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The main aim of this work is to optimize a Quantum Drift Diffusion model (QDD) (V. Romano, M. Torrisi, and R. Tracinà, "Approximate solutions to the quantum drift-diffusion model of semiconductors," J. Math. Phys., vol. 48, p. 023501, 2007; A. El Ayyadi and A. Jüngel, "Semiconductor simulations using a coupled quantum drift-diffusion schrödinger-Poisson model," SIAM J. Appl. Math., vol. 66, no. 2, pp. 554–572, 2005; L. Barletti and C. Cintolesi, "Derivation of isothermal quantum fluid equations with Fermi-Dirac and bose-einstein statistics," J. Stat. Phys., vol. 148, pp. 353–386, 2012) by comparing it with the Boltzmann-Wigner Transport Equation (BWTE) (O. Muscato, "Wigner ensemble Monte Carlo simulation without splitting error of a GaAs resonant tunneling diode," J. Comput. Electron., vol. 20, pp. 2062–2069, 2021) solved using a signed Monte Carlo method (M. Nedjalkov, H. Kosina, S. Selberherr, C. Ringhofer, and D. K. Ferry, "Unified particle approach to Wigner-Boltzmann transport in small semiconductor devices," Phys. Rev. B, vol. 70, pp. 115–319, 2004). A situation of high non equilibrium regime is investigated: electron transport in a Resonant Tunneling Diode (RTD) made of GaAs with two potential barriers in GaAlAs. The range of the suitable voltage bias applied to the RTD is analyzed. We find an acceptable agreement between QDD model and BWTE when the applied bias is low or moderate with a threshold of about 0.225 V over a length of 150 nm; it is found out that the use of a field dependent mobility is crucial for getting a good description of the negative differential conductivity in such a range. At higher bias voltages, we expect that QDD model loses accuracy. [ABSTRACT FROM AUTHOR]

The article is an editorial introducing a special issue of the scientific journal Axioms titled "Mathematical Models and Simulations." The issue contains 13 papers that cover various mathematical models and simulations in fields such as physics, biology, finance, and engineering. The papers explore different types of mathematical models, including deterministic and stochastic models, and discuss their applications and numerical simulations. The authors provide a brief overview of each paper, highlighting their main findings and methodologies. The article aims to provide library patrons with a concise summary of the special issue, allowing them to decide if they want to explore the individual papers further. [Extracted from the article]

A graphene FET (GFET), where the active area is made of monolayer large-area graphene, is simulated including a full 2-D Poisson equation and a drift-diffusion model with mobilities deduced by a direct numerical solution of the semiclassical Boltzmann equations for charge transport by a suitable discontinuous Galerkin approach. The critical issue in a GFET is the difficulty of fixing the OFF state which requires an accurate calibration of the gate voltages. In this article, we propose and simulate a GFET structure which has well-behaved characteristic curves similar to those of conventional (with gap) semiconductor materials. The introduced device has a clear off region and can be the prototype of devices suited for postsilicon nanoscale electron technology. The specific geometry overcomes the problems of triggering the minority charge current and gives a viable way for the design of electron devices based on large area monolayer graphene as a substitute of standard semiconductors in the active area. The good FET behavior of the current versus the gate voltage makes the simulated device very promising and a challenging case for experimentalists, even if it is crucial to better understand the resistance effect of charge carriers at the contact-graphene region. [ABSTRACT FROM AUTHOR]

This paper is devoted to the formulation and numerical solution by Monte Carlo (MC) methods of an optimal control problem governed by the linear space-homogeneous Keilson-Storer (KS) master equation. The KS master equation is a representative model of the class of linear Boltzmann equations with many applications ranging from spectroscopy to transport theory. The purpose of the optimal control in the collision kernel of this model is to drive an ensemble of particles to acquire a desired mean velocity and to achieve a desired final velocity configuration. For this purpose, a KS optimality system characterizing the solution of the proposed optimal control problem is derived and used to construct a gradient-based optimization strategy in the framework of MC methods. This task requires to accommodate the resulting adjoint KS model in a form that is consistent with the kinetic formulation. Results of numerical experiments successfully validate the proposed control framework. [ABSTRACT FROM AUTHOR]

