Spatial aspects affecting acidification factors in European acidification modelling

Plain linear models have recently been used in methodologies to model fate and transport for assessing acidification in life cycle impact assessment (LCIA), or in support of air pollution abatement policies. These models originate from a statistical analysis of the relationship between inputs and outputs of physically-based models that reflect the mechanics of a system in detail. Linear models applied to assess acidification use an acidification factor (AF), which relates changes in the magnitude of emissions to changes in the total area that is protected against acidification in Europe. The changes in emission volume refer to changes of one substance, within one country and one sector or one grid cell.This paper evaluates the dependence of AFs on three spatial characteristics, i.e. the spatial emission and deposition resolution, the spatial emission distribution and the actual spatial location of emissions.The applied spatial resolutions of emission and deposition cause non-systematic variations in AFs of up to 60%, relative to the finest resolution. The manner in which the distribution of emissions is modelled, i.e. grid or sector-specific, is shown to affect AFs considerably, as well. We conclude that spatial characteristics of the physically-based acidification model can affect the assessment of acidification by means of plain linear models.     

Alternative equations of magnetophotoelasticity and approximate solution of the inverse problem

In magnetophotoelasticity, photoelastic models are investigated in a magnetic field in order to initiate rotation of the plane of polarization that is due to the Faraday effect. The method has been used for the measurement of stress distributions that are in equilibrium on the wave normal and therefore cannot be measured with the traditional photoelastic technique. In this category belong bending stresses in plates and shells and residual stresses in glass plates. Two new systems of equations of magnetophotoelasticity are derived. One of them describes evolution of the polarization of light in a magnetophotoelastic medium in terms of eigenvectors, the other in terms of distinctive parameters. For the latter system, an approximate closed-form solution has been found. The integral Wertheim law has been generalized for the case of stress states in equilibrium when rotation of the plane of polarization is present.     

Isochromatic fringes in photoelasticity

The structure of the isochromatic fringe pattern in a two-dimensional photoelastic model is investigated with the phase diagram method of the theory of dynamic systems. Isochromatics are interpreted as phase paths (or level curves) of a Hamiltonian system. Possible singularities of the fringe pattern are analyzed.     

Transformation equations in polarization optics of inhomogeneous birefringent media

The quaternion formalism has been used to derive new systems of equations that describe transformation of the polarization of light in inhomogeneous birefringent media. In quaternion algebra the problem of parametric representation of the unitary transformation matrix reduces to the problem of formulation of the quaternion in trigonometric form. It is shown that this can be done in 30 different ways and that to each trigonometric form corresponds its own system of transformation equations. The six simplest systems of transformation equations have been derived.     

Modern Photoelasticity for Residual Stress Measurement in Glass

Abstract:  This paper gives a review of modern photoelastic technology for residual stress measurement in various glass articles, including glass articles of complicated shape. For residual stress measurement in axisymmetric glass articles, integrated photoelasticity is being used by many glass companies and research laboratories. In case of non-axisymmetric glass articles of complicated shape, photoelastic tomography is used. As for automotive and architectural glass panels used in buildings, surface stress can be measured with the mirage method. More complete stress analysis can be carried out with the scattered light method. The paper is illustrated by numerous examples.     

Strange interference blots in the interferometry of inhomogeneous birefringent objects

We show both experimentally and by numerical simulation that in the polarization interferometry of inhomogeneous birefringent objects, besides the usual interference fringes, interference blots may appear. In a light-field circular polariscope, interference blots are dark areas that may expand through a number of interference fringes. In a dark-field circular polariscope, interference blots are bright. In the vicinity of the interference blots interference fringes are deformed and their bifurcation may occur. It is shown that the cause of the interference blots is rotation of the principal birefringence axes.     

On the generalized Wertheim law in integrated photoelasticity

Two-dimensional photoelasticity is based on the classical Wertheim law. The integral Wertheim law can be used in integrated photoelasticity only in the case when the directions of the secondary principal stresses are constant on the light beam. We generalize the integral Wertheim law for the case when a slight rotation of the secondary principal directions takes place.     

Validation of space-based polarization measurements by use of a single-scattering approximation,with application to the global ozone monitoring experiment

A method is presented for in-flight validation of space-based polarization measurements based on approximation of the direction of polarization of scattered sunlight by the Rayleigh single-scattering value. This approximation is verified by simulations of radiative transfer calculations for various atmospheric conditions. The simulations show locations along an orbit where the scattering geometries are such that the intensities of the parallel and orthogonal polarization components of the light are equal, regardless of the observed atmosphere and surface. The method can be applied to any space-based instrument that measures the polarization of reflected solar light. We successfully applied the method to validate the Global Ozone Monitoring Experiment (GOME) polarization measurements. The error in the GOME's three broadband polarization measurements appears to be approximately 1%.     

Factorization of the polarization transformation matrix in integrated photoelasticity

In integrated photoelasticity, assessment of stresses in a three-dimensional specimen is based on the measurement of the change of polarization on many light rays that pass the specimen. Since the medium is optically anisotropic and inhomogeneous, the optical phenomena are nonlinear and solution of the inverse problem is complicated. Several methods of solving the inverse problem demand an efficient algorithm for solving the direct problem, i.e., for the calculation of the polarization transformation matrix on the basis of the stress field in the medium. We propose for this use factorization of the transformation matrix. We show that if the transformation of polarization is described by characteristic parameters, the three characteristic parameters can be determined by solving a single third-order differential equation. Since characteristic parameters can be measured experimentally, this approach can be used in practical three-dimensional stress analysis with integrated photoelasticity.     

HYBRID MECHANICS FOR AXISYMMETRIC THERMOELASTICITY PROBLEMS

The present article extends the integrated photoelasticity technique for the case where stresses are due to an unknown axisymmetric temperature field. Relationships that express radial and circumferential stresses through the axial and shear stresses are derived. Since residual stresses in glass can be described by the equations of thermoelasticity, the results of this article offer a means for complete determination of the residual stresses in axisymmetric glass articles using integrated photoelasticity. The results are verified by numerical and physical experiments.