1,721,262 research outputs found
An elastic model for volcanology
No full textThis monograph presents a rigorous mathematical framework for a linear elastic model arising from volcanology that explains deformation effects generated by inflating or deflating magma chambers in the Earth’s interior. From a mathematical perspective, these modeling assumptions manifest as a boundary value problem that has long been known by researchers in volcanology, but has not, until now, been given a thorough mathematical treatment. This mathematical study gives an explicit formula for the solution of the boundary value problem which generalizes the few well-known, explicit solutions found in geophysics literature. Using two distinct analytical approaches—one involving weighted Sobolev spaces, and the other using single and double layer potentials—the well-posedness of the elastic model is proven. An Elastic Model for Volcanology will be of particular interest to mathematicians researching inverse problems, as well as geophysicists studying volcanology
Asymptotic expansion for harmonic functions in the half-space with a pressurized cavity
No full textIn this paper, we address a simplied version of a problem arising from volcanology. Specifically, as reduced form of the
boundary value problem for the Lame system, we consider a Neumann problem for harmonic functions in the half-space with
a cavity C. Zero normal derivative is assumed at the boundary of the half-space; differently, at the boundary of C, the normal derivative
of the function is required to be given by an external datum g, corresponding to a pressure term exerted on the medium
at the boundary of C. Under the assumption that the (pressurized) cavity is small with respect to the distance from the boundary of
the half-space, we establish an asymptotic formula for the solution of the problem. Main ingredients are integral equation
formulations of the harmonic solution of the Neumann problem and a spectral analysis of the integral operators involved
in the problem. In the special case of a datum g which describes a constant pressure at the boundary of C, we recover a simplied
representation based on a polarization tensor
Analysis of a Mogi-type model describing surface deformations induced by a magma chamber embedded in an elastic half-space
No full textMotivated by a vulcanological problem, we establish a sound mathematical approach for surface deformation effects generated by a magma chamber embedded into Earth’s interior and exerting on it a uniform hydrostatic pressure. Modeling assumptions translate the problem into classical elasto-static system (homogeneous and isotropic) in an half-space with an embedded cavity. The boundary conditions are traction-free for the air/crust boundary and uniformly hydrostatic for the chamber boundary. These are complemented with zero-displacement condition at infinity (with
decay rate). After a short presentation of the model and of its geophysical interest, we establish the well-posedness of the problem and provide an appropriate integral formulation for its solution for cavity with general shape. Based on that, assuming that the
chamber is centred at some fixed point z and has diameter r > 0, small with respect to the depth d, we derive rigorously the principal term in the asymptotic expansion for the surface deformation as r/d --> 0+. Such formula provides a rigorous proof of the Mogi point source model in the case of spherical cavities generalizing it to the case of cavities of arbitrary shape
On an elastic model arising from volcanology: An analysis of the direct and inverse problem
No full textIn this paper we investigate a mathematical model arising from volcanology describing surface deformation effects generated by a magma chamber embedded into Earth's interior and exerting on it a uniform hydrostatic pressure. The modeling assumptions translate mathematically into a Neumann boundary value problem for the classical Lamé system in a half-space with an embedded pressurized cavity. We establish well-posedness of the problem in suitable weighted Sobolev spaces and analyse the inverse problem of determining the pressurized cavity from partial measurements of the displacement field proving uniqueness and stability estimates
Data driven regularization by projection
No full textWe study linear inverse problems under the premise that the forward operator is not at hand but given indirectly through some input-output training pairs. We demonstrate that regularization by projection and variational regularization can be formulated by using the training data only and without making use of the forward operator. We study convergence and stability of the regularized solutions in view of Seidman (1980 J. Optim. Theory Appl. 30 535), who showed that regularization by projection is not convergent in general, by giving some insight on the generality of Seidman's nonconvergence example. Moreover,we show, analytically and numerically, that regularization by projection is indeed capable of learning linear operators, such as the Radon transform
Screen production studies and ASPRI : The Australian screen production research index
No full textScreen production studies and ASPRI : The Australian screen production research inde
Asymptotic expansions for higher order elliptic equations with an application to quantitative photoacoustic tomography
No full textIn this paper, we derive new asymptotic expansions for the solutions of higher order elliptic equations in the presence of small inclusions. As a byproduct, we derive a topological derivative based algorithm for the reconstruction of piecewise smooth functions. This algorithm can be used for edge detection in imaging, topological optimization, and inverse problems, such as quantitative photoacoustic tomography, for which we demonstrate the effectiveness of our asymptotic expansion method numerically
Iulii Aspri e Maesii Titiani in un documento epigrafico dell'ager Tusculanus
No full textMaria Grazia Granino Cecere, Iulii Aspri e Maesii Titiani in un documento epigrafico dell'ager Tusculanus, p. 139-157.
Il recente rinvenimento presso l'abbazia di S. Nilo a Grottaferrata del frammento di un coperchio di sarcofago relativo ad una Mesia Titiana c(larissima) p(uella), pronipote di un Asper iunior, riferibile alla nota proprietà dei Iulii Aspri nell'ager Tusculanus, consente da un lato di riprendere in esame i numerosi problemi connessi allò stemma di quella famiglia, di notevole importanza nella scena politica della prima metà del III secolo; dall'altro di conoscerne successivi legami matrimoniali con la non meno influente gens senatoria siciliana dei Maesii Titiani, i cui interessi in Roma e nel Lazio potrebbero essere stati ben più ampi di quanto finora supposto.Granino Cecere Maria Grazia. Iulii Aspri e Maesii Titiani in un documento epigrafico dell'ager Tusculanus. In: Mélanges de l'École française de Rome. Antiquité, tome 102, n°1. 1990. pp. 139-157
Analysis of a linear elastic model relative to a small pressurized cavity embedded in the half-space
No full textMotivated by a vulcanological problem, a sound mathematical approach is established for surface deformation effects
generated by a magma chamber embedded into Earth's interior and exerting on it a uniform hydrostatic pressure.
Modeling assumptions translate the problem into classical elasto-static system (homogeneous and isotropic) in an
half-space with an embedded pressurized cavity.
The boundary conditions are traction-free for the air/crust boundary and uniformly hydrostatic for the chamber boundary.
These are complemented with zero-displacement condition at infinity (with decay rate).
The well-posedness of the mathematical problem is established and it is provided an appropriate integral formulation for its solution for cavity with general shape.
Based on that, assuming that the pressurized cavity is small with respect to the depth, in the thesis is derived rigorously the principal term of the asymptotic expansion for the surface deformation when the ratio "diameter of the cavity and depth" goes to zero. These are new results in the field of the asymptotic analysis since the case of a no null Neumann boundary conditions on the boundary of the cavity and unbounded domains are jointly considered. Moreover a simplified mathematical scalar version of the problem, based on harmonic functions, is analysed. Using again the setting of the integral equations, the well-posedness of the problem is studied. Some new results on asymptotic expansions in unbounded domains contained a small hole with no null Neumann boundary condition are obtained
Identification of cavities and inclusions in linear elasticity with a phase-field approach
No full textIn this paper, we deal with the inverse problem of the shape reconstruction
of cavities and inclusions embedded in a linear elastic isotropic medium from
boundary displacement's measurements. For, we consider a constrained
minimization problem involving a boundary quadratic misfit functional with a
regularization term that penalizes the perimeter of the cavity or inclusion to
be identified. Then using a phase-field approach we derive a robust algorithm
for the reconstruction of elastic inclusions and of cavities modeled as
inclusions with a very small elasticity tensor
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