We study the initial-boundary value problem (Formula presented.) with measure-valued initial data. Here ? is a bounded open interval, ?(0)=?(?)=0, ? is increasing in (0,?) and decreasing in (?,?), and the regularising term ? is increasing but bounded. It is natural to study measure-valued solutions since singularities may appear spontaneously in finite time. Nonnegative Radon measure-valued solutions are known to exist and their construction is based on an approximation procedure. Until now nothing was known about their uniqueness.

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.

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]

Rollout methodology is a constructive metaheuristic algorithm and its main characteristics are its modularity, the adaptability to different objectives and constraints and the easiness of implementation. Multi-heuristic Rollout extends the Rollout by incorporating several constructive heuristics in the Rollout framework and it is able to easily incorporate human experience inside its research patterns to fulfil complex requirements dictated by the application at hand. However, a drawback for both Rollout and multi-heuristic Rollout is often represented by the required computation time.

We present the results obtained by using an evolution of our CUDA-based solution for the exploration, via a breadth first search, of large graphs. This latest version exploits at its best the features of the Kepler architecture and relies on a combination of techniques to reduce both the number of communications among the GPUs and the amount of exchanged data. The final result is a code that can visit more than 800 billion edges in a second by using a cluster equipped with 4,096 Tesla K20X GPUs.

We consider the problem of determining quantitative information about corrosion occurring on an inaccesible part of a specimen. The data for the problem consist of prescribed current flux and voltage measurements on an accessible part of the specimen boundary. The problem is modelled by Laplace's equation with an unknown term in the boundary conditions. Our goal is recovering from the data. We prove uniqueness under certain regularity assumptions and construct a regularized numerical method for obtaining approximate solutions to the problem.

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.