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.

In this paper, a complete picture of the different plastic failure modes that can be predicted by the strain gradient plasticity model proposed in Del Piero et al. (J. Mech. Mater. Struct. 8:109-151, 2013) is drawn. The evolution problem of the elasto-plastic strain is formulated in Del Piero et al. (J. Mech. Mater. Struct. 8:109-151, 2013) as an incremental minimization problem acting on an energy functional which includes a local plastic term and a non-local gradient contribution.

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 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.

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).

The present work extends a previous paper where an agent-based and two-dimensional partial differential diffusion model was introduced for describing immune cell dynamics (leukocytes) in cancer-on-chip experiments. In the present work, new features are introduced for the dynamics of leukocytes and for their interactions with tumor cells, improving the adherence of the model to what is observed in laboratory experiments. Each system's solution realization is a family of biased random walk trajectories, affected by the chemotactic gradients and in turn affecting them.