673 research outputs found
First-principles calculation of mechanical properties of Si <001> nanowires and comparison to nanomechanical theory
We report the results of first-principles density functional theory
calculations of the Young's modulus and other mechanical properties of
hydrogen-passivated Si nanowires. The nanowires are taken to have
predominantly {100} surfaces, with small {110} facets according to the Wulff
shape. The Young's modulus, the equilibrium length and the constrained residual
stress of a series of prismatic beams of differing sizes are found to have size
dependences that scale like the surface area to volume ratio for all but the
smallest beam. The results are compared with a continuum model and the results
of classical atomistic calculations based on an empirical potential. We
attribute the size dependence to specific physical structures and interactions.
In particular, the hydrogen interactions on the surface and the charge density
variations within the beam are quantified and used both to parameterize the
continuum model and to account for the discrepancies between the two models and
the first-principles results.Comment: 14 pages, 10 figure
A statistical mechanics framework for static granular matter
The physical properties of granular materials have been extensively studied
in recent years. So far, however, there exists no theoretical framework which
can explain the observations in a unified manner beyond the phenomenological
jamming diagram [1]. This work focuses on the case of static granular matter,
where we have constructed a statistical ensemble [2] which mirrors equilibrium
statistical mechanics. This ensemble, which is based on the conservation
properties of the stress tensor, is distinct from the original Edwards ensemble
and applies to packings of deformable grains. We combine it with a field
theoretical analysis of the packings, where the field is the Airy stress
function derived from the force and torque balance conditions. In this
framework, Point J characterized by a diverging stiffness of the pressure
fluctuations. Separately, we present a phenomenological mean-field theory of
the jamming transition, which incorporates the mean contact number as a
variable. We link both approaches in the context of the marginal rigidity
picture proposed by [3, 4].Comment: 21 pages, 15 figure
Thermodynamics of non-local materials: extra fluxes and internal powers
The most usual formulation of the Laws of Thermodynamics turns out to be
suitable for local or simple materials, while for non-local systems there are
two different ways: either modify this usual formulation by introducing
suitable extra fluxes or express the Laws of Thermodynamics in terms of
internal powers directly, as we propose in this paper. The first choice is
subject to the criticism that the vector fluxes must be introduced a posteriori
in order to obtain the compatibility with the Laws of Thermodynamics. On the
contrary, the formulation in terms of internal powers is more general, because
it is a priori defined on the basis of the constitutive equations. Besides it
allows to highlight, without ambiguity, the contribution of the internal powers
in the variation of the thermodynamic potentials. Finally, in this paper, we
consider some examples of non-local materials and derive the proper expressions
of their internal powers from the power balance laws.Comment: 16 pages, in press on Continuum Mechanics and Thermodynamic
Stretching and folding versus cutting and shuffling: An illustrated perspective on mixing and deformations of continua
We compare and contrast two types of deformations inspired by mixing
applications -- one from the mixing of fluids (stretching and folding), the
other from the mixing of granular matter (cutting and shuffling). The
connection between mechanics and dynamical systems is discussed in the context
of the kinematics of deformation, emphasizing the equivalence between stretches
and Lyapunov exponents. The stretching and folding motion exemplified by the
baker's map is shown to give rise to a dynamical system with a positive
Lyapunov exponent, the hallmark of chaotic mixing. On the other hand, cutting
and shuffling does not stretch. When an interval exchange transformation is
used as the basis for cutting and shuffling, we establish that all of the map's
Lyapunov exponents are zero. Mixing, as quantified by the interfacial area per
unit volume, is shown to be exponentially fast when there is stretching and
folding, but linear when there is only cutting and shuffling. We also discuss
how a simple computational approach can discern stretching in discrete data.Comment: REVTeX 4.1, 9 pages, 3 figures; v2 corrects some misprints. The
following article appeared in the American Journal of Physics and may be
found at http://ajp.aapt.org/resource/1/ajpias/v79/i4/p359_s1 . Copyright
2011 American Association of Physics Teachers. This article may be downloaded
for personal use only. Any other use requires prior permission of the author
and the AAP
Atomistic calculations of interface elastic properties in noncoherent metallic bilayers
The paper describes theoretical and computational studies associated with the interface elastic properties of noncoherent metallic bicrystals. Analytical forms of interface energy, interface stresses, and interface elastic constants are derived in terms of interatomic potential functions. Embedded-atom method potentials are then incorporated into the model to compute these excess thermodynamics variables, using energy minimization in a parallel computing environment. The proposed model is validated by calculating surface thermodynamic variables and comparing them with preexisting data. Next, the interface elastic properties of several fcc-fcc bicrystals are computed. The excess energies and stresses of interfaces are smaller than those on free surfaces of the same crystal orientations. In addition, no negative values of interface stresses are observed. Current results can be applied to various heterogeneous materials where interfaces assume a prominent role in the systems' mechanical behavior.open322
Diffraction microstrain in nanocrystalline solids under load - heterogeneous medium approach
This is an account of the computation of X-ray microstrain in a polycrystal
with anisotropic elasticity under uniaxial external load. The results have been
published in the article "Microstrain in nanocrystalline solids under load by
virtual diffraction", at Europhysics Letters 89, 66002 (2010). The present
information was submitted to Europhysics Letters as part of the manuscript
package, and was available to the reviewers who recommended the paper for
publication.Comment: Supporting online material for J. Markmann, D. Bachurin, L.-H. Shao,
P. Gumbsch, J. Weissm\"uller, Microstrain in nanocrystalline solids under
load by virtual diffraction, Europhys. Lett. 89, 66002 (2010
Kinetic theory of age-structured stochastic birth-death processes
Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov-–Born–-Green–-Kirkwood-–Yvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution
Numerical computations of facetted pattern formation in snow crystal growth
Facetted growth of snow crystals leads to a rich diversity of forms, and
exhibits a remarkable sixfold symmetry. Snow crystal structures result from
diffusion limited crystal growth in the presence of anisotropic surface energy
and anisotropic attachment kinetics. It is by now well understood that the
morphological stability of ice crystals strongly depends on supersaturation,
crystal size and temperature. Until very recently it was very difficult to
perform numerical simulations of this highly anisotropic crystal growth. In
particular, obtaining facet growth in combination with dendritic branching is a
challenging task. We present numerical simulations of snow crystal growth in
two and three space dimensions using a new computational method recently
introduced by the authors. We present both qualitative and quantitative
computations. In particular, a linear relationship between tip velocity and
supersaturation is observed. The computations also suggest that surface energy
effects, although small, have a larger effect on crystal growth than previously
expected. We compute solid plates, solid prisms, hollow columns, needles,
dendrites, capped columns and scrolls on plates. Although all these forms
appear in nature, most of these forms are computed here for the first time in
numerical simulations for a continuum model.Comment: 12 pages, 28 figure
Distributed optimal control of a nonstandard system of phase field equations
We investigate a distributed optimal control problem for a phase field model
of Cahn-Hilliard type. The model describes two-species phase segregation on an
atomic lattice under the presence of diffusion; it has been recently introduced
by the same authors in arXiv:1103.4585v1 [math.AP] and consists of a system of
two highly nonlinearly coupled PDEs. For this reason, standard arguments of
optimal control theory do not apply directly, although the control constraints
and the cost functional are of standard type. We show that the problem admits a
solution, and we derive the first-order necessary conditions of optimality.Comment: Key words: distributed optimal control, nonlinear phase field
systems, first-order necessary optimality condition
- …