angular speed of
the roller tape, the peel angle and the pull force used in earlier
investigations using a Lagrangian. Due to the constraint between the pull
force, peel angle and the peel force, it falls into the category of
differential-algebraic equations requiring an appropriate algorithm for its
numerical solution. Using such a scheme, we show that stick-slip jumps emerge
in a purely dynamical manner. Our detailed numerical study shows that these set
of equations exhibit rich dynamics hitherto not reported. In particular, our
analysis shows that inertia has considerable influence on the nature of the
dynamics. Following studies in the Portevin-Le Chatelier effect, we suggest a
phenomenological peel force function which includes the influence of the pull
speed. This reproduces the decreasing nature of the rupture force with the pull
speed observed in experiments. This rich dynamics is made transparent by using
a set of approximations valid in different regimes of the parameter space. The
approximate solutions capture major features of the exact numerical solutions
and also produce reasonably accurate values for the various quantities of
interest.Comment: 12 pages, 9 figures. Minor modifications as suggested by refere
A dynamical approach to the spatiotemporal aspects of the Portevin-Le Chatelier effect: Chaos,turbulence and band propagation
Experimental time series obtained from single and poly-crystals subjected to
a constant strain rate tests report an intriguing dynamical crossover from a
low dimensional chaotic state at medium strain rates to an infinite dimensional
power law state of stress drops at high strain rates. We present results of an
extensive study of all aspects of the PLC effect within the context a model
that reproduces this crossover. A study of the distribution of the Lyapunov
exponents as a function of strain rate shows that it changes from a small set
of positive exponents in the chaotic regime to a dense set of null exponents in
the scaling regime. As the latter feature is similar to the GOY shell model for
turbulence, we compare our results with the GOY model. Interestingly, the null
exponents in our model themselves obey a power law. The configuration of
dislocations is visualized through the slow manifold analysis. This shows that
while a large proportion of dislocations are in the pinned state in the chaotic
regime, most of them are at the threshold of unpinning in the scaling regime.
The model qualitatively reproduces the different types of deformation bands
seen in experiments. At high strain rates where propagating bands are seen, the
model equations are reduced to the Fisher-Kolmogorov equation for propagative
fronts. This shows that the velocity of the bands varies linearly with the
strain rate and inversely with the dislocation density, consistent with the
known experimental results. Thus, this simple dynamical model captures the
complex spatio-temporal features of the PLC effect.Comment: 17 pages, 18 figure
Relaxation oscillations and negative strain rate sensitivity in the Portevin - Le Chatelier effect
A characteristic feature of the Portevin - Le Chatelier effect or the jerky
flow is the stick-slip nature of stress-strain curves which is believed to
result from the negative strain rate dependence of the flow stress. The latter
is assumed to result from the competition of a few relevant time scales
controlling the dynamics of jerky flow. We address the issue of time scales and
its connection to the negative strain rate sensitivity of the flow stress
within the framework of a model for the jerky flow which is known to reproduce
several experimentally observed features including the negative strain rate
sensitivity of the flow stress. We attempt to understand the above issues by
analyzing the geometry of the slow manifold underlying the relaxational
oscillations in the model. We show that the nature of the relaxational
oscillations is a result of the atypical bent geometry of the slow manifold.
The analysis of the slow manifold structure helps us to understand the time
scales operating in different regions of the slow manifold. Using this
information we are able to establish connection with the strain rate
sensitivity of the flow stress. The analysis also helps us to provide a proper
dynamical interpretation for the negative branch of the strain rate
sensitivity.Comment: 7 figures, To appear in Phys. Rev.
Adhesion between elastic solids with randomly rough surfaces: comparison of analytical theory with molecular dynamics simulations
The adhesive contact between elastic solids with randomly rough, self affine
fractal surfaces is studied by molecular dynamics (MD) simulations. The
interfacial binding energy obtained from the simulations of nominally flat and
curved surfaces is compared with the predictions of the contact mechanics
theory by Persson. Theoretical and simulation results agree rather well, and
most of the differences observed can be attributed to finite size effects and
to the long-range nature of the interaction between the atoms in the block and
the substrate in the MD model, as compared to the analytical theory which is
for an infinite system with interfacial contact interaction. For curved
surfaces (JKR-type of problem) the effective interfacial energy exhibit a weak
hysteresis which may be due to the influence of local irreversible detachment
processes in the vicinity of the opening crack tip during pull-off.Comment: 6 pages, 6 figure
On the nature of surface roughness with application to contact mechanics, sealing, rubber friction and adhesion
Surface roughness has a huge impact on many important phenomena. The most
important property of rough surfaces is the surface roughness power spectrum
C(q). We present surface roughness power spectra of many surfaces of practical
importance, obtained from the surface height profile measured using optical
methods and the Atomic Force Microscope. We show how the power spectrum
determines the contact area between two solids. We also present applications to
sealing, rubber friction and adhesion for rough surfaces, where the power
spectrum enters as an important input.Comment: Topical review; 82 pages, 61 figures; Format: Latex (iopart). Some
figures are in Postscript Level
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