A flexible framework is obtained for enhancing both the thermal and electrical performance of fin field-effect transistor (FinFET) technology. Investigation of the nanoscale heat conduction within a short-channel field-effect transistor can be regarded as an emerging challenge related to future-generation transistors. In this work, we report the electrothermal transport in a 10 nm silicon-on-insulator (SOI) FinFET based on the dual-phase-lag model and modified drift-diffusion motions. We found that electron mobility decreases along the channel due to carrier confinement under higher electric field. In addition, the surface detection temperature indicates that the self-heating process is localized between the source and drain region. As promising results, high-κ metal-oxide and lower thermal boundary resistance can optimize the nanoscale heat transport in the SOI FinFET device. [ABSTRACT FROM AUTHOR]

Graphene has attracted the attention of several researchers because of its peculiar features. In particular, the study of charge transport in graphene is challenging for future electron devices. Usually, the physical description of electron flow in graphene given by the semiclassical Boltzmann equation is considered to be a good one. However, due to the computational complexity, its use in simulation tools is not practical and, as already done for traditional semiconductors such as Si or GaAs, simpler models are warranted. Here we will assess the validity of a class of hydrodynamical models based on the maximum entropy principle (MEP), by comparing, in the case of suspended monolayer graphene, the direct solution of the semiclassical Boltzmann equation for electrons, obtained by employing a discontinuous Galerkin approach, with the MEP distribution function. A reasonable agreement is observed. [ABSTRACT FROM AUTHOR]

During the evolution of the COVID-19 pandemic, each country has adopted different control measures to contrast the epidemic's diffusion. Restrictions to mobility, public transport, and social life in general have been actuated to contain the spread of the pandemic. In this paper, we consider the deterministic SIRD model with delays proposed by Calleri et al., which is improved by adding the vaccinated compartment V (SIRDV model) and considering a time-dependent contact frequency. The three delays take into account the incubation time of the disease, the healing time, and the death time. The aim of this work is to study the effect of the vaccination campaigns in Great Britain (GBR) and Israel (ISR) during the pandemic period. The different restriction periods are included by fitting the contact frequency on real datasets as a piecewise constant function. As expected, the vaccination campaign reduces the amount of deaths and infected people. Furthermore, for the different levels of restriction policy, we find specific values of the contact frequency that can be used to predict the trend of the pandemic. [ABSTRACT FROM AUTHOR]

The aim of this work is to simulate charge transport in a monolayer graphene on different substrates. This requires the inclusion of the scatterings of charge carriers with impurities and phonons of the substrate, besides the interaction mechanisms already present in the graphene layer. As mathematical model, the semiclassical Boltzmann equation is assumed and the results are based on Direct Simulation Monte Carlo (DSMC) method. A crucial point is the correct inclusion of the Pauli Exclusion Principle (PEP). Most simulations use the approach proposed by Jacoboni e Lugli which, however, allows an occupation number greater than one with an evident violation of PEP. Here the Monte Carlo scheme devised by Romano et al. (J. Comput. Phys. 302, 267-284, 2015) is employed. It predicts occupation numbers consistent with PEP and therefore is physically more accurate. Two different substrates are investigated: SiO2 and hexagonal boron nitride (h-BN). We adopt the model for charge-impurities scattering described by E. H. Hwang and S. Das Sarma (Phys. Rev. B 75, 205418, 2007). In such a model a crucial parameter is the distance d between the graphene layer and the impurities of the substrate. Usually d is considered constant. Here we assume that d is a random variable in order to take into account the roughness of the substrate and the randomness of the location of the impurities. Our results confirm that h-BN is one of the most promising substrate also for the high-field mobility on account of the reduced degradation of the velocity due to the remote impurities. This is in agreement with results shown by Hirai et al. (J. Appl. Phys. 116, 083703, 2014) where only the low-field mobility has been investigated. [ABSTRACT FROM AUTHOR]