Appendices include the basic equations involved in coupling the population balance equation (PBE) with fluid flow, heat and mass transfer (Appendix A), the implementation of the conservative finite volume discretisation method (Appendix B), the derivation of the probability density function (PDF) transport equation (Appendix C) and the derivation of the stochastic field equation (Appendix D).

Appendices include the basic equations involved in coupling the population balance equation (PBE) with fluid flow, heat and mass transfer (Appendix A), the implementation of the conservative finite volume discretisation method (Appendix B), the derivation of the probability density function (PDF) transport equation (Appendix C) and the derivation of the stochastic field equation (Appendix D).

Appendices include the basic equations involved in coupling the population balance equation (PBE) with fluid flow, heat and mass transfer (Appendix A), the implementation of the conservative finite volume discretisation method (Appendix B), the derivation of the probability density function (PDF) transport equation (Appendix C) and the derivation of the stochastic field equation (Appendix D).

Appendices include the basic equations involved in coupling the population balance equation (PBE) with fluid flow, heat and mass transfer (Appendix A), the implementation of the conservative finite volume discretisation method (Appendix B), the derivation of the probability density function (PDF) transport equation (Appendix C) and the derivation of the stochastic field equation (Appendix D).

The primary assumptions and formulations for single-phase flow regimes are reviewed in this chapter. This includes the governing partial differential equations for general fluid dynamics (mass, momentum, energy, and species), equations of state and associated flow regimes, rotational effects and the stream function for incompressible flow, and viscous effects with the Reynolds number, including flow instability mechanisms.

Hydrology deals mainly with the cycling of water in the natural environment, as related specifically to the continental water processes, at all scales. Globally, precipitation on the land surfaces averages roughly 0.8 m per year, of which around 60% is evaporated back into the atmosphere and 40% runs off into the oceans. Beside statistical analysis of direct measurements, several methodologies are available to describe the various components of the hydrologic cycle. These can be distinguished from one another primarily by the spatial and temporal scales at which the particular hydrologic phenomena are parameterized.

Here, we develop cosmological perturbation theory. This is the basics of CMB physics. The main reason why the CMB allows such an accurate determination of cosmological parameters lies in the fact that its anisotropies are small and can be determined mainly within first-order perturbation theory. We derive the perturbations of Einstein’s equations and the energy {momentum conservation equations and solve them for some simple but relevant cases. We also discuss the perturbation equation for light-like geodesics. This is sufficient to calculate the CMB anisotropies in the so-called instant recombination approximation. The main physical efffects that are missed in such a treatment are Silk damping on small scales and polarization. We then introduce the matter and CMB power spectrum and draw our first conclusions for its dependence on cosmological and primordial parameters. For example, we derive an approximate formula for the position of the acoustic peaks. In the last section we discuss fluctuations not laid down at some initial time but continuously sourced by some inhomogeneous component, a source, such as, for topological defects example, / that / may form during a phase transition in the early universe.

Here, we develop cosmological perturbation theory. This is the basics of CMB physics. The main reason why the CMB allows such an accurate determination of cosmological parameters lies in the fact that its anisotropies are small and can be determined mainly within first-order perturbation theory. We derive the perturbations of Einstein’s equations and the energy {momentum conservation equations and solve them for some simple but relevant cases. We also discuss the perturbation equation for light-like geodesics. This is sufficient to calculate the CMB anisotropies in the so-called instant recombination approximation. The main physical effects that are missed in such a treatment are Silk damping on small scales and polarization. We then introduce the matter and CMB power spectrum and draw our first conclusions for its dependence on cosmological and primordial parameters. For example, we derive an approximate formula for the position of the acoustic peaks. In the last section we discuss fluctuations not laid down at some initial time but continuously sourced by some inhomogeneous component, a source, such as, for topological defects example, / that / may form during a phase transition in the early universe.