We study a quasilinear parabolic equation of forward-backward type, under assumptions on the nonlinearity which hold for a wide class of mathematical models, using a pseudo-parabolic regularization of power type.We prove existence and uniqueness of positive solutions of the regularized problem in a space of Radon measures. It is shown that these solutions satisfy suitable entropy inequalities. We also study their qualitative properties, in particular proving that the singular part of the solution with respect to the Lebesgue measure is constant in time.

Graphics Processing Units (GPUs) exhibit significantly higher peak performance than conventional CPUs. However, in general only highly parallel algorithms can exploit their potential. In this scenario, the iterative solution to sparse linear systems of equations could be carried out quite efficiently on a GPU as it requires only matrix-by-vector products, dot products, and vector updates. However, to be really effective, any iterative solver needs to be properly preconditioned and this represents a major bottleneck for a successful GPU implementation.

This paper proposes a crowd dynamic macroscopic model grounded on microscopic phenomenological observations which are upscaled by means of a formal mathematical procedure. The actual applicability of the model to real-world problems is tested by considering the pedestrian traffic along footbridges, of interest for Structural and Transportation Engineering. The genuinely macroscopic quantitative description of the crowd flow directly matches the engineering need of bulk results.

The effects of a nonminimally coupled curvature-matter model of gravity on a perturbed Minkowski metric are presented.

We derive a rule for the reconstruction of the internal heat transfer coefficient hint of a pipe, from temperature maps collected on the external face. The pipe is subjected to internal heating by connecting two electrodes to the external surface. To estimate hint we apply the perturbation theory to a thin plate approximation of a boundary value problem for the stationary heat equation.[object Object]

By means of mesoscopic numerical simulations of a model soft-glassy material, we investigate the role of boundary roughness on the flow behaviour of the material, probing the bulk/wall and global/local rheologies. We show that the roughness reduces the wall slip induced by wettability properties and acts as a source of fluidisation for the material. A direct inspection of the plastic events suggests that their rate of occurrence grows with the fluidity field, reconciling our simulations with kinetic elasto-plastic descriptions of jammed materials.

Unlike for systems in equilibrium, a straightforward definition of a metastable set in the non-stationary, non-equilibrium case may only be given case-by-case-and therefore it is not directly useful any more, in particular in cases where the slowest relaxation time scales are comparable to the time scales at which the external field driving the system varies. We generalize the concept of metastability by relying on the theory of coherent sets.

Connections between microscopic follow-the-leader and macroscopic fluid-dynamics traffic flow models are already well understood in the case of vehicles moving on a single road. Analogous connections in the case of road networks are instead lacking. This is probably due to the fact that macroscopic traffic models on networks are in general ill-posed, since the conservation of the mass is not sufficient alone to characterize a unique solution at junctions.

Graphics processing units (GPU) are currently used as a cost-effective platform forcomputer simulations and big-data processing. Large scale applications require thatmultiple GPUs work together but the efficiency obtained with cluster of GPUs is, at times,sub-optimal because the GPU features are not exploited at their best. We describe how itis possible to achieve an excellent efficiency for applications in statistical mechanics,particle dynamics and networks analysis by using suitable memory access patterns andmechanisms like CUDA streams, profiling tools, etc.