Linear and Nonlinear Physical Models

2009 ◽  
pp. 353-413 ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Physical Models ◽  
Linear And Nonlinear

On the topography of the cost functional in linear and nonlinear inverse problems

Geophysics ◽  
2012 ◽  
Vol 77 (1) ◽  
pp. W1-W15 ◽  
Author(s):  
Juan L. Fernández Martínez ◽  
M. Zulima Fernández Muñiz ◽  
Michael J. Tompkins
Keyword(s):  
Inverse Problems ◽  
Null Space ◽  
Order Approximation ◽  
Singular Values ◽  
Physical Models ◽  
Local Data ◽  
Cost Functional ◽  
Nonlinear Inverse Problems ◽  
Linear And Nonlinear ◽  
The Cost

We analyze, through linear algebra, the topography of the cost functional in linear and nonlinear inverse problems with the aim of illuminating general characteristics. To a first-order approximation, the local data misfit function in any inverse problem is valley-shaped and elongated in the directions of the null space of the Jacobian and/or in the directions of the smallest singular values. In nonlinear inverse problems, valleys persist; however, local minima might also coexist in the misfit space and might be related to nonlinear effects ignored by the Gauss-Newton approximation to the Hessian, the regularization term designed to provide convexity to the misfit function, or to noise in the data. Furthermore, noise perturbs the size of the equivalence region making location of solutions easier but finding a global minimum harder (in the case of existence). Understanding the behavior of the cost functional is an important step in the developing techniques to appraise inverse solutions and estimate uncertainties caused by noise, incomplete sampling, regularization, and more fundamentally, simplified physical models.

Recent Radiative and Collisional Atomic Data of Astrophysical Interest

1988 ◽  
Vol 102 ◽  
pp. 129-132
Author(s):  
K.L. Baluja ◽  
K. Butler ◽  
J. Le Bourlot ◽  
C.J. Zeippen
Keyword(s):  
Mass Production ◽  
Bound States ◽  
Physical Models ◽  
Impact Excitation ◽  
Electron Impact Excitation ◽  
Atomic Data ◽  
Isoelectronic Sequence ◽  
Astrophysical Interest ◽  
Radiative Transitions ◽  
Forbidden Transitions

SummaryUsing sophisticated computer programs and elaborate physical models, accurate radiative and collisional atomic data of astrophysical interest have been or are being calculated. The cases treated include radiative transitions between bound states in the 2p4and 2s2p5configurations of many ions in the oxygen isoelectronic sequence, the photoionisation of the ground state of neutral iron, the electron impact excitation of the fine-structure forbidden transitions within the 3p3ground configuration of CℓIII, Ar IV and K V, and the mass-production of radiative data for ions in the oxygen and fluorine isoelectronic sequences, as part of the international Opacity Project.

Cryo-TEM of amphiphilic polymer and amphiphile/polymer solutions

1993 ◽  
Vol 51 ◽  
pp. 876-877
Author(s):  
Yeshayahu Talmon
Keyword(s):  
Microstructural Characterization ◽  
Building Blocks ◽  
Quantitative Information ◽  
Physical Models ◽  
Specimen Preparation ◽  
Time Resolved ◽  
Temperature Changes ◽  
Temperature And Humidity ◽  
Microstructured Fluids ◽  
Air Streams

To achieve complete microstructural characterization of self-aggregating systems, one needs direct images in addition to quantitative information from non-imaging, e.g., scattering or Theological measurements, techniques. Cryo-TEM enables us to image fluid microstructures at better than one nanometer resolution, with minimal specimen preparation artifacts. Direct images are used to determine the “building blocks” of the fluid microstructure; these are used to build reliable physical models with which quantitative information from techniques such as small-angle x-ray or neutron scattering can be analyzed.To prepare vitrified specimens of microstructured fluids, we have developed the Controlled Environment Vitrification System (CEVS), that enables us to prepare samples under controlled temperature and humidity conditions, thus minimizing microstructural rearrangement due to volatile evaporation or temperature changes. The CEVS may be used to trigger on-the-grid processes to induce formation of new phases, or to study intermediate, transient structures during change of phase (“time-resolved cryo-TEM”). Recently we have developed a new CEVS, where temperature and humidity are controlled by continuous flow of a mixture of humidified and dry air streams.

