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Integral operators on space of Borel measurable functions bounded considering weight function, giving condition for infinite complex matrices, mapping analytic sequence spaces
Evaluation of weighting functions in the atmospheric remote sensing is usually the most computer-intensive part of the inversion algorithms. We present an analytic approach to computations of temperature and mixing ratio weighting functions that is based on our previous results but the resulting expressions use the intermediate variables that are generated in computations of observable radiances themselves. Upwelling radiances at the given level in the atmosphere and atmospheric transmittances from space to the given level are combined with local values of the total absorption coefficient and its components due to absorption of atmospheric constituents under study. This makes it possible to evaluate the temperature and mixing ratio weighting functions in parallel with evaluation of radiances. This substantially decreases the computer time required for evaluation of weighting functions. Implications for the nadir and limb viewing geometries are discussed.
In a recent publication (Ustinov, 2002), we proposed an analytic approach to evaluation of radiative and geophysical weighting functions for remote sensing of a blackbody planetary atmosphere, based on general linearization approach applied to the case of nadir viewing geometry. In this presentation, the general linearization approach is applied to the limb viewing geometry. The expressions, similar to those obtained in (Ustinov, 2002), are obtained for weighting functions with respect to the distance along the line of sight. Further on, these expressions are converted to the expressions for weighting functions with respect to the vertical coordinate in the atmosphere. Finally, the numerical representation of weighting functions in the form of matrices of partial derivatives of grid limb radiances with respect to the grid values of atmospheric parameters is used for a convolution with the finite field of view of the instrument.
A closed form expression for the weight function for a strip with a single edge crack is presented. The expression is valid for relative crack lengths from zero to unity. It is based on the assumption that the shape of an opened edge crack can be approximated by a conic section. The results agree well with published values for weight functions, stress intensity factors, and crack mouth opening displacements.
A closed form expression for the weight function for a strip with a single edge crack is presented. The expression is valid for relative crack lengths from zero to unity. It is based on the assumption that the shape of an opened edge crack can be approximated by a conic section. The results agree well with published values for weight functions, stress intensity factors, and crack mouth opening displacements.
Gauss quadrature rules involving some nonclassical weight functions
Stress intensity factors for quarter-elliptical corner cracks emanating from a circular hole are determined using a 3-D weight function method combined with a 3-D finite element method. The 3-D finite element method is used to analyze uncracked configuration and provide stress distribution in the region where crack is to occur. Using this stress distribution as input, the 3-D weight function method is used to determine stress intensity factors. Three different loading conditions, i.e. remote tension, remote bending and wedge loading, are considered for a wide range in geometrical parameters. The significance in using 3-D uncracked stress distribution and the difference between single and double corner cracks are studied. Typical crack opening displacements are also provided. Comparisons are made with solutions available in the literature.
One class of methods for converting satellite measured radiances into atmospheric temperature profiles, involves a linearization of the radiative transfer equation: delta r = the sum of (W sub i) (delta T sub i) where (i=1...s) and where delta T sub i is the deviation of the temperature in layer i from that of a reference atmosphere, delta R is the difference in the radiance at satellite altitude from the corresponding radiance for the reference atmosphere, and W sub i is the discrete (or vector) form of the T-weighting (i.e., temperature weighting) function W(P), where P is pressure. The top layer of the atmosphere corresponds to i = 1, the bottom layer to i = s - 1, and i = s refers to the surface. Linearization in temperature (or some function of temperature) is at the heart of all linear or matrix methods. The weighting function that should be used is developed.
Fracture mechanics calculations using the finite element method can be computationally expensive, which makes them challenging to use in engineering evaluations of flaws in pressure vessels. The weight function (WF) technique is a reduced order fracture modeling method that is widely used to greatly reduce these computational costs. Its computational efficiency is essential for use in probabilistic fracture mechanics evaluations of embrittled nuclear reactor pressure vessels (RPVs), due to the large number of sampled flaws that must be evaluated. Although the WF technique is general, it is typically used only for axis-aligned flaws. Recent discoveries of off-axis flaws in operating nuclear reactors have necessitated detailed simulations of such flaws and the interactions between neighboring flaws. This paper presents a generalized WF approach applicable for analyzing arbitrary flaw geometries in thick-walled cylindrical vessels, including surface-breaking and subsurface flaws, which can either axis-aligned or off-axis, and can account for interactions with other flaws. Herein, this approach is demonstrated on representative simulations of multiple flaw geometries in a RPV subjected to transient loading conditions. In all cases, the WF technique gives good comparison with benchmark results from direct simulation with greatly reduced computational effort.
This slide presentation reviews the observable radiances as functions of atmospheric parameters and of surface parameters; the mathematics of atmospheric weighting functions (WFs) and surface partial derivatives (PDs) are presented; and the equation of the forward radiative transfer (RT) problem is presented. For non-scattering atmospheres this can be done analytically, and all WFs and PDs can be computed analytically using the direct linearization approach. For scattering atmospheres, in general case, the solution of the forward RT problem can be obtained only numerically, but we need only two numerical solutions: one of the forward RT problem and one of the adjoint RT problem to compute all WFs and PDs we can think of. In this presentation we discuss applications of both the linearization and adjoint approaches
We present an analytic approach to computations of temperature and mixing ratio weighting functions that is based on our previous results but the resulting expressons use the intermediate variables that are generated in computations of observable radiances themselves.
In this presentation, we apply the adjoint sensitivity analysis of radiative transfer in thermal IR to the general case of the analytic evaluation of the weighting functions of atmospheric parameters together with the partial derivatives for the surface parameters. Applications to remote sensing of atmospheres of Mars and Venus are discussed.
Parallel with the work in Part-1, stress intensity factors for semi-elliptical surface cracks emanating from a circular hole are determined. The 3-D weight function method with the 3D finite element solutions for the uncracked stress distribution as in Part-1 is used for the analysis. Two different loading conditions, i.e. remote tension and wedge loading, are considered for a wide range in geometrical parameters. Both single and double surface cracks are studied and compared with other solutions available in the literature. Typical crack opening displacements are also provided.
Severe reduction of stratospheric ozone over Antarctica has focused increasing concern on the biological effects of ultraviolet-B (UVB) radiation (280 to 320 nanometers). Measurements of photosynthesis from an experimental system, in which phytoplankton are exposed to a broad range of irradiance treatments, are fit to an analytical model to provide the spectral biological weighting function that can be used to predict the short-term effects of ozone depletion on aquatic photosynthesis. Results show that UVA (320 to 400 nanometers) significantly inhibits the photosynthesis of a marine diatom and a dinoflagellate, and that the effects of UVB are even more severe. Application of the model suggests that the Antarctic ozone hole might reduce near-surface photosynthesis by 12 to 15 percent, but less so at depth. The experimental system makes possible routine estimation of spectral weightings for natural phytoplankton.
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Analysis of data from biochemical and physiological tracer experiments - linear system
Point 7 of a list of works conducted by the USSR in accordance with the Joint Soviet-American Research Program on improving methods of heat probes from satellites is discussed. Numerous calculations of transmission functions, along with tables are enclosed.
Distributed-effect sensors, which respond to spatially distributed inputs over a significant gauge length, encompass piezoelectric laminate films, modal-domain optical fiber sensors, and holographic sensors; they can be fabricated with spatially varying sensitivity to a distributed measurand for spatial filtering. Such spatial filters are configurable to extract various structural parameters from distributed measurements that cannot be directly measured by sensors. A modeling is presently conducted for distributed-effect sensors' integration into state-space structural models, noting the effects of fabrication errors on sensor operation.