scholarly journals Identifying Elastic and Viscoelastic Material Parameters by Means of a Tikhonov Regularization

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Stefan Diebels ◽  
Tobias Scheffer ◽  
Thomas Schuster ◽  
Aaron Wewior
Keyword(s):  
Viscoelastic Material ◽  
Tikhonov Regularization ◽  
Nonlinear Differential Equations ◽  
A Priori ◽  
Material Behavior ◽  
Solution Technique ◽  
A Priori Information ◽  
Noisy Input ◽  
Priori Information ◽  
The One

For studying the interaction of displacements, stresses, and acting forces for elastic and viscoelastic materials, it is of utmost importance to have a decent mathematical model available. Usually such a model consists of a coupled set of nonlinear differential equations together with appropriate boundary conditions. However, since the different material classes vary significantly with respect to their physical and mechanical behavior, the parameters which appear in these equations are unknown and therefore have to be determined before the equations can be used for further investigations or simulations. It is this very step which is addressed in this article where we consider elastic as well as viscoelastic material behavior. The idea is to compute the parameters as solutions of a minimization problem for Tikhonov functionals. Tikhonov regularization is a well-established solution technique for tackling inverse problems. On the one hand, it assures a computation that is stable with respect to noisy input data, and on the other hand, it involves desired a priori information on the solution. In this article we develop problem adapted Tikhonov functionals and prove that a Tikhonov regularization improves the accuracy especially when the underlying system is ill-conditioned.

scholarly journals On Sequencing a Protein with Nanopores, tRNAs, and RNAs with Matching Terminal Codons

2019 ◽  
Author(s):  
G Sampath
Keyword(s):  
De Novo ◽  
A Priori ◽  
Protein Molecule ◽  
Electrolytic Cell ◽  
A Priori Information ◽  
Unfolded Protein ◽  
In Trans ◽  
Priori Information ◽  
The One ◽  
A Current

A method for sequencing a protein from a codon sequence is proposed. An unfolded protein molecule is threaded through a nano-sized pore in an electrolytic cell carboxyl end first and held with a voltage such that only the first residue is exposed in the trans chamber of the cell. A tRNA molecule in trans with matching anticodon for the residue binds itself to the latter in the presence of suitable catalysts. It is then cleaved and transferred to an extended electrolytic cell with N pores, 40 ≤ N ≤ 61, in N individual cis chambers and a single trans chamber. Each pore holds an RNA molecule ending in a unique codon that is held exposed in the trans chamber. In the presence of suitable catalysts the anticodon in the transferred tRNA binds with the codon of a matching RNA molecule. By reversing the voltages in the extended cell every RNA molecule except the one to which the transferred tRNA is bound retracts into its cis chamber, this identifies the residue unambiguously. The detected residue in the first cell is cleaved and the process repeated. Unlike in other nanopore-based methods, it suffices to detect the occurrence of a current blockade without having to measure the pore current precisely. A simplified but more time-consuming version that uses only the first cell is also described. In either case no a priori information about the protein is needed so de novo sequencing is possible. A feasibility analysis of the proposed scheme is presented.

A STOPPING RULE FOR THE CONJUGATE GRADIENT REGULARIZATION METHOD APPLIED TO INVERSE PROBLEMS IN ACOUSTICS

2006 ◽  
Vol 14 (04) ◽  
pp. 397-414 ◽  
Author(s):  
THOMAS DELILLO ◽  
TOMASZ HRYCAK
Keyword(s):  
Conjugate Gradient ◽  
A Priori ◽  
A Priori Information ◽  
Parameter Choice ◽  
Regularization Algorithm ◽  
Lanczos Process ◽  
Choice Strategy ◽  
Priori Information ◽  
The One ◽  
Parameter Choice Strategy

We present a novel parameter choice strategy for the conjugate gradient regularization algorithm which does not assume a priori information about the magnitude of the measurement error. Our approach is to regularize within the Krylov subspaces associated with the normal equations. We implement conjugate gradient via the Lanczos bidiagonalization process with reorthogonalization, and then we construct regularized solutions using the SVD of a bidiagonal projection constructed by the Lanczos process. We compare our method with the one proposed by Hanke and Raus and illustrate its performance with numerical experiments, including detection of acoustic boundary vibrations.

scholarly journals Multi-Frequency GPR Microwave Imaging of Sparse Targets through a Multi-Task Bayesian Compressive Sensing Approach

2021 ◽  
Vol 7 (11) ◽  
pp. 247
Author(s):  
Marco Salucci ◽  
Nicola Anselmi
Keyword(s):  
Compressive Sensing ◽  
Quantitative Imaging ◽  
A Priori ◽  
Wide Band ◽  
Frequency Diversity ◽  
A Priori Information ◽  
Spectral Components ◽  
Priori Information ◽  
The One ◽  
Ground Penetrating

An innovative inverse scattering (IS) method is proposed for the quantitative imaging of pixel-sparse scatterers buried within a lossy half-space. On the one hand, such an approach leverages on the wide-band nature of ground penetrating radar (GPR) data by jointly processing the multi-frequency (MF) spectral components of the collected radargrams. On the other hand, it enforces sparsity priors on the problem unknowns to yield regularized solutions of the fully non-linear scattering equations. Towards this end, a multi-task Bayesian compressive sensing (MT-BCS) methodology is adopted and suitably customized to take full advantage of the available frequency diversity and of the a-priori information on the class of imaged targets. Representative results are reported to assess the proposed MF-MT-BCS strategy also in comparison with competitive state-of-the-art alternatives.

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