During melting under gravity in the presence of a horizontal thermal gradient, buoyancy-driven convection in the liquid phase affects significantly the evolution of the liquid-solid interface. Due to the obvious engineering interest in understanding and controlling melting processes, fluid dynamicists and applied mathematicians have spent many efforts to model and simulate them numerically. Their endeavors concentrated in the twenty-five years period between the publication of the paper by Brent, Voller & Reid (1988) and that by Mansutti & Bucchignani (2011).

Regular physical exercise and appropriate nutrition affect metabolic and hormonal responses and may reduce the risk of developing chronic non-communicable diseases such as high blood pressure, ischemic stroke, coronary heart disease, some types of cancer, and type 2 diabetes mellitus. Computational models describing the metabolic and hormonal changes due to the synergistic action of exercise and meal intake are, to date, scarce and mostly focussed on glucose absorption, ignoring the contribution of the other macronutrients.

In this paper, an algorithm for the numerical evaluation of hypersingular finite-part integrals with rapidly oscillating kernels is proposed. The method is based on an interpolatory procedure at zeros of the orthogonal polynomials with respect to the first kind Chebyshev weight. Bounds of the error and of the amplification factor are also provided. Numerically stable procedure are obtained and the corresponding algorithms can be implemented in a fast way.

The simulations for the inverse problem of radiative transfer, even if built with a correct Bayesian approach, do not represent the full source of errors present in the experimental data. We point out two categories of errors (atmospheric model errors and non-Gaussian instrumental errors due to the optics and hardware, that are not considered by standard methods. Moreover, we show cases taken from FORUM simulated radiances using an End to End simulator, where se show how the instrument reacts to a non homogeneousneous filed of view.

We deal with integral equations with a singular kernel of Carlman type. A method to approach to the solution of these equations is given. Infinite matrix theory is used to determine the Fourier coefficients of the solution in the expansion in a series of orthogonal polynomials.

A reaction-diffusion model, known as the Sel'kov-Schnakenberg model, is considered. The nonlinear stability of the constant steady state is studied by using a special Liapunov functional and a maximum principle for regular solutions.

The non-equilibrium structural and dynamical properties of a flexible polymer pinned to a reflecting wall and subject to oscillatory linear flow are studied by numerical simulations. Polymer is confined in two dimensions and is modeled as a bead-spring chain while the interaction with the fluid is described by the Brownian multiparticle collision dynamics. At low strain the polymer is stretched along the flow direction. When increasing strain, chains are completely elongated and compressed against the wall when the flow is reverted.

To evaluate changes in the Soil Organic Carbon (SOC) index, one of the key indicators of land degradation neutrality, soil carbon modeling is of primary importance. In litera-ture, the analysis has been focused on the stability characterization of soil carbon steady states and in the calculation of the resilience of the stable equilibria. Neither stability nor resilience, however, provide any information about transient dynamics, and models with highly resilient equilibria can exhibit dramatic transient responses to perturbations.