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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]

A field effect transistor having the active area made of monolayer graphene is simulated by a drift-diffusion model coupled with the Poisson equation. The adopted geometry, already proposed in (Nastasi and Romano in IEEE Trans. Electron. Devices 68:4729–4734, 2021, https://doi.org/10.1109/TED.2021.3096492), gives a good current-ON/current-OFF ratio as it is evident in the simulations. In this paper, we compare the numerical simulations of the standard (non-degenerate) drift-diffusion model, that includes the Einstein diffusion coefficient, with the degenerate case. [ABSTRACT FROM AUTHOR]

Two stochastic models are proposed to describe the evolution of the COVID-19 pandemic. In the first model the population is partitioned into four compartments: susceptible S, infected I, removed R and dead people D. In order to have a cross validation, a deterministic version of such a model is also devised which is represented by a system of ordinary differential equations with delays. In the second stochastic model two further compartments are added: the class A of asymptomatic individuals and the class L of isolated infected people. Effects such as social distancing measures are easily included and the consequences are analyzed. Numerical solutions are obtained with Monte Carlo simulations. Quantitative predictions are provided which can be useful for the evaluation of political measures, e.g. the obtained results suggest that strategies based on herd immunity are too risky. Finally, the models are calibrated on data referring to the second wave of infection in Italy. [ABSTRACT FROM AUTHOR]

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]

We present a hydrodynamical model for graphene nanoribbons that takes into account the electron collisions with the lattice and with the edge of the ribbon. Moreover the bandgap due to the low dimension of the ribbon is considered. The simulation shows that the model describes qualitatively the macroscopic behavior of the charges and the results are comparable with that ones obtained by solving numerically the Boltzmann equation but with a remarkable reduction of the computational time. [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]

Background: Sigma (σ) receptors are accepted as a particular receptor class consisting of two subtypes: sigma-1 (σ) and sigma-2 (σ). The two receptor subtypes have specific drug actions, pharmacological profiles and molecular characteristics. The σ receptor is overexpressed in several tumor cell lines, and its ligands are currently under investigation for their role in tumor diagnosis and treatment. The σ receptor structure has not been disclosed, and researchers rely on σ receptor radioligand binding assay to understand the receptor's pharmacological behavior and design new lead compounds. Description: Here we present the sigma-2 Receptor Selective Ligands Database (S2RSLDB) a manually curated database of the σ receptor selective ligands containing more than 650 compounds. The database is built with chemical structure information, radioligand binding affinity data, computed physicochemical properties, and experimental radioligand binding procedures. The S2RSLDB is freely available online without account login and having a powerful search engine the user may build complex queries, sort tabulated results, generate color coded 2D and 3D graphs and download the data for additional screening. Conclusion: The collection here reported is extremely useful for the development of new ligands endowed of σ receptor affinity, selectivity, and appropriate physicochemical properties. The database will be updated yearly and in the near future, an online submission form will be available to help with keeping the database widely spread in the research community and continually updated. The database is available at . Graphical abstract: [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]

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]

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]