1,721,041 research outputs found
Detecting cavities by electrostatic boundary measurements
No full textWe prove upper and lower bounds on the size of an unknown cavity, or of a perfectly conducting inclusion, in an electrical conductor in terms of boundary measurements of voltage and current. Such bounds, which might be used as a decision tool in quality testing of materials, are obtained by a nontrivial extension of previous results (Alessandrini G, Rosset E and Seo J K 2000 Proc. Am. Math. Soc. 128 53-64) regarding inclusions of finite, nonzero conductivity
Estimating the area of extreme inclusions in Reissner–Mindlin plates
Full text linkWe derive upper and lower estimates of the area of unknown defects in the form of either cavities or rigid inclusions in Mindlin–Reissner elastic plates in terms of the difference δW of the works exerted by boundary loads on the defected and on the reference plate. It turns out that the upper estimates depend linearly on δW, whereas the lower ones depend quadratically on δW. These results continue a line of research concerning size estimates of extreme inclusions in electric conductors, elastic bodies and plates
The linear constraints in Poincarè and Korn type inequalities
No full textWe investigate the character of the linear constraints which are
needed for Poincarè and Korn type inequalities to hold. We
especially analyze constraints which depend on restriction on
subsets of positive measure and on the trace on a portion of the
boundary
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Recent results about the detection of unknown boundaries and inclusions in elastic plates
No full textIn this paper we review some recent results concerning
inverse problems for thin elastic plates. The plate is assumed to
be made by non-homogeneous linearly elastic material belonging to
a general class of anisotropy. A first group of results concerns
uniqueness and stability for the determination of unknown
boundaries, including the cases of cavities and rigid inclusions.
In the second group of results, we consider upper and lower
estimates of the area of unknown inclusions given in terms of the
work exerted by a couple field applied at the boundary of the
plate. In particular, we extend previous size estimates for
elastic inclusions to the case of cavities and rigid inclusions
Numerical validation of the size estimates approach for electrical conductors
No full textThis work deals with the so-called size estimates approach for detecting inclusions in electrical conductors on the basis of boundary measurements of the current density and of the corresponding voltage. Following the guidelines drawn up in Alessandrini et al. [1] and the experience made in Alessandrini et al. [2], an extended numerical investigation has been performed in order to prove the effectiveness of this approach. The sensitivity with respect to various relevant parameters is also analyzed. The work is supported by MIUR grant 2003082352 "Metodi non distruttivi per l'identificazione e la diagnosi di materiali e strutture
Stable determination of a rigid inclusion in an anisotropic plate
No full textIn this paper we consider the inverse problem of determining a rigid inclusion inside a thin plate by applying a couple field at the boundary and by measuring the induced transversal displacement
and its normal derivative at the boundary of the plate. The plate is made by non-homogeneous linearly elastic material belonging to
a general class of anisotropy. For this severely ill-posed
problem, under suitable a priori regularity assumptions on the boundary of the inclusion, we prove a stability estimate of
log-log type
- …