Linear and Nonlinear Optical Properties of Natural Dyes Freestanding Films and Application in Optical Limiting

2020 ◽  
pp. 139-143
Keyword(s):  
Absorption Coefficient ◽  
Water Solution ◽  
Optical Limiting ◽  
Refraction Index ◽  
Laser Wavelength ◽  
Solid State Laser ◽  
Natural Dyes ◽  
Linear And Nonlinear ◽  
532 Nm ◽  
Absorbance Spectra

Natural dyes were followed and prepared from a pomegranate, purple carrot, and eggplant peel. The absorbance spectra was measured in the wavelength range 300-800 nm. The linear properties measurements of the prepared natural dye freestanding films were determined include absorption coefficient (α0), extinction coefficient (κ), and linear refraction index (n). The nonlinear refractive index n2 and nonlinear absorption coefficient β2 of the natural dyes in the water solution were measured by the optical z-scan technique under a pumped solid state laser at a laser wavelength of 532 nm. The results indicated that the pomegranate dye can be promising candidates for optical limiting applications with significantly low optical limiting of 3.5 mW.

Rheological characterization of tack and viscoelasticity of compositions of crepe coating used in the Yankee dryer

TAPPI Journal ◽  
2019 ◽  
Vol 18 (11) ◽  
pp. 641-649
Author(s):  
JOSHUA OMAMBALA ◽  
CARL MCINTYRE
Keyword(s):  
Normal Force ◽  
Weight Ratio ◽  
Good Combination ◽  
Rheological Characterization ◽  
Nonlinear Viscoelastic ◽  
Coating Composition ◽  
Linear And Nonlinear ◽  
Work Done ◽  
Tissue Production

The vast majority of tissue production uses creping to achieve the required set of properties on the base sheet. The Yankee coating helps to develop the desired crepe that in turn determines properties such as bulk and softness. The adhesion of the sheet to the Yankee surface is a very important characteristic to consider in achieving the desired crepe. The coating mix usually consists of the adhesive, modifier, and release. A good combination of these components is essential to achieving the desired properties of the tissue or towel, which often are determined by trials on the machine that can be time consuming and lead to costly rejects. In this paper, five compositions of an industrial Yankee coating adhesive, modifier, and release were examined rheologically. The weight ratio of the adhesive was kept constant at 30% in all five compositions and the modifier and release ratios were varied. The normal force and work done by the different compositions have been shown at various temperatures simulating that of the Yankee surface, and the oscillatory test was carried out to explain the linear and nonlinear viscoelastic characteristic of the optimal coating composition.

THE MECHANISM OF RAISING AND QUANTIFICATION OF SPECIFIC HEAT FLUX AT BOILING OF NANOFLUIDS IN FREE CONVECTION CONDITIONS

2017 ◽  
pp. 25-34
Author(s):  
V.N. Moraru
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Heat Capacity ◽  
Specific Heat ◽  
Chemical Properties ◽  
Heating Surface ◽  
Physical Models ◽  
Superheated Liquid ◽  
Two Phase ◽  
Boiling Process

The results of our work and a number of foreign studies indicate that the sharp increase in the heat transfer parameters (specific heat flux q and heat transfer coefficient _) at the boiling of nanofluids as compared to the base liquid (water) is due not only and not so much to the increase of the thermal conductivity of the nanofluids, but an intensification of the boiling process caused by a change in the state of the heating surface, its topological and chemical properties (porosity, roughness, wettability). The latter leads to a change in the internal characteristics of the boiling process and the average temperature of the superheated liquid layer. This circumstance makes it possible, on the basis of physical models of the liquids boiling and taking into account the parameters of the surface state (temperature, pressure) and properties of the coolant (the density and heat capacity of the liquid, the specific heat of vaporization and the heat capacity of the vapor), and also the internal characteristics of the boiling of liquids, to calculate the value of specific heat flux q. In this paper, the difference in the mechanisms of heat transfer during the boiling of single-phase (water) and two-phase nanofluids has been studied and a quantitative estimate of the q values for the boiling of the nanofluid is carried out based on the internal characteristics of the boiling process. The satisfactory agreement of the calculated values with the experimental data is a confirmation that the key factor in the growth of the heat transfer intensity at the boiling of nanofluids is indeed a change in the nature and microrelief of the heating surface. Bibl. 20, Fig. 9, Tab. 2.

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