Resolution of the incompressible inverse problem by singularities perturbation: Theory and industrial applications

1992 ◽  
Vol 43 (3) ◽  
pp. 567-580
Author(s):  
Jean -Nicolas Favre
Keyword(s):  
Inverse Problem ◽  
Perturbation Theory ◽  
Industrial Applications

Linearization of the eikonal equation

Geophysics ◽  
1994 ◽  
Vol 59 (10) ◽  
pp. 1631-1632 ◽  
Author(s):  
David F. Aldridge
Keyword(s):  
Inverse Problem ◽  
Perturbation Theory ◽  
Path Integral ◽  
Seismic Waves ◽  
Eikonal Equation ◽  
Nonlinear Inverse Problem ◽  
Nonlinear Functional ◽  
Arrival Times ◽  
Traveltime Tomography ◽  
Fermat's Principle

Seismic traveltime tomography is a nonlinear inverse problem wherein an unknown slowness model is inferred from the observed arrival times of seismic waves. Nonlinearity arises because the raypath connecting a given source and receiver depends on the slowness. Specifically, if L(s) designates a raypath through the slowness model s between two fixed endpoints, then the path integral for traveltime [Formula: see text] is a nonlinear functional of s because it does not, in general, satisfy the superposition condition (i.e., [Formula: see text] where [Formula: see text] and [Formula: see text] are two different slowness models). The tomographic inverse problem can be solved after linearizing the traveltime expression about a known slowness model [Formula: see text]. This linearized expression is usually obtained by appealing to Fermat’s principle (e.g., Nolet, 1987). Alternately, the required relation can be rigorously derived via ray‐perturbation theory (Snieder and Sambridge, 1992). The purpose of this note is to present a straightforward derivation of the same result by linearizing the eikonal equation for traveltimes. Wenzel (1988) adopts this approach, but his method of proof cannot be generalized to heterogeneous 3-D media. A full 3-D treatment is given here. The proof is remarkably simple, and thus it is quite possible that others have discovered it previously.

scholarly journals On a Spectral Inverse Problem in Perturbation Theory

2021 ◽  
Vol 17 (1) ◽  
pp. 95-115
Author(s):  
V.A. Marchenko ◽  
◽  
A.V. Marchenko ◽  
V.A. Zolotarev ◽  
◽  
...  
Keyword(s):  
Inverse Problem ◽  
Perturbation Theory ◽  
Spectral Inverse Problem

Mathematical Imbalance Determination From Vibrational Measurements and Industrial Applications

2008 ◽  
Author(s):  
Jenny Niebsch ◽  
Ronny Ramlau
Keyword(s):  
Inverse Problem ◽  
Direct Problem ◽  
Industrial Applications ◽  
Rotating Machinery ◽  
Regularization Techniques ◽  
Ill Posed ◽  
Linear And Nonlinear ◽  
Nonlinear Nature

The paper focuses on the identification of imbalances from vibrational measurements in rotating machinery and its application to industrial problems. Since it is an ill-posed inverse problem the reconstruction is based on regularization techniques. To handle the direct problem, a model of the rotor under consideration has to be provided. We have employed the imbalance reconstruction principle to several industrial applications of linear and nonlinear nature.

A Perturbation Theory for the Population of Atomic Energy Levels in Non-Lte Plasmas

1988 ◽  
Vol 102 ◽  
pp. 343-347
Author(s):  
M. Klapisch
Keyword(s):  
Perturbation Theory ◽  
Small Parameter ◽  
Classification Scheme ◽  
Sum Rules ◽  
Energy Levels ◽  
Natural Classification ◽  
Quantum Numbers ◽  
Formal Expansion ◽  
Atomic Energy Levels ◽  
As Effects

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.

