Highly accurate quadrature-based Scharfetter--Gummel schemes for charge transport in degenerate semiconductors

We introduce a family of two point flux expressions for charge carrier transport described by drift-diffusion problems in degenerate semiconductors with non-Boltzmann statistics which can be used in Vorono"i finite volume discretizations. In the case of Boltzmann statistics, Scharfetter and Gummel derived such fluxes by solving a linear two point boundary value problem yielding a closed form expression for the flux. Instead, a generalization of this approach to the nonlinear case yields a flux value given implicitly as the solution of a nonlinear integral equation. We examine the solution of this integral equation numerically via quadrature rules to approximate the integral as well as Newton's method to solve the resulting approximate integral equation. This approach results into a family of quadrature-based Scharfetter-Gummel flux approximations. We focus on four quadrature rules and compare the resulting schemes with respect to execution time and accuracy. A convergence study reveals that the solution of the approximate integral equation converges exponentially in terms of the number of quadrature points. With very few integration nodes they are already more accurate than a state-of-the-art reference flux, especially in the challenging physical scenario of high nonlinear diffusion. Finally, we show that thermodynamic consistency is practically guaranteed

Comparison of thermodynamically consistent charge carrier flux discretizations for Fermi--Dirac and Gauss--Fermi statistics

We compare three thermodynamically consistent Scharfetter--Gummel schemes for different distribution functions for the carrier densities, including the Fermi--Dirac integral of order 1/2 and the Gauss--Fermi integral. The most accurate (but unfortunately also most costly) generalized Scharfetter--Gummel scheme requires the solution of an integral equation. We propose a new method to solve this integral equation numerically based on Gauss quadrature and Newton's method. We discuss the quality of this approximation and plot the resulting currents for Fermi--Dirac and Gauss--Fermi statistics. Finally, by comparing two modified (diffusion-enhanced and inverse activity based) Scharfetter--Gummel schemes with the more accurate generalized scheme, we show that the diffusion-enhanced ansatz leads to considerably lower flux errors, confirming previous results (J. Comp. Phys. 346:497-513, 2017)

Highly accurate quadrature-based Scharfetter-Gummel schemes for charge transport in degenerate semiconductors

We introduce a family of two point flux expressions for charge carrier transport described by drift-diffusion problems in degenerate semiconductors with non-Boltzmann statistics which can be used in Voronoi finite volume discretizations. In the case of Boltzmann statistics, Scharfetter and Gummel derived such fluxes by solving a linear two point boundary value problem yielding a closed form expression for the flux. Instead, a generalization of this approach to the nonlinear case yields a flux value given implicitly as the solution of a nonlinear integral equation. We examine the solution of this integral equation numerically via quadrature rules to approximate the integral as well as Newtons method to solve the resulting approximate integral equation. This approach results into a family of quadrature-based Scharfetter-Gummel flux approximations. We focus on four quadrature rules and compare the resulting schemes with respect to execution time and accuracy. A convergence study reveals that the solution of the approximate integral equation converges exponentially in terms of the number of quadrature points. With very few integration nodes they are already more accurate than a state-of-the-art reference flux, especially in the challenging physical scenario of high nonlinear diffusion. Finally, we show that thermodynamic consistency is practically guaranteed

Comparison of thermodynamically consistent charge carrier flux discretizations for Fermi-Dirac and Gauss-Fermi statistics

We compare three thermodynamically consistent ScharfetterGummel schemes for different distribution functions for the carrier densities, including the FermiDirac integral of order 1/2 and the GaussFermi integral. The most accurate (but unfortunately also most costly) generalized ScharfetterGummel scheme requires the solution of an integral equation. We propose a new method to solve this integral equation numerically based on Gauss quadrature and Newtons method. We discuss the quality of this approximation and plot the resulting currents for FermiDirac and GaussFermi statistics. Finally, by comparing two modified (diffusion-enhanced and inverse activity based) ScharfetterGummel schemes with the more accurate generalized scheme, we show that the diffusion-enhanced ansatz leads to considerably lower flux errors, confirming previous results (J. Comp. Phys. 346:497-513, 2017)

Exploring forest infrastructures equipment through multivariate analysis: complementarities, gaps and overlaps in the Mediterranean basin

The countries of the Mediterranean basin face several challenges regarding the sustainability of forest ecosystems and the delivery of crucial goods and services that they provide in a context of rapid global changes. Advancing scientific knowledge and foresting innovation is essential to ensure the sustainable management of Mediterranean forests and maximize the potential role of their unique goods and services in building a knowledge-based bioeconomy in the region. In this context, the European project FORESTERRA ("Enhancing FOrest RESearch in the MediTERRAnean through improved coordination and integration”) aims at reinforcing the scientific cooperation on Mediterranean forests through an ambitious transnational framework in order to reduce the existing research fragmentation and maximize the effectiveness of forest research activities. Within the FORESTERRA project framework, this work analyzed the infrastructures equipment of the Mediterranean countries belonging to the project Consortium. According to the European Commission, research infrastructures are facilities, resources and services that are used by the scientific communities to conduct research and foster innovation. To the best of our knowledge, the equipment and availability of infrastructures, in terms of experimental sites, research facilities and databases, have only rarely been explored. The aim of this paper was hence to identify complementarities, gaps and overlaps among the different forest research institutes in order to create a scientific network, optimize the resources and trigger collaborations

