283 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
Contact area of rough spheres: Large scale simulations and simple scaling laws
We use molecular simulations to study the nonadhesive and adhesive
atomic-scale contact of rough spheres with radii ranging from nanometers to
micrometers over more than ten orders of magnitude in applied normal load. At
the lowest loads, the interfacial mechanics is governed by the contact
mechanics of the first asperity that touches. The dependence of contact area on
normal force becomes linear at intermediate loads and crosses over to Hertzian
at the largest loads. By combining theories for the limiting cases of nominally
flat rough surfaces and smooth spheres, we provide parameter-free analytical
expressions for contact area over the whole range of loads. Our results
establish a range of validity for common approximations that neglect curvature
or roughness in modeling objects on scales from atomic force microscope tips to
ball bearings.Comment: 2 figures + Supporting Materia
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
Missing physics in stick-slip dynamics of a model for peeling of an adhesive tape
It is now known that the equations of motion for the contact point during
peeling of an adhesive tape mounted on a roll introduced earlier are singular
and do not support dynamical jumps across the two stable branches of the peel
force function. By including the kinetic energy of the tape in the Lagrangian,
we derive equations of motion that support stick-slip jumps as a natural
consequence of the inherent dynamics. In the low mass limit, these equations
reproduce solutions obtained using a differential-algebraic algorithm
introduced for the earlier equations. Our analysis also shows that mass of the
ribbon has a strong influence on the nature of the dynamics.Comment: Accepted for publication in Phys. Rev. E (Rapid Communication
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
Relation between composition, microstructure and oxidation in iron aluminides
The relation between chemical composition, microstructure and oxidation properties has been investigated on various FeAl based alloys, the aim being to induce changes in the microstructure of the compound by selective oxidation of aluminium. Oxidation kinetics that was evaluated on bulk specimens showed that, due to fast diffusion in the alloys, no composition gradient is formed during the aluminium selective oxidation. Accordingly, significant aluminium depletion in the compound could be observed in the thinnest part of oxidised wedge-shape specimens. Another way to obtain samples of variable aluminium content was to prepare diffusion couples with one aluminide and pure iron as end members. These latter specimens have been characterised using electron microscopy and first results of oxidation experiments are presented
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
Self-stresses and Crack Formation by Particle Swelling in Cohesive Granular Media
We present a molecular dynamics study of force patterns, tensile strength and
crack formation in a cohesive granular model where the particles are subjected
to swelling or shrinkage gradients. Non-uniform particle size change generates
self-equilibrated forces that lead to crack initiation as soon as strongest
tensile contacts begin to fail. We find that the coarse-grained stresses are
correctly predicted by an elastic model that incorporates particle size change
as metric evolution. The tensile strength is found to be well below the
theoretical strength as a result of inhomogeneous force transmission in
granular media. The cracks propagate either inward from the edge upon shrinkage
and outward from the center upon swelling
- …