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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]

Some properties of the electron–electron collision operator in graphene are analyzed along with the evaluation of collision rate. Monte Carlo simulations complete the study and highlight the non-negligible role of the electron–electron scattering for an accurate evaluation of the currents and, as a consequence, of the characteristic curves. [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]

For the first time in sigma-2 (σ 2 ) receptor field, a quantitative structure–activity relationship (QSAR) model has been built using p K i values of the whole set of known selective σ 2 receptor ligands (548 compounds), taken from the Sigma-2 Receptor Selective Ligands Database (S2RSLDB) ( http://www.researchdsf.unict.it/S2RSLDB/ ), through the Monte Carlo technique and employing the software CORAL. The model has been developed by using a large and structurally diverse set of compounds, allowing for a prediction of different populations of chemical compounds endpoint (σ 2 receptor p K i ). The statistical quality reached, suggested that model for p K i determination is robust and possesses a satisfactory predictive potential. The statistical quality is high for both visible and invisible sets. The screening of the FDA approved drugs, external to our dataset, suggested that sixteen compounds might be repositioned as σ 2 receptor ligands (predicted p K i ≥ 8). A literature check showed that six of these compounds have already been tested for affinity at σ 2 receptor and, of these, two (Flunarizine and Terbinafine) have shown an experimental σ 2 receptor p K i > 7. This suggests that this QSAR model may be used as focusing screening filter in order to prospectively find or repurpose new drugs with high affinity for the σ 2 receptor, and overall allowing for an enhanced hit rate respect to a random screening. [ABSTRACT FROM AUTHOR]