11,496 research outputs found
On a multiscale strategy and its optimization for the simulation of combined delamination and buckling
This paper investigates a computational strategy for studying the
interactions between multiple through-the-width delaminations and global or
local buckling in composite laminates taking into account possible contact
between the delaminated surfaces. In order to achieve an accurate prediction of
the quasi-static response, a very refined discretization of the structure is
required, leading to the resolution of very large and highly nonlinear
numerical problems. In this paper, a nonlinear finite element formulation along
with a parallel iterative scheme based on a multiscale domain decomposition are
used for the computation of 3D mesoscale models. Previous works by the authors
already dealt with the simulation of multiscale delamination assuming small
perturbations. This paper presents the formulation used to include geometric
nonlinearities into this existing multiscale framework and discusses the
adaptations that need to be made to the iterative process in order to ensure
the rapid convergence and the scalability of the method in the presence of
buckling and delamination. These various adaptations are illustrated by
simulations involving large numbers of DOFs
Recovery Guarantees for Quadratic Tensors with Limited Observations
We consider the tensor completion problem of predicting the missing entries
of a tensor. The commonly used CP model has a triple product form, but an
alternate family of quadratic models which are the sum of pairwise products
instead of a triple product have emerged from applications such as
recommendation systems. Non-convex methods are the method of choice for
learning quadratic models, and this work examines their sample complexity and
error guarantee. Our main result is that with the number of samples being only
linear in the dimension, all local minima of the mean squared error objective
are global minima and recover the original tensor accurately. The techniques
lead to simple proofs showing that convex relaxation can recover quadratic
tensors provided with linear number of samples. We substantiate our theoretical
results with experiments on synthetic and real-world data, showing that
quadratic models have better performance than CP models in scenarios where
there are limited amount of observations available
Properties of the Cosmological Density Distribution Function
The properties of the probability distribution function of the cosmological
continuous density field are studied. We present further developments and
compare dynamically motivated methods to derive the PDF. One of them is based
on the Zel'dovich approximation (ZA). We extend this method for arbitrary
initial conditions, regardless of whether they are Gaussian or not. The other
approach is based on perturbation theory with Gaussian initial fluctuations. We
include the smoothing effects in the PDFs. We examine the relationships between
the shapes of the PDFs and the moments. It is found that formally there are no
moments in the ZA, but a way to resolve this issue is proposed, based on the
regularization of integrals. A closed form for the generating function of the
moments in the ZA is also presented, including the smoothing effects. We
suggest the methods to build PDFs out of the whole series of the moments, or
out of a limited number of moments -- the Edgeworth expansion. The last
approach gives us an alternative method to evaluate the skewness and kurtosis
by measuring the PDF around its peak. We note a general connection between the
generating function of moments for small r.m.s and the non-linear
evolution of the overdense spherical fluctuation in the dynamical models. All
these approaches have been applied in 1D case where the ZA is exact, and simple
analytical results are obtained. The 3D case is analyzed in the same manner and
we found a mutual agreement in the PDFs derived by different methods in the the
quasi-linear regime. Numerical CDM simulation was used to validate the accuracy
of considered approximations. We explain the successful log-normal fit of the
PDF from that simulation at moderate as mere fortune, but not as a
universal form of density PDF in general.Comment: 30 pages in Plain Tex, 1 table and 11 figures available as postscript
files by anonymous ftp from ftp.cita.utoronto.ca in directory
/cita/francis/lev, IFA-94-1
Holography and the Polyakov action
In two dimensional conformal field theory the generating functional for
correlators of the stress-energy tensor is given by the non-local Polyakov
action associated with the background geometry. We study this functional
holographically by calculating the regularized on-shell action of
asymptotically AdS gravity in three dimensions, associated with a specified
(but arbitrary) boundary metric. This procedure is simplified by making use of
the Chern-Simons formulation, and a corresponding first-order expansion of the
bulk dreibein, rather than the metric expansion of Fefferman and Graham. The
dependence of the resulting functional on local moduli of the boundary metric
agrees precisely with the Polyakov action, in accord with the AdS/CFT
correspondence. We also verify the consistency of this result with regard to
the nontrivial transformation properties of bulk solutions under Brown-Henneaux
diffeomorphisms.Comment: 20 pages, RevTeX, v2: minor typos corrected and references adde
The constitutive tensor of linear elasticity: its decompositions, Cauchy relations, null Lagrangians, and wave propagation
In linear anisotropic elasticity, the elastic properties of a medium are
described by the fourth rank elasticity tensor C. The decomposition of C into a
partially symmetric tensor M and a partially antisymmetric tensors N is often
used in the literature. An alternative, less well-known decomposition, into the
completely symmetric part S of C plus the reminder A, turns out to be
irreducible under the 3-dimensional general linear group. We show that the
SA-decomposition is unique, irreducible, and preserves the symmetries of the
elasticity tensor. The MN-decomposition fails to have these desirable
properties and is such inferior from a physical point of view. Various
applications of the SA-decomposition are discussed: the Cauchy relations
(vanishing of A), the non-existence of elastic null Lagrangians, the
decomposition of the elastic energy and of the acoustic wave propagation. The
acoustic or Christoffel tensor is split in a Cauchy and a non-Cauchy part. The
Cauchy part governs the longitudinal wave propagation. We provide explicit
examples of the effectiveness of the SA-decomposition. A complete class of
anisotropic media is proposed that allows pure polarizations in arbitrary
directions, similarly as in an isotropic medium.Comment: 1 figur
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