Mathematical Models for Transport in Macroscopic and Mesoscopic Systems

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: closed (31 January 2022) | Viewed by 374

Special Issue Editors

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Guest Editor
Department of Mathematics and Computer Science, University of Catania, Viale Andrea Doria 6, 95125 Catania, Italy
Interests: semiconductor modeling and simulations; kinetic models; numerical solutions of PDEs; Monte Carlo methods; optimization
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
Department of Mathematics and Computer Science, University of Catania, Viale A. Doria, 6, 95125 Catania, Italy
Interests: mathematical modeling and simulation of semiconductors; radiative transfer; charge and heat transport in solids
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

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

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.


  • 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

Published Papers

There is no accepted submissions to this special issue at this moment.
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