Search results for "geometrical [transition]"
showing 10 items of 50 documents
Optical studies of laser-induced gray-tracking in KTP
1999
We have studied gray-tracking induced by a pulsed and polarized 532-nm laser beam in flux grown KTiOPO/sub 4/ (KTP) crystals. Transmission spectra measured under polarized light give different results: gray-tracking leads to an increase in the initial anisotropy of the linear optical properties of KTP, and the polar axis is the most sensitive to this process. The dynamics of relaxation of gray-tracking is anisotropic and depends on the wavelength under analysis. We show a possible induced modification of the crystal surface and also the existence of an intensity above which gray-tracking reaches the saturation point. We then measure the temperature above which gray-tracking no longer exists.
Inverse problems for elliptic equations with power type nonlinearities
2021
We introduce a method for solving Calder\'on type inverse problems for semilinear equations with power type nonlinearities. The method is based on higher order linearizations, and it allows one to solve inverse problems for certain nonlinear equations in cases where the solution for a corresponding linear equation is not known. Assuming the knowledge of a nonlinear Dirichlet-to-Neumann map, we determine both a potential and a conformal manifold simultaneously in dimension $2$, and a potential on transversally anisotropic manifolds in dimensions $n \geq 3$. In the Euclidean case, we show that one can solve the Calder\'on problem for certain semilinear equations in a surprisingly simple way w…
The Calderon problem in transversally anisotropic geometries
2016
We consider the anisotropic Calderon problem of recovering a conductivity matrix or a Riemannian metric from electrical boundary measurements in three and higher dimensions. In the earlier work \cite{DKSaU}, it was shown that a metric in a fixed conformal class is uniquely determined by boundary measurements under two conditions: (1) the metric is conformally transversally anisotropic (CTA), and (2) the transversal manifold is simple. In this paper we will consider geometries satisfying (1) but not (2). The first main result states that the boundary measurements uniquely determine a mixed Fourier transform / attenuated geodesic ray transform (or integral against a more general semiclassical…
Partial data inverse problems for the Hodge Laplacian
2017
We prove uniqueness results for a Calderon type inverse problem for the Hodge Laplacian acting on graded forms on certain manifolds in three dimensions. In particular, we show that partial measurements of the relative-to-absolute or absolute-to-relative boundary value maps uniquely determine a zeroth order potential. The method is based on Carleman estimates for the Hodge Laplacian with relative or absolute boundary conditions, and on the construction of complex geometric optics solutions which reduce the Calderon type problem to a tensor tomography problem for 2-tensors. The arguments in this paper allow to establish partial data results for elliptic systems that generalize the scalar resu…
Determining an unbounded potential from Cauchy data in admissible geometries
2011
In [4 Dos Santos Ferreira , D. , Kenig , C.E. , Salo , M. , Uhlmann , G. ( 2009 ). Limiting Carleman weights and anisotropic inverse problems . Invent. Math. 178 : 119 – 171 . [Crossref], [Web of Science ®], [Google Scholar] ] anisotropic inverse problems were considered in certain admissible geometries, that is, on compact Riemannian manifolds with boundary which are conformally embedded in a product of the Euclidean line and a simple manifold. In particular, it was proved that a bounded smooth potential in a Schrödinger equation was uniquely determined by the Dirichlet-to-Neumann map in dimensions n ≥ 3. In this article we extend this result to the case of unbounded potentials, namely tho…
A discontinuous Galerkin formulation for nonlinear analysis of multilayered shells refined theories
2023
A novel pure penalty discontinuous Galerkin method is proposed for the geometrically nonlinear analysis of multilayered composite plates and shells, modelled via high-order refined theories. The approach allows to build different two-dimensional equivalent single layer structural models, which are obtained by expressing the covariant components of the displacement field through-the-thickness via Taylor’s polynomial expansion of different order. The problem governing equations are deduced starting from the geometrically nonlinear principle of virtual displacements in a total Lagrangian formulation. They are addressed with a pure penalty discontinuous Galerkin method using Legendre polynomial…
Retrieving leaf area index from multi-angular airborne data
2009
This work is aimed to demonstrate the feasibility of a methodology for retrieving bio-geophysical variables whilst at the same time fully accounting for additional information on directional anisotropy. A model-based approach has been developed to deconvolve the angular reflectance into single landcovers reflectances, attempting to solve the inconsistencies of 1D models and linear mixture approaches. The model combines the geometric optics of large scale canopy structure with principles of radiative transfer for volume scattering within individual crowns. The reliability of the model approach to retrieve LAI has been demonstrated using data from DAISEX- 99 campaign at Barrax, Spain. Airborn…
Tecsis: Low-Cost Methodology To Distinguish Archaeological Findings
2006
The automatic or semi-automatic research of archaeological findings includes some methodologies and algorithms of the Computer Vision. Reconstruction of a scene is one of the key step to get the solution to that challenge. This paper will address a methodology to reconstruction underwater scenes with mosaicing techniques. The reconstruction of scene will be the video-mosaic of sea bottom landscapes starting from single video frames. The methodology is based on the evaluation of the optic °ow in between frames, and its motion estimation has been evaluated on the extracted features from the common areas of consecutive pairs frames. This approach carried out the motion model from a geometric p…
Single cigar-shaped nanopores functionalized with amphoteric amino acid chains: experimental and theoretical characterization.
2012
We present an experimental and theoretical characterization of single cigar-shaped nanopores with pH-responsive carboxylic acid and lysine chains functionalized on the pore surface. The nanopore characterization includes (i) optical images of the nanostructure obtained by FESEM; (ii) different chemical procedures for the nanopore preparation (etching time and functionalizations; pH and electrolyte concentration of the external solution) allowing externally tunable nanopore responses monitored by the current-voltage (I-V) curves; and (iii) transport simulations obtained with a multilayer nanopore model. We show that a single, approximately symmetric nanopore can be operated as a reconfigurab…
Chess Thinking and Configural Concepts
2012
The purpose of this work is to connect chess and mathematics education. First, we introduce the idea of configural concepts in chess thinking and then we outline a scheme to show the phases of chess reasoning and how to apply this idea to some conflictual situations. We conclude this work proposing two research problems in introducing chess in mathematical classroom activities.