Noticias en español
Uniform estimates for small volume asymptotics.
RESUMEN: We revisit the problem of studying the impact of a perturbation of the coefficients of an elliptic PDE on a set of small size. We show that the asymptotic structure of the perturbed solution can be described in terms of the spectrum of the Poincaré variational operators defined by the perturbations. This approach turns out to be useful in obtaining estimates which are uniform in the coefficient contrast.
Read MoreOptimization of accessibility and application to supports in additive manufacturing.
RESUMEN: In this talk I will discuss a geometric constraint, called accessibility constraint, for shape and topology optimization of structures built by additive manufacturing. The motivation comes from the use of sacrificial supports to maintain a structure, submitted to intense thermal residual stresses during its building process. Once the building stage is finished, the supports are of no more use and should be removed. However, such a removal can be very difficult or even impossible if the supports are hidden deep inside the complex geometry of the structure. A rule of thumb for...
Read MoreReconstructing elastic strain fields from its Longitudinal Ray Transform.
RESUMEN: In the problem of Bragg-edge elastic strain tomography, measurements are obtained from energy resolved neutron transmission imaging, which provides information about the Longitudinal Ray Transform (LRT) of the elastic strain field. The goal is to recover the elastic strain field by inverting its LRT. The inversion of the ray transform for tensor fields is a well studied problem [1]. It is known that only the solenoidal part of symmetric tensor fields can be recovered from their LRT, there are inversion formulas available that reconstruct such solenoidal component and there are...
Read MoreOn the reachable space for the heat equation.
RESUMEN: The goal of this talk is to explain how perturbative arguments can be applied to derive a sharp description of the reachable space for heat equations having lower order terms. The main result I will present is the following one. Let us consider an abstract system $y’ = Ay + Bu$, where $A$ is an operator generating a $C^0$ semigroup $(exp(tA))_{t\geq 0}$ on a Hilbert space $X$, and $B$ is a control operator, for instance a linear operator from an Hilbert space $U$ to $X$, and let us assume that this system is null-controllable in $X$ in any positive time. Then, setting $R$ the...
Read MoreSingular perturbation method for stability of infinite-dimensional systems.
RESUMEN: Coupled systems appear everywhere in complex models and in some cases there are different time scales involved. The coupling and the scales make this kind of system very difficult to study from theoretical and computational viewpoints. One hopes that some particular properties of the system could be studied through simpler uncoupled systems. This is what the singular perturbation method (SPM) does concerning stability properties. The SPM approach has been introduced for ordinary differential equations and can also be applied for partial differential equations but in the latter case...
Read More