This paper presents the formulation and validation of a spectral least squares method for solving the steady state population balance equations in Rd+1, with d the physical spatial dimension and 1 the internal property dimension.
The very scale of the problem is a big constraint, while the inadequate understanding of the common property dimension of these resources is another problem.
The characterization and calibration of ultrasound imaging systems requires tissue-mimicking phantoms with known acoustic properties, dimensions and internal features.
The probabilistic analysis included the uncertainty of CO2 concentration, deterioration processes, material properties, dimensions, and predictive models.
Various uncertain systematic parameters, which are including the material properties, dimensions of structural elements, as well as applied forces, can be simultaneously incorporated within the unified analysis framework.
This chapter discusses random variables, which may be used to describe the uncertainties in the basic variables such as spatial and time variation of external loads, material properties, dimensions, etc. under the subdivisions of statistical descriptions and probabilistic distributions.
Afterwards it is used to analyse some aspects such as the influence of slit dimensions, opening position, room properties (dimensions and absorption) that cannot be taken into account with the available models.
The spatial time-dependent reliability analysis takes into account the uncertainties and variabilities related to material properties, dimensions, loads and corrosion parameters as well as the spatial variability of pitting corrosion of prestressing strands.
Oil resources are located in various types of reservoir formations, varying with properties, dimensions and architectures.