The Application of Ultra-Thin Sectioning Techniques to Non-Biological Samples

1968 ◽  
Vol 26 ◽  
pp. 332-333
Author(s):  
C. F. Oster
Keyword(s):  
Biological Sciences ◽  
Epoxy Resin ◽  
Cross Sections ◽  
Biological Samples ◽  
Industrial Applications ◽  
Photographic Film ◽  
Silver Particles ◽  
Thin Sectioning ◽  
Embedding Medium

Although ultra-thin sectioning techniques are widely used in the biological sciences, their applications are somewhat less popular but very useful in industrial applications. This presentation will review several specific applications where ultra-thin sectioning techniques have proven invaluable.The preparation of samples for sectioning usually involves embedding in an epoxy resin. Araldite 6005 Resin and Hardener are mixed so that the hardness of the embedding medium matches that of the sample to reduce any distortion of the sample during the sectioning process. No dehydration series are needed to prepare our usual samples for embedding, but some types require hardening and staining steps. The embedded samples are sectioned with either a prototype of a Porter-Blum Microtome or an LKB Ultrotome III. Both instruments are equipped with diamond knives.In the study of photographic film, the distribution of the developed silver particles through the layer is important to the image tone and/or scattering power. Also, the morphology of the developed silver is an important factor, and cross sections will show this structure.

The mensuration of interfaces

1992 ◽  
Vol 50 (1) ◽  
pp. 216-217
Author(s):  
W.M. Stobbs
Keyword(s):  
Electron Microscopy ◽  
50Th Anniversary ◽  
Numerical Data ◽  
Industrial Applications ◽  
Dynamical Theory ◽  
Large Strains ◽  
Reasonable Approach ◽  
Lattice Resolution ◽  
Analogue To Digital ◽  
The Way

I do not have access to the abstracts of the first meeting of EMSA but at this, the 50th Anniversary meeting of the Electron Microscopy Society of America, I have an excuse to consider the historical origins of the approaches we take to the use of electron microscopy for the characterisation of materials. I have myself been actively involved in the use of TEM for the characterisation of heterogeneities for little more than half of that period. My own view is that it was between the 3rd International Meeting at London, and the 1956 Stockholm meeting, the first of the European series , that the foundations of the approaches we now take to the characterisation of a material using the TEM were laid down. (This was 10 years before I took dynamical theory to be etched in stone.) It was at the 1956 meeting that Menter showed lattice resolution images of sodium faujasite and Hirsch, Home and Whelan showed images of dislocations in the XlVth session on “metallography and other industrial applications”. I have always incidentally been delighted by the way the latter authors misinterpreted astonishingly clear thickness fringes in a beaten (”) foil of Al as being contrast due to “large strains”, an error which they corrected with admirable rapidity as the theory developed. At the London meeting the research described covered a broad range of approaches, including many that are only now being rediscovered as worth further effort: however such is the power of “the image” to persuade that the above two papers set trends which influence, perhaps too strongly, the approaches we take now. Menter was clear that the way the planes in his image tended to be curved was associated with the imaging conditions rather than with lattice strains, and yet it now seems to be common practice to assume that the dots in an “atomic resolution image” can faithfully represent the variations in atomic spacing at a localised defect. Even when the more reasonable approach is taken of matching the image details with a computed simulation for an assumed model, the non-uniqueness of the interpreted fit seems to be rather rarely appreciated. Hirsch et al., on the other hand, made a point of using their images to get numerical data on characteristics of the specimen they examined, such as its dislocation density, which would not be expected to be influenced by uncertainties in the contrast. Nonetheless the trends were set with microscope manufacturers producing higher and higher resolution microscopes, while the blind faith of the users in the image produced as being a near directly interpretable representation of reality seems to have increased rather than been generally questioned. But if we want to test structural models we need numbers and it is the analogue to digital conversion of the information in the image which is required.

