The Generalized Integral Transform Technique (GITT) is reviewed as a hybrid numerical–analytical approach for fluid flow problems, with or without heat and mass transfer, here with emphasis on the literature related to flow problems formulated through the full Navier–Stokes equations. A brief overview of the integral transform methodology is first provided for a general nonlinear convection–diffusion problem. Then, different alternatives of eigenfunction expansion strategies are discussed in the integral transformation of problems for which the fluid flow model is either based on the primitive variables or the streamfunction-only formulations, as applied to both steady and transient states. Representative test cases are selected to illustrate the different eigenfunction expansion approaches, with convergence being analyzed for each situation. In addition, fully converged integral transform results are critically compared to previously reported simulations obtained from traditional purely discrete methods.

The True’s beaked whale (Mesoplodon mirus, True 1913) is a poorly known member of the Ziphiidae family. Its distribution in the northern hemisphere is thought to be restricted to the temperate or warm temperate waters of the North Atlantic, while a few stranding records from the southern hemisphere suggest a wider and antitropical distribution, extending to waters from the Atlantic coast of Brazil to South Africa, Mozambique, Australia and the Tasman Sea coast of New Zealand. This paper (i) reports the first molecular confirmation of the occurrence of the True’s beaked whale at the southern limit of its distribution recorded in the northeast Atlantic: the Azores and Canary Islands (macaronesian ecoregion); (ii) describes a new colouration for this species using evidence from a whale with molecular species confirmation; and (iii) contributes to the sparse worldwide database of live sightings, including the first underwater video recording of this species and close images of a calf. Species identification was confirmed in two cases using mitochondrial DNA control region and cytochromebgene markers: a subadult male True’s beaked whale that stranded in El Hierro, Canary Islands, in November 2012, and a subadult male found floating dead near Faial, the Azores, in July 2004. The whale that stranded in the Canary Islands had a clearly delimited white area on its head, extending posteriorly from the tip of the beak to cover the blowhole dorsally and the gular grooves ventrally. This colouration contrasts with previous descriptions for the species and it may be rare, but it exemplifies the variability of the colouration of True’s beaked whales in the North Atlantic, further confirmed here by live sightings data. The recording of several observations of this species in deep but relatively coastal waters off the Azores and the Canary Islands suggests that these archipelagos may be unique locations to study the behaviour of the enigmatic True’s beaked whale.

In this work, the Markov Chain Monte Carlo is applied to estimate parameters that represent mechanisms that describe particles' dynamics in particulate systems from the literature's proposed models. Initially, the reduced sensitivity coefficient is evaluated to verify which parameters could be estimated simultaneously. The technique is then applied to estimate the models' parameters in different numerical scenarios to determine the rates that influence population dynamics. After the analyzes are performed, the estimates show good precision, accuracy, and a good fit between the measured and estimated state variables. The results show that the Markov chain Monte Carlo can determine the rates of population balance phenomenon.

A hybrid numerical–analytical solution based on the generalized integral transform technique is proposed to handle the two‐dimensional Navier–Stokes equations in cylindrical coordinates, expressed in terms of the streamfunction‐only formulation. The proposed methodology is illustrated in solving steady‐state incompressible laminar flow of Newtonian fluids in the developing region of a circular tube. The flow modeling also considers two limiting inlet conditions, namely, uniform velocity profile representing a parallel flow, and zero vorticity that characterizes irrotational inlet flow. The integral transform analysis for such a full cylindrical region brings up singularities at the channel centerline, and, as previously described in a work dealing with the boundary‐layer formulation, a way to alleviate this difficulty is to adopt a recently introduced fourth‐order eigenvalue problem as the basis for the eigenfunction expansion. A thorough convergence analysis of the proposed expansion is then undertaken, for different values of Reynolds number, and a set of reference results for the velocity distributions and friction factors are then presented in tabular and graphical forms. Copyright © 2009 John Wiley & Sons, Ltd.

The Generalized Integral Transform Technique (GITT) was employed to simulate transient one-dimensional flow in variably saturated porous media, as well as radioactive waste transport within different layers (a solid waste pile, nearby soil, and a granular aquifer) towards the edge of a uranium mining installation under institutional control. Computational codes, written using the Mathematica software system, were implemented and tested for solution of the coupled advection-dispersion equations for an arbitrary number of daughter products within a radioactive chain migrating in saturated and unsaturated soil layers. The computer simulations were verified in great detail against results obtained using the built-in routine NDSolve of the Mathematica platform and the HYDRUS-1D software system. The present work reports the main results for 238U chain radionuclide transport using data extracted from a safety assessment of solid waste repositories at a uranium mining and milling installation in Caetité, state of Bahia, Brazil, operated by INB (Indústrias Nucleares do Brasil). Concentration evolutions of the various radionuclides obtained with the simulations were analyzed for five different cases to explore variations in the infiltration and recharge rates, the effect of assuming physical equilibrium or non-equilibrium transport conditions, and of different initial concentrations of some of the radionuclides.