Mathematical Models for Transport in Macroscopic and Mesoscopic Systems

Dear Colleagues,

Low-dimensional materials are widely studied in micro- and nanoelectronics for their many interesting features and looking toward the growing need for new technological applications. The progenitor of such a class is graphene, and today, a large family of low-dimensional materials is taking on an increasingly important role in material science. The new physical setting requires new efficient mathematical models, able to consider the peculiar properties of such materials. In order to design new electron devices, numerical simulations also play a fundamental role.

In this Special Issue, the focus is placed on mathematical modeling and simulation of charge transport in graphene and other 2D materials and in structures, such as double gate MOSFETs, nanoribbons and nanowires, where the presence of confinement effects allows for the formal description of the carrier flow as that of a two-dimensional or one-dimensional electron gas. Moreover, by increasing the miniaturization of devices, hotspots are observed, that is, zones with very high crystal temperature due to the release of energy by high energetic electrons. The effect is particularly relevant in materials with reduced dimensionality and confined structures.

In particular, we would encourage the submission of manuscripts discussing the following topics: ab initio calculations to furnish the correct band structures for the materials, e.g., doped graphene or graphene nanoribbons; thermal effects in the crystal lattice; rippling in suspended graphene as a result of coupling between elasticity and Dirac fermions; analytical properties of the Schrödinger equation; Monte Carlo simulations; Wigner transport equation; nonlinear dynamics in charge transport; numerical schemes for the charge carrier transport equation; fluid models deduced from the kinetic transport equations; optimization methods for transport phenomena.

Dr. Giovanni Nastasi
Prof. Dr. Vittorio Romano
Guest Editors

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• graphene
• low-dimensional material
• nanoribbons
• nanowires
• field effect transistors
• charge and phonon transport
• semiclassical boltzmann equation
• schrödinger equation
• wigner transport equation
• hydrodynamical models
• ab initio calculations
• monte carlo simulations
• optimization methods