The influence of confocal microscope design on imaging performance

1993 ◽  
Vol 51 ◽  
pp. 144-145
Author(s):  
C J R Sheppard
Keyword(s):  
Image Quality ◽  
Fluorescence Imaging ◽  
Confocal Microscope ◽  
Industrial Applications ◽  
Three Dimensions ◽  
Design Parameters ◽  
Weak Signals ◽  
Size And Shape ◽  
Imaging Performance ◽  
Fundamental Limitation

The confocal microscope is now widely used in both biomedical and industrial applications for imaging, in three dimensions, objects with appreciable depth. There are now a range of different microscopes on the market, which have adopted a variety of different designs. The aim of this paper is to explore the effects on imaging performance of design parameters including the method of scanning, the type of detector, and the size and shape of the confocal aperture.It is becoming apparent that there is no such thing as an ideal confocal microscope: all systems have limitations and the best compromise depends on what the microscope is used for and how it is used. The most important compromise at present is between image quality and speed of scanning, which is particularly apparent when imaging with very weak signals. If great speed is not of importance, then the fundamental limitation for fluorescence imaging is the detection of sufficient numbers of photons before the fluorochrome bleaches.

Microstructural characterization of sol-gel coating on PET films

1994 ◽  
Vol 52 ◽  
pp. 886-887
Author(s):  
R. T. Chen ◽  
R.A. Norwood
Keyword(s):  
Ion Beam ◽  
Sol Gel ◽  
Industrial Applications ◽  
Hard Coatings ◽  
Nanometer Scale ◽  
Ion Beam Sputtering ◽  
Process Technology ◽  
Refractive Index Measurement ◽  
Organically Modified ◽  
Pet Films

Sol-gel processing has been used to control the structure of a material on a nanometer scale in preparing advanced ceramics and glasses. Film coating using the sol-gel process was also found to be a viable process technology in applications such as optical, porous, antireflection and hard coatings. In this study, organically modified silicate (Ormosil) coatings are applied to PET films for various industrial applications. Sol-gel materials are known to exhibit nanometer scale structures which havepreviously been characterized by small-angle X-ray scattering (SAXS), neutron scattering and light scattering. Imaging of the ultrafine sol-gel structures has also been performed using an ultrahigh resolution replica/TEM technique. The objective of this study was to evaluate the ultrafine structures inthe sol gel coatings using a direct imaging technique: atomic force microscopy (AFM). In addition, correlation of microstructures with processing parameters, coating density and other physical properties will be discussed.The materials evaluated are organically modified silicate coatings on PET film substrates. Refractive index measurement by the prism coupling method was used to assess density of the sol-gel coating.AFM imaging was performed on a Nanoscope III AFM (by Digital Instruments) using constant force mode. Solgel coating samples coated with a thin layer of Ft (by ion beam sputtering) were also examined by STM in order to confirm the structures observed in the contact type AFM. In addition, to compare the previous results, sol-gel powder samples were also prepared by ultrasonication followed by Pt/Au shadowing and examined using a JEOL 100CX TEM.

Electron energy loss near edge structures of intermetallic alloys and grain boundaries in NiAl

1996 ◽  
Vol 54 ◽  
pp. 522-523
Author(s):  
G.A. Botton ◽  
C.J. Humphreys
Keyword(s):  
High Temperature ◽  
Transition Metal ◽  
Energy Loss ◽  
Grain Boundaries ◽  
Industrial Applications ◽  
Edge Structure ◽  
Structural Applications ◽  
Yield Behaviour ◽  
Late Transition ◽  
Metal Aluminides

Transition metal aluminides are of great potential interest for high temperature structural applications. Although these materials exhibit good mechanical properties at high temperature, their use in industrial applications is often limited by their intrinsic room temperature brittleness. Whilst this particular yield behaviour is directly related to the defect structure, the properties of the defects (in particular the mobility of dislocations and the slip system on which these dislocations move) are ultimately determined by the electronic structure and bonding in these materials. The lack of ductility has been attributed, at least in part, to the mixed bonding character (metallic and covalent) as inferred from ab-initio calculations. In this work, we analyse energy loss spectra and discuss the features of the near edge structure in terms of the relevant electronic states in order to compare the predictions on bonding directly with spectroscopic experiments. In this process, we compare spectra of late transition metal (TM) to early TM aluminides (FeAl and TiAl) to assess whether differences in bonding can also be detected. This information is then discussed in terms of bonding changes at grain boundaries in NiAl.

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