Breakdown of the mean-field approximation in a wealth distribution model

One of the key socioeconomic phenomena to explain is the distribution of wealth. Bouchaud and M\'ezard have proposed an interesting model of economy [Bouchaud and M\'ezard (2000)] based on trade and investments of agents. In the mean-field approximation, the model produces a stationary wealth distribution with a power-law tail. In this paper we examine characteristic time scales of the model and show that for any finite number of agents, the validity of the mean-field result is time-limited and the model in fact has no stationary wealth distribution. Further analysis suggests that for heterogeneous agents, the limitations are even stronger. We conclude with general implications of the presented results.Comment: 11 pages, 3 figure

Risk Factors and Outcomes of Infections by Multidrug-Resistant Gram-Negative Bacteria in Patients Undergoing Hematopoietic Stem Cell Transplantation

Abstract The objective of this study was to determine risk factors and outcomes of infections by multidrug-resistant gram-negative (MDR GN) bacteria in 241 recipients of hematopoietic stem cell transplantation (HSCT). The cumulative incidence of infections was 10.5% (95% CI, 12.0% to 25.8%), with 57% of infections occurring during the period of severe neutropenia (neutrophil count  6 /L). In multivariate analysis, allogeneic transplant and colonization with MDR GN bacteria at admission to the transplant unit were significantly associated with an increased risk of infection. Although we observed neither transplant-related mortality (TRM) nor deaths due to infections by MDR GN bacteria after autologous transplant, in the allogeneic setting a significant difference was reported in terms of overall survival (OS) and TRM between patients who developed infections and those who did not (1-year OS, 39% versus 68%; 1-year TRM, 42% versus 19%). In multivariate analysis, refractory disease and development of grades III to IV graft-versus-host disease (GVHD) were factors that affected both TRM and OS, whereas occurrence of infections by MDR GN pathogens significantly reduced OS. We conclude that eligibility to allogeneic HSCT in MDR GN bacteria carriers should be carefully evaluated together with all other factors that independently influence outcome (disease status, donor, and GVHD risk)

Immune checkpoint inhibitor therapy and outcomes from SARS-CoV-2 infection in patients with cancer: a joint analysis of OnCovid and ESMO-CoCARE registries

BackgroundAs management and prevention strategies against COVID-19 evolve, it is still uncertain whether prior exposure to immune checkpoint inhibitors (ICIs) affects COVID-19 severity in patients with cancer.MethodsIn a joint analysis of ICI recipients from OnCovid (NCT04393974) and European Society for Medical Oncology (ESMO) CoCARE registries, we assessed severity and mortality from SARS-CoV-2 in vaccinated and unvaccinated patients with cancer and explored whether prior immune-related adverse events (irAEs) influenced outcome from COVID-19.FindingsThe study population consisted of 240 patients diagnosed with COVID-19 between January 2020 and February 2022 exposed to ICI within 3 months prior to COVID-19 diagnosis, with a 30-day case fatality rate (CFR30) of 23.6% (95% CI 17.8 to 30.7%). Overall, 42 (17.5%) were fully vaccinated prior to COVID-19 and experienced decreased CFR30 (4.8% vs 28.1%, p=0.0009), hospitalization rate (27.5% vs 63.2%, p<0.0001), requirement of oxygen therapy (15.8% vs 41.5%, p=0.0030), COVID-19 complication rate (11.9% vs 34.6%, p=0.0040), with a reduced need for COVID-19-specific therapy (26.3% vs 57.9%, p=0.0004) compared with unvaccinated patients. Inverse probability of treatment weighting (IPTW)-fitted multivariable analysis, following a clustered-robust correction for the data source (OnCovid vs ESMO CoCARE), confirmed that vaccinated patients experienced a decreased risk of death at 30 days (adjusted OR, aOR 0.08, 95% CI 0.01 to 0.69).Overall, 38 patients (15.8%) experienced at least one irAE of any grade at any time prior to COVID-19, at a median time of 3.2 months (range 0.13-48.7) from COVID-19 diagnosis. IrAEs occurred independently of baseline characteristics except for primary tumor (p=0.0373) and were associated with a significantly decreased CFR30 (10.8% vs 26.0%, p=0.0462) additionally confirmed by the IPTW-fitted multivariable analysis (aOR 0.47, 95% CI 0.33 to 0.67). Patients who experienced irAEs also presented a higher median absolute lymphocyte count at COVID-19 (1.4 vs 0.8 10(9) cells/L, p=0.0098).ConclusionAnti-SARS-CoV-2 vaccination reduces morbidity and mortality from COVID-19 in ICI recipients. History of irAEs might identify patients with pre-existing protection from COVID-19, warranting further investigation of adaptive immune determinants of protection from SARS-CoV-2

Colloquium: Statistical mechanics of money, wealth, and income

This Colloquium reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since the late 1990s. By analogy with the Boltzmann-Gibbs distribution of energy in physics, it is shown that the probability distribution of money is exponential for certain classes of models with interacting economic agents. Alternative scenarios are also reviewed. Data analysis of the empirical distributions of wealth and income reveals a two-class distribution. The majority of the population belongs to the lower class, characterized by the exponential ("thermal") distribution, whereas a small fraction of the population in the upper class is characterized by the power-law ("superthermal") distribution. The lower part is very stable, stationary in time, whereas the upper part is highly dynamical and out of equilibrium.Comment: 24 pages, 13 figures; v.2 - minor stylistic changes and updates of references corresponding to the published versio