Search results for "inverse problem"
showing 10 items of 163 documents
Study of the $\bar K N$ system and coupled channels in a finite volume
2013
We investigate the $\bar KN$ and coupled channels system in a finite volume and study the properties of the $\Lambda(1405)$ resonance. We calculate the energy levels in a finite volume and solve the inverse problem of determining the resonance position in the infinite volume. We devise the best strategy of analysis to obtain the two poles of the $\Lambda(1405)$ in the infinite volume case, with sufficient precision to distinguish them.
A magnetic source imaging camera
2016
We describe a magnetic source imaging camera (MSIC) allowing a direct dynamic visualization of the two-dimensional spatial distribution of the individual components Bx(x,y), By(x,y) and Bz(x,y) of a magnetic field. The field patterns allow—in principle— a reconstruction of the distribution of sources that produce the field B→ by inverse problem analysis. We compare experimentally recorded point-spread functions, i.e., field patterns produced by point-like magnetic dipoles of different orientations with anticipated field patterns. Currently, the MSIC can resolve fields of ≈10 pT (1 s measurement time) range in a field of view up to ∼20 × 20 mm2. The device has a large range of possible appli…
Total decay and transition rates from LQCD
2018
We present a new technique for extracting total transition rates into final states with any number of hadrons from lattice QCD. The method involves constructing a finite-volume Euclidean four-point function whose corresponding infinite-volume spectral function gives access to the decay and transition rates into all allowed final states. The inverse problem of calculating the spectral function is solved via the Backus-Gilbert method, which automatically includes a smoothing procedure. This smoothing is in fact required so that an infinite-volume limit of the spectral function exists. Using a numerical toy example we find that reasonable precision can be achieved with realistic lattice data. …
Relativistic perfect fluids in local thermal equilibrium
2017
Every evolution of a fluid is uniquely described by an energy tensor. But the converse is not true: an energy tensor may describe the evolution of different fluids. The problem of determining them is called here the {\em inverse problem}. This problem may admit unphysical or non-deterministic solutions. This paper is devoted to solve the inverse problem for perfect energy tensors in the class of perfect fluids evolving in local thermal equilibrium (l.t.e.). The starting point is a previous result (Coll and Ferrando in J Math Phys 30: 2918-2922, 1989) showing that thermodynamic fluids evolving in l.t.e. admit a purely hydrodynamic characterization. This characterization allows solving this i…
Conductivity imaging with interior potential measurements
2011
In this article, we present two reconstruction methods intended to be used for conductivity imaging with data obtained from a planar electrical impedance tomography device for breast cancer detection. The inverse problem to solve is different from the classical inverse conductivity problem. We reconstruct the electrical conductivity of a two-dimensional domain from boundary measurements of currents and interior measurements of the potential. One reconstruction algorithm is based on a discrete resistor model; the other one is an integral equation approach for smooth conductivity distributions.
On the numerical solution of the distributed parameter identification problem
1991
A new error estimate is derived for the numerical identification of a distributed parameter a(x) in a two point boundary value problem, for the case that the finite element method and the fit-to-data output-least-squares technique are used for the identifications. With a special weighted norm, we get a pointwise estimate. Prom the error estimate and also from the numerical tests, we find that if we decrease the mesh size, the maximum error between the identified parameter and the true parameter will increase. In order to improve the accuracy, higher order finite element spaces should be used in the approximations.
Propagation of errors due to incorrect positions of sources and detectors in wave-field tomography
2004
Tomographic data processed by 2D inversion programs can produce fairly large distortions due to incorrect source and/or detector positions. This problem is very serious in high-frequency electromagnetic tomography (GPR), due to the dimensions of the transmitter and receiver antennae. The errors can even be larger when coupled antennae are used (receiver and transmitter inside the same box) whose positions are not clearly known. Similar errors can be involved in seismic tomography, for instance when the mechanical connection between transducers and sample is defective. In this paper the problem has been studied using synthetic data which were calculated for different acquisition geometries. …
Stability of the Calderón problem in admissible geometries
2014
In this paper we prove log log type stability estimates for inverse boundary value problems on admissible Riemannian manifolds of dimension n ≥ 3. The stability estimates correspond to the uniqueness results in [13]. These inverse problems arise naturally when studying the anisotropic Calderon problem. peerReviewed
Further results on generalized centro-invertible matrices
2019
[EN] This paper deals with generalized centro-invertible matrices introduced by the authors in Lebtahi et al. (Appl. Math. Lett. 38, 106¿109, 2014). As a first result, we state the coordinability between the classes of involutory matrices, generalized centro-invertible matrices, and {K}-centrosymmetric matrices. Then, some characterizations of generalized centro-invertible matrices are obtained. A spectral study of generalized centro-invertible matrices is given. In addition, we prove that the sign of a generalized centro-invertible matrix is {K}-centrosymmetric and that the class of generalized centro-invertible matrices is closed under the matrix sign function. Finally, some algorithms ha…
Unique continuation property and Poincar�� inequality for higher order fractional Laplacians with applications in inverse problems
2020
We prove a unique continuation property for the fractional Laplacian $(-\Delta)^s$ when $s \in (-n/2,\infty)\setminus \mathbb{Z}$. In addition, we study Poincar\'e-type inequalities for the operator $(-\Delta)^s$ when $s\geq 0$. We apply the results to show that one can uniquely recover, up to a gauge, electric and magnetic potentials from the Dirichlet-to-Neumann map associated to the higher order fractional magnetic Schr\"odinger equation. We also study the higher order fractional Schr\"odinger equation with singular electric potential. In both cases, we obtain a Runge approximation property for the equation. Furthermore, we prove a uniqueness result for a partial data problem of the $d$-…