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A reaction–diffusion system governing the predator–prey interaction with specialist predator and herd behavior for prey is investigated. Linear stability of the interior equilibrium is studied, and conditions guaranteeing the occurrence of Turing instability, induced by cross‐diffusion, are found, with a full characterization of the Turing instability region in the parameter space. Numerical simulations on the obtained results are provided. [ABSTRACT FROM AUTHOR]

In the Mediterranean basin, coniferous reforestation mainly comprises forest stands highly susceptible to fires. When silvicultural treatments have not been performed for decades after plantation, these stands often exhibit high vertical and horizontal tree density, along with a significant occurrence of lying and standing deadwood, thereby increasing the fuel load. On average, these pine forests are characterized by high values of above-ground biomass, ranging from 175 to 254 Mg ha−1 for the younger and the older ones, respectively. The theoretical heat energy produced per surface unit, in the case of the total combustion of the above-ground biomass, is also high, varying from 300 to 450 MJ ha−1 depending on the stage of stand development. In this study, we demonstrated the importance of silvicultural interventions in reducing the pyrological potential in pine reforested stands located in southern Italy, also giving attention to the water savings needed during extinction phases. In detail, we applied a preliminary mathematical reaction-diffusion model aimed at predicting the development of forest fires. The model was applied using data obtained through the estimation of the pyrological potential in terms of heat energy produced per surface unit (1 hectare) and the variation in the critical surface intensity. We verified that, when silvicultural interventions are applied, they induce a reduction of heat energy ranging between 17 and 21%, while the extinguishing water saved ranges between 600 and 1000 Mg ha−1. Moreover, when the silvicultural interventions are implemented, the probability of the transition from surface fire to crown fire can be reduced by up to 31%. The most effective results on fire risk mitigation are mainly obtained when thinning aimed at reducing canopy and tree density is carried out in the younger phases of the reforested pine stands. [ABSTRACT FROM AUTHOR]

This paper addresses the theoretical foundation of a localization method for crack detection in a concrete sample based on the time of arrival of the elastic wave generated by the crack formation to a group of sensors positioned on the boundary of the sample. The equations of motion for the elastic waves are carefully presented, including a body force term which accounts for the sudden formation of a crack. Then, a localization method based on the detection of acoustic emissions, and specifically on their arrival times, is described. Finally, a discretization scheme for the 2D equations of elasticity is developed, and some numerical experiments are performed to assess the validity of the method. [ABSTRACT FROM AUTHOR]

This paper concerns with a compact network model combined with distributed models for semiconductor devices. For linear RLC networks containing distributed semiconductor devices, we construct a mathematical model that joins the differential‐algebraic initial value problem for the electric circuit with multidimensional parabolic‐elliptic boundary value problems for the devices. We prove an existence and uniqueness result and the asymptotic behavior of this mixed initial boundary value problem of partial differential‐algebraic equations. [ABSTRACT FROM AUTHOR]

We present the first macroscopical model for charge transport in compound semiconductors to make use of analytic ellipsoidal approximations for the energy dispersion relationships in the neighbours of the lowest minima of the conduction bands. The model considers the main scattering mechanisms charges undergo in polar semiconductors, that is the acoustic, polar optical, intervalley non-polar optical phonon interactions and the ionized impurity scattering. Simulations are shown for the cases of bulk 4H and 6H-SiC. [ABSTRACT FROM PUBLISHER]

Abstract: We consider a system of partial differential–algebraic equations which model an electric network containing semiconductor devices. The zero-dimensional differential–algebraic network equations are coupled with multi-dimensional elliptic partial differential equations which model the devices. For this coupled system we prove an existence result. [Copyright &y& Elsevier]

Abstract: The limit of the vanishing ratio of the electron mass to the ion mass in the isentropic transient Euler–Poisson equations with periodic boundary conditions is proved. The equations consist of the balance laws for the electron density and current density for a given ion density, coupled to the Poisson equation for the electrostatic potential. The limit is related to the low-Mach-number limit of Klainerman and Majda. In particular, the limit velocity satisfies the incompressible Euler equations with damping. The difference to the zero-Mach-number limit comes from the electrostatic potential which needs to be controlled. This is done by a reformulation of the equations in terms of the enthalpy, higher-order energy estimates and a careful use of the Poisson equation. [Copyright &y& Elsevier]

In refined network analysis, a compact network model is combined with distributed models for semiconductor devices in a multidimensional approach. For linear RLC networks containing diodes as distributed devices, we construct a mathematical model that joins the differential-algebraic initial value problem for the electric circuit with parabolic-elliptic boundary value problems modeling the diodes. For this mixed initial boundary value problem of partial differential-algebraic equations a first existence and uniqueness result is given, and its asymptotic behavior is discussed. [ABSTRACT FROM AUTHOR]

We consider a one-dimensional, isentropic, hydrodynamical model for a unipolar semiconductor, with the mobility depending on the electric field. The mobility is related to the momentum relaxation time, and field-dependent mobility models are commonly used to describe the occurrence of saturation velocity, that is, a limit value for the electron mean velocity as the electric field increases. For the steady state system, we prove the existence of smooth solutions in the subsonic case, with a suitable assumption on the mobility function. Furthermore, we prove uniqueness of subsonic solutions for sufficiently small currents. [ABSTRACT FROM AUTHOR]