Numerical studies of the Lagrangian approach for reconstruction of the conductivity in a waveguide

We consider an inverse problem of reconstructing the conductivity function in a hyperbolic equation using single space-time domain noisy observations of the solution on the backscattering boundary of the computational domain. We formulate our inverse problem as an optimization problem and use Lagrangian approach to minimize the corresponding Tikhonov functional. We present a theorem of a local strong convexity of our functional and derive error estimates between computed and regularized as well as exact solutions of this functional, correspondingly. In numerical simulations we apply domain decomposition finite element-finite difference method for minimization of the Lagrangian. Our computational study shows efficiency of the proposed method in the reconstruction of the conductivity function in three dimensions

Reconstruction of dielectric constants of multi-layered optical fibers using propagation constants measurements

We present new method for the numerical reconstruction of the variable refractive index of multi-layered circular weakly guiding dielectric waveguides using the measurements of the propagation constants of their eigenwaves. Our numerical examples show stable reconstruction of the dielectric permittivity function $\varepsilon$ for random noise level using these measurements

Imaging of buried objects from experimental backscattering time dependent measurements using a globally convergent inverse algorithm

We consider the problem of imaging of objects buried under the ground using backscattering experimental time dependent measurements generated by a single point source or one incident plane wave. In particular, we estimate dielectric constants of those objects using the globally convergent inverse algorithm of Beilina and Klibanov. Our algorithm is tested on experimental data collected using a microwave scattering facility at the University of North Carolina at Charlotte. There are two main challenges working with this type of experimental data: (i) there is a huge misfit between these data and computationally simulated data, and (ii) the signals scattered from the targets may overlap with and be dominated by the reflection from the ground's surface. To overcome these two challenges, we propose new data preprocessing steps to make the experimental data to be approximately the same as the simulated ones, as well as to remove the reflection from the ground's surface. Results of total 25 data sets of both non blind and blind targets indicate a good accuracy.Comment: 34 page

Reconstruction from blind experimental data for an inverse problem for a hyperbolic equation

We consider the problem of reconstruction of dielectrics from blind backscattered experimental data. Experimental data were collected by a device, which was built at University of North Carolina at Charlotte. This device sends electrical pulses into the medium and collects the time resolved backscattered data on a part of a plane. The spatially distributed dielectric constant $\varepsilon_{r}(\mathbf{x}),\mathbf{x}\in \mathbb{R}^{3}$ is the unknown coefficient of a wave-like PDE. This coefficient is reconstructed from those data in blind cases. To do this, a globally convergent numerical method is used.Comment: 27 page

Reconstruction of the refractive index from experimental backscattering data using a globally convergent inverse method

The problem to be studied in this work is within the context of coefficient identification problems for the wave equation. More precisely, we consider the problem of reconstruction of the refractive index (or equivalently, the dielectric constant) of an inhomogeneous medium using one backscattering boundary measurement. The goal of this paper is to analyze the performance of a globally convergent algorithm of Beilina and Klibanov on experimental data acquired in the Microwave Laboratory at University of North Carolina at Charlotte. The main challenge working with experimental data is the the huge misfit between these data and computationally simulated data. We present data pre-processing steps to make the former somehow look similar to the latter. Results of both non-blind and blind targets are shown indicating good reconstructions even for high contrasts between the targets and the background medium.Comment: 25 page

Reconstruction of dielectric constants of core and cladding of optical fibers using propagation constants measurements

© 2014 E. M. Karchevskii et al. We present new numerical methods for the solution of inverse spectral problem to determine the dielectric constants of core and cladding in optical fibers. These methods use measurements of propagation constants. Our algorithms are based on approximate solution of a nonlinear nonselfadjoint eigenvalue problem for a system of weakly singular integral equations. We study three inverse problems and prove that they are well posed. Our numerical results indicate good accuracy of new algorithms

Lysosomal positioning regulates Rab10 phosphorylation at LRRK2+ lysosomes

Genetic variation at the leucine-rich repeat kinase 2 (LRRK2) locus contributes to an enhanced risk of familial and sporadic Parkinson’s disease. Previous data have demonstrated that recruitment to various membranes of the endolysosomal system results in LRRK2 activation. However, the mechanism(s) underlying LRRK2 activation at endolysosomal membranes and the cellular consequences of these events are still poorly understood. Here, we directed LRRK2 to lysosomes and early endosomes, triggering both LRRK2 autophosphorylation and phosphorylation of the direct LRRK2 substrates Rab10 and Rab12. However, when directed to the lysosomal membrane, pRab10 was restricted to perinuclear lysosomes, whereas pRab12 was visualized on both peripheral and perinuclear LRRK2+ lysosomes, suggesting that lysosomal positioning provides additional regulation of LRRK2-dependent Rab phosphorylation. Anterograde transport of lysosomes to the cell periphery by increasing the expression of ARL8B and SKIP or by knockdown of JIP4 blocked the recruitment and phosphorylation of Rab10 by LRRK2. The absence of pRab10 from the lysosomal membrane prevented the formation of a lysosomal tubulation and sorting process we previously named LYTL. Conversely, overexpression of RILP resulted in lysosomal clustering within the perinuclear area and increased LRRK2-dependent Rab10 recruitment and phosphorylation. The regulation of Rab10 phosphorylation in the perinuclear area depends on counteracting phosphatases, as the knockdown of phosphatase PPM1H significantly increased pRab10 signal and lysosomal tubulation in the perinuclear region. Our findings suggest that LRRK2 can be activated at multiple cellular membranes, including lysosomes, and that lysosomal positioning further provides the regulation of some Rab substrates likely via differential phosphatase activity or effector protein presence in nearby cellular compartments

Towards sustainable development through bridging digital penetration gaps

The aim of the article is to study the impact of the digital environment on the economic conditions of economic entities, as well as to assess the gaps between economic development, changes in social relations and environmental well-being. It is proved that gaps in digital penetration can cause the deepening of existing inequalities and risks: digital inequality, social inequality, inequality in the appropriation of benefits, environmental risks. Approaches to assessing the impact of digital artifacts on the environment (in the context of the concept of "circular economy") and sustainable development of the economic system are investigate

INDUSTRIAL SAFETY IN THE PRODUCTION OF RUBBER

Russian industry of synthetic rubber, is one of the most competitive and occupies a prominent place in the global petrochemical industry. However, the company production of synthetic rubber are among the most hazardous industrial facilities. The main operational risks are to fire and explosion hazards of raw materials used. Accidents in such establishments can damage not only the equipment, materials or buildings, but also cause serious environmental and economic consequences for the region. For the prevention of accidents, mitigation and elimination of losses, it is necessary to apply a set of measures aimed at the management and control of industrial safety. The legal basis of industrial safety in the Russian Federation is the Federal Law № 116-FZ dated 21.07.97 "On industrial safety of hazardous production facilities." Industrial Safety at work an important part of its normal functioning. The most important condition of industrial safety of hazardous production facilities is the examination of industrial safety. Federal rules and regulations in the field of industrial safety "rules of examination of industrial safety", approved by Order of RTN on November 14, 2013 N 538 established: the procedure of examination of industrial safety requirements for the design of expert opinions and requirements for experts