Evolution of the distribution of wealth in an economic environment driven by local Nash equilibria

International audienceWe present and analyze a model for the evolution of the wealth distribution within a heterogeneous economic environment. The model considers a system of rational agents interacting in a game theoretical framework, through fairly general assumptions on the cost function. This evolution drives the dynamic of the agents in both wealth and economic configuration variables. We consider a regime of scale separation where the large scale dynamics is given by a hydrodynamic closure with a Nash equilibrium serving as the local thermodynamic equilibrium. The result is a system of gas dynamics-type equations for the density and average wealth of the agents on large scales. We recover the inverse gamma distribution as an equilibrium in the particular case of quadratic cost functions which has been previously considered in the literature

Экспериментальное исследование процессов зажигания плёнок жидких топлив локальным источником энергии.

Объект исследования – Мазут марки М-100 и зимнее дизельное топливо ДТ-З-К3-38. Источником нагрева в экспериментах являлась монолитная стальная частица в форме диска характерного размера диаметром (dp =6х10-3 м) и высотой (hp=3х10-3 м). Цель работы – экспериментальное исследование условий и характеристик зажигания при нагреве изменяющихся толщин пленок жидких топлив, а именно дизельного топлива и мазута М-100, металлическими локальными источниками характерных размеров. Личный вклад автора состоит в том, что была составлена методика проведения экспериментальных исследований, а также были проведены серии экспериментальных опытов с последующей обработкой экспериментальных данных и их обобщением. Проведены экспериментальные исследования по зажиганию пленок жидких топлив локальным источником энергии. Проведен анализ влияния толщины пленки и начальной температуры одиночной нагретой частицы. Область применения полученных экспериментальных данных возможна в создании фундаментальной теории зажигания локальными источниками энергии.The object of study – Mazut M-100 and diesel fuel DT-Z-K3-38. The source of heating in the experiments was a monolithic steel particle in the shape of a disk of typical size with a diameter (dp =6 × 10-3 m) and a height (hp=3x10-3 m). The aim of this work is the experimental study of the conditions and characteristics of ignition when heated, the changing of the thickness of films of liquid fuels, namely diesel fuel and fuel oil M-100, metal by local sources of characteristic sizes. Personal contribution of the author consists in the fact that was compiled by technique for experimental studies, and also conducted a series of pilot experiments with subsequent processing of the experimental data and their generalization. Experimental studies on the ignition films liquid fuels local energy source. The analysis of influence of film thickness and initial temperature of individual heated particles. The scope of experimental data is possible in the creation of fundamental theory of ignition by a local energy sources

Quantum Energy-Transport and Drift-Diffusion Models