scholarly journals A non-local inverse problem with boundary response

2021 ◽  
Author(s):  
Tuhin Ghosh
Keyword(s):  
Inverse Problem ◽  
Non Local

COMPARISON OF ALGORITHMS FOR DETERMINING THE THICKNESS OF OPTICAL COATING LAYERS BASED ON THE MONOCHROMATIC MONITORING DATA

2021 ◽  
Vol 9 (4) ◽  
pp. 89-99
Author(s):  
A. V. Tikhonravov ◽  
◽  
Iu. S. Lagutin ◽  
A. A. Lagutina ◽  
D. V. Lukyanenko ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Reverse Engineering ◽  
Deposition Process ◽  
Systematic Errors ◽  
Engineering Problem ◽  
Optical Coatings ◽  
Random Errors ◽  
Local Algorithms ◽  
On Line ◽  
Non Local

The reverse engineering problem of determining the layer thicknesses of deposited optical coatings from on-line monochromatic measurements is considered. To solve this inverse problem, non-local algorithms are proposed that use all the data accumulated during the deposition process. For the proposed algorithms, the accuracy of solving the inverse problem is compared in the presence of random and systematic errors. It is shown that in the case when the measured data contains only random errors, the best accuracy is provided by the algorithm based on minimizing the discrepancy functional. In the case of systematic errors, the advantage of one the algorithms based on minimizing the variance functionals is demonstrated. Key words: inverse problems, reverse engineering, optical coatings, thin films.

scholarly journals Strong well-posedness and inverse identification problem of a non-local phase field tumour model with degenerate mobilities

2021 ◽  
pp. 1-42
Author(s):  
SERGIO FRIGERI ◽  
KEI FONG LAM ◽  
ANDREA SIGNORI
Keyword(s):  
Inverse Problem ◽  
Phase Field ◽  
Necessary Optimality Conditions ◽  
Strong Solutions ◽  
Reaction Diffusion Equation ◽  
Diffuse Interface ◽  
Well Posedness ◽  
Tumour Model ◽  
Degenerate Mobility ◽  
Non Local

We extend previous weak well-posedness results obtained in Frigeri et al. (2017, Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs, Vol. 22, Springer, Cham, pp. 217–254) concerning a non-local variant of a diffuse interface tumour model proposed by Hawkins-Daarud et al. (2012, Int. J. Numer. Method Biomed. Engng.28, 3–24). The model consists of a non-local Cahn–Hilliard equation with degenerate mobility and singular potential for the phase field variable, coupled to a reaction–diffusion equation for the concentration of a nutrient. We prove the existence of strong solutions to the model and establish some high-order continuous dependence estimates, even in the presence of concentration-dependent mobilities for the nutrient variable in two spatial dimensions. Then, we apply the new regularity results to study an inverse problem identifying the initial tumour distribution from measurements at the terminal time. Formulating the Tikhonov regularised inverse problem as a constrained minimisation problem, we establish the existence of minimisers and derive first-order necessary optimality conditions.

scholarly journals SIMULTANEOUS DETERMINATION OF A SOURCE TERM AND DIFFUSION CONCENTRATION FOR A MULTI-TERM SPACE-TIME FRACTIONAL DIFFUSION EQUATION

2021 ◽  
Vol 26 (3) ◽  
pp. 411-431
Author(s):  
Salman A. Malik ◽  
Asim Ilyas ◽  
Arifa Samreen
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Source Term ◽  
Fractional Diffusion ◽  
Adjoint Problem ◽  
Space Time ◽  
Fractional Diffusion Equation ◽  
Diffusion Temperature ◽  
Non Local ◽  
Time Fractional Diffusion Equation

An inverse problem of determining a time dependent source term along with diffusion/temperature concentration from a non-local over-specified condition for a space-time fractional diffusion equation is considered. The space-time fractional diffusion equation involve Caputo fractional derivative in space and Hilfer fractional derivatives in time of different orders between 0 and 1. Under certain conditions on the given data we proved that the inverse problem is locally well-posed in the sense of Hadamard. Our method of proof based on eigenfunction expansion for which the eigenfunctions (which are Mittag-Leffler functions) of fractional order spectral problem and its adjoint problem are considered. Several properties of multinomial Mittag-Leffler functions are proved.

Toward High-Resolution Low-Voltage SEM

1988 ◽  
Vol 46 ◽  
pp. 218-219
Author(s):  
Zhifeng Shao
Keyword(s):  
Low Voltage ◽  
Spherical Aberration ◽  
Chromatic Aberration ◽  
Limiting Factor ◽  
Operating Voltage ◽  
Probe Radius ◽  
Non Local ◽  
Electron Microscopes ◽  
Image Position ◽  
Scanning Electron Microscopes

Recently, low voltage (≤5kV) scanning electron microscopes have become popular because of their unprecedented advantages, such as minimized charging effects and smaller specimen damage, etc. Perhaps the most important advantage of LVSEM is that they may be able to provide ultrahigh resolution since the interaction volume decreases when electron energy is reduced. It is obvious that no matter how low the operating voltage is, the resolution is always poorer than the probe radius. To achieve 10Å resolution at 5kV (including non-local effects), we would require a probe radius of 5∽6 Å. At low voltages, we can no longer ignore the effects of chromatic aberration because of the increased ratio δV/V. The 3rd order spherical aberration is another major limiting factor. The optimized aperture should be calculated as

Chromatic aberration and low-voltage SEM

1987 ◽  
Vol 45 ◽  
pp. 546-547
Author(s):  
Zhifeng Shao ◽  
A.V. Crewe
Keyword(s):  
Electron Energy ◽  
Low Voltage ◽  
Spherical Aberration ◽  
Chromatic Aberration ◽  
Primary Electron ◽  
Probe Size ◽  
Non Local ◽  
Optical Treatment ◽  
Electron Microscopes ◽  
Scanning Electron Microscopes

For scanning electron microscopes, it is plausible that by lowering the primary electron energy, one can decrease the volume of interaction and improve resolution. As shown by Crewe /1/, at V0 =5kV a 10Å resolution (including non-local effects) is possible. To achieve this, we would need a probe size about 5Å. However, at low voltages, the chromatic aberration becomes the major concern even for field emission sources. In this case, δV/V = 0.1 V/5kV = 2x10-5. As a rough estimate, it has been shown that /2/ the chromatic aberration δC should be less than ⅓ of δ0 the probe size determined by diffraction and spherical aberration in order to neglect its effect. But this did not take into account the distribution of electron energy. We will show that by using a wave optical treatment, the tolerance on the chromatic aberration is much larger than we expected.

AN INVERSE PROBLEM IN THE DYNAMICAL REATOR THEORY

1982 ◽  
Vol 2 (1) ◽  
pp. 9-16 ◽  
Author(s):  
Dexing Feng ◽  
Guangtian Zhu
Keyword(s):  
Inverse Problem

Magic of signs: a non-local interpretation of homeopathy

2000 ◽  
Vol 89 (3) ◽  
pp. 127-140 ◽  
Author(s):  
H Walach
Keyword(s):  
Non Local

Discussion: the magic of non‐local concepts or the chair in the Rabbi's castle

2000 ◽  
Vol 89 (3) ◽  
pp. 141-145
Author(s):  
M Brands
Keyword(s):  
Non Local
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