By applying Helmholtz decomposition, the unknowns of a linearized Euler system can be recast as solutions of uncoupled linearwave equations. Accordingly, the Kirchhoff expression of the exact solutions is recast as a time-marching, Lax-Wendroff type, numerical scheme for which consistency with one-dimensional upwinding is checked. This discretization, involving spherical means, is set up on a 2D uniform Cartesian grid, so that the resulting numerical fluxes can be shown to be conservative.

We study spreading dynamics of a reaction diffusion process in a special class of heterogeneous graphs with Poissonian degree distribution and composed of both local and long range links. The behavior of the spreading dynamics on such networks are investigated by relating them to the topological features of graphs.

Proteins are the core and the engine of every process in cells thus the study of mechanisms that drive the regulation of protein expression, is essential. Transcription factors play a central role in this extremely complex task and they synergically co-operate in order to provide a fine tuning of protein expressions. In the present study, we designed a mathematically well-founded procedure to investigate the mutual positioning of transcription factors binding sites related to a given couple of transcription factors in order to evaluate the possible association between them.

[object Object]Metals, extensively used in technology applications as well as in art metal works, have a chemical affinity for oxygen, water, sulphur and are particularly susceptible to electrochemical processes due to the environment. For this reason the monitoring of the effect of environmental conditions (temperature, humidity, pollutant concentration) on their mechanical and physical properties are considered a primary necessity for metal conservation and preservation.

We propose a model of a density-dependent compressible-incompressible fluid, which is intended as a simplified version of models based on mixture theory as, for instance, those arising in the study of biofilms, tumor growth and vasculogenesis. Though our model is, in some sense, close to the density-dependent incompressible Euler equations, it presents some differences that require a different approach from an analytical point of view. In this paper, we establish a result of local existence and uniqueness of solutions in Sobolev spaces to our model, using the Leray projector.

Effectively dealing with invasive species is a pervasive problem in environmental management. The damages, and associated costs, that stem from invasive species are well known, as is the benefit from their removal. We investigate problems where optimal control theory has been implemented, and we show that these problems can easily become hypersensitive, making their numerical solutions unstable. We show that transforming these problems from state-adjoint systems to state-control systems can provide useful insights into the system dynamics and simplify the numerics.