876 research outputs found
Scale transition and enforcement of RVE boundary conditions in second-order computational homogenization
Formulation of the scale transition equations coupling the microscopic and macroscopic variables in the second-order computational homogenization of heterogeneous materials and the enforcement of generalized boundary conditions for the representative volume element (RVE) are considered. The proposed formulation builds on current approaches by allowing any type of RVE boundary conditions (e.g. displacement, traction, periodic) and arbitrary shapes of RVE to be applied in a unified manner. The formulation offers a useful geometric interpretation for the assumptions associated with the microstructural displacement fluctuation field within the RVE, which is here extended to second-order computational homogenization. A unified approach to the enforcement of the boundary conditions has been undertaken using multiple constraint projection matrices. The results of an illustrative shear layer model problem indicate that the displacement and traction RVE boundary conditions provide the upper and lower bounds of the response determined via second-order computational homogenization, and the solution associated with the periodic RVE boundary conditions lies between them
Log-concave measures
We study the log-concave measures, their characterization via the
Pr\'ekopa-Leindler property and also define a subset of it whose elements are
called super log-concave measures which have the property of satisfying a
logarithmic Sobolev inequality. We give some results about their stability.
Certain relations with measure transportation of Monge-Kantorovitch and the
Monge-Amp\'ere equation are also indicated with applications
Some remarks about the positivity of random variables on a Gaussian probability space
Let be an abstract Wiener space and be a probability density
of class LlogL. Using the measure transportation of Monge-Kantorovitch, we
prove that the kernel of the projection of L on the second Wiener chaos defines
an (Hilbert-Schmidt) operator which is lower bounded by another Hilbert-Schmidt
operator.Comment: 6 page
A non commutative sewing lemma
In a preceding paper [E.J.ofProb.34,860-892,(2006)], we proved a sewing lemma
which was a key result for the study of Holder continuous functions. In this
paper we give a non-commutative version of this lemma with some applications.Comment: 11 page
Flows driven by Banach space-valued rough paths
We show in this note how the machinery of C^1-approximate flows devised in
the work "Flows driven by rough paths", and applied there to reprove and extend
most of the results on Banach space-valued rough differential equations driven
by a finite dimensional rough path, can be used to deal with rough differential
equations driven by an infinite dimensional Banach space-valued weak geometric
Holder p-rough paths, for any p>2, giving back Lyons' theory in its full force
in a simple way.Comment: 8 page
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