4,049 research outputs found
Periodic homogenization of a pseudo-parabolic equation via a spatial-temporal decomposition
Pseudo-parabolic equations have been used to model unsaturated fluid flow in
porous media. In this paper it is shown how a pseudo-parabolic equation can be
upscaled when using a spatio-temporal decomposition employed in the
Peszyn'ska-Showalter-Yi paper [8]. The spatial-temporal decomposition
transforms the pseudo-parabolic equation into a system containing an elliptic
partial differential equation and a temporal ordinary differential equation. To
strengthen our argument, the pseudo-parabolic equation has been given
advection/convection/drift terms. The upscaling is done with the technique of
periodic homogenization via two-scale convergence. The well-posedness of the
extended pseudo-parabolic equation is shown as well. Moreover, we argue that
under certain conditions, a non-local-in-time term arises from the elimination
of an unknown.Comment: 6 pages, 0 figure
Chlamydia trachomatis: Management in Pregnancy
Chlamydia trachomatis is a sexually transmitted disease (STD) commonly diagnosed in pregnancy. C. trachomatis has been linked to several pregnancy complications including premature rupture of membranes (PROM), preterm labor and birth, low birth weight, intrauterine growth retardation, and postpartum endometritis. Infants born to mothers through an infected birth canal are at risk for acquiring C. trachomatis pneumonitis, conjunctivitis, and nasopharyngeal infection. The standard treatment of C. trachomatis in pregnancy is erythromycin. Recently, amoxicillin and clindamycin have been added as alternative regimens for those patients intolerant of erythromycin. This paper reviews the effectiveness and tolerance of the alternative regimens compared with erythromycin and the success of antepartum treatment of chlamydia in preventing the poor pregnancy outcome and neonatal morbidity associated with C. trachomatis
Asymptotic homogenisation in strength and fatigue durability analysis of composites
This is the post-print version of the Article. Copyright @ 2003 Kluwer Academic Publishers.Asymptotic homogenisation technique and two-scale convergence is used for analysis of macro-strength and fatigue durability of composites with a periodic structure under cyclic loading. The linear damage accumulation rule is employed in the phenomenological micro-durability conditions (for each component of the composite) under varying cyclic loading. Both local and non-local strength and durability conditions are analysed. The strong convergence of the strength as the structure period tends to zero is proved and its limiting value is estimated.This work was supported under the research grant GR/M24592 from the Engineering and Physical Sciences Research Council, UK
Stress minimization for lattice structures. Part I: Micro-structure design
This work is partially supported by the SOFIA project, funded by Bpifrance (Banque Publique d’Investissement). This work has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 833092.Peer ReviewedPostprint (published version
Homogenization of the one-dimensional wave equation
We present a method for two-scale model derivation of the periodic
homogenization of the one-dimensional wave equation in a bounded domain. It
allows for analyzing the oscillations occurring on both microscopic and
macroscopic scales. The novelty reported here is on the asymptotic behavior of
high frequency waves and especially on the boundary conditions of the
homogenized equation. Numerical simulations are reported
Effective macroscopic dynamics of stochastic partial differential equations in perforated domains
An effective macroscopic model for a stochastic microscopic system is
derived. The original microscopic system is modeled by a stochastic partial
differential equation defined on a domain perforated with small holes or
heterogeneities. The homogenized effective model is still a stochastic partial
differential equation but defined on a unified domain without holes. The
solutions of the microscopic model is shown to converge to those of the
effective macroscopic model in probability distribution, as the size of holes
diminishes to zero. Moreover, the long time effectivity of the macroscopic
system in the sense of \emph{convergence in probability distribution}, and the
effectivity of the macroscopic system in the sense of \emph{convergence in
energy} are also proved
SIMP-ALL: a generalized SIMP method based on the topological derivative concept
Topology optimization has emerged in the last years as a promising research fieldwith a wide range of applications. One of the most successful approaches, theSIMP method, is based on regularizing the problem and proposing a penaliza-tion interpolation function. In this work, we propose an alternative interpolationfunction, the SIMP-ALL method that is based on the topological derivative con-cept. First, we show the strong relation in plane linear elasticity between theHashin-Shtrikman (H-S) bounds and the topological derivative, providing anew interpretation of the last one. Then, we show that the SIMP-ALL interpo-lation remains always in between the H-S bounds regardless the materials tobe interpolated. This result allows us to interpret intermediate values as realmicrostructures. Finally, we verify numerically this result and we show the con-venience of the proposed SIMP-ALL interpolation for obtaining auto-penalizedoptimal design in a wider range of cases. A MATLAB code of the SIMP-ALLinterpolation function is also provide
On the commutability of homogenization and linearization in finite elasticity
We study non-convex elastic energy functionals associated to (spatially)
periodic, frame indifferent energy densities with a single non-degenerate
energy well at SO(n). Under the assumption that the energy density admits a
quadratic Taylor expansion at identity, we prove that the Gamma-limits
associated to homogenization and linearization commute. Moreover, we show that
the homogenized energy density, which is determined by a multi-cell
homogenization formula, has a quadratic Taylor expansion with a quadratic term
that is given by the homogenization of the quadratic term associated to the
linearization of the initial energy density
Locally periodic unfolding method and two-scale convergence on surfaces of locally periodic microstructures
In this paper we generalize the periodic unfolding method and the notion of
two-scale convergence on surfaces of periodic microstructures to locally
periodic situations. The methods that we introduce allow us to consider a wide
range of non-periodic microstructures, especially to derive macroscopic
equations for problems posed in domains with perforations distributed
non-periodically. Using the methods of locally periodic two-scale convergence
(l-t-s) on oscillating surfaces and the locally periodic (l-p) boundary
unfolding operator, we are able to analyze differential equations defined on
boundaries of non-periodic microstructures and consider non-homogeneous Neumann
conditions on the boundaries of perforations, distributed non-periodically
Correctors for some nonlinear monotone operators
In this paper we study homogenization of quasi-linear partial differential
equations of the form -\mbox{div}\left( a\left( x,x/\varepsilon _h,Du_h\right)
\right) =f_h on with Dirichlet boundary conditions. Here the
sequence tends to as
and the map is periodic in monotone in
and satisfies suitable continuity conditions. We prove that
weakly in as where
is the solution of a homogenized problem of the form -\mbox{div}\left(
b\left( x,Du\right) \right) =f on We also derive an explicit
expression for the homogenized operator and prove some corrector results,
i.e. we find such that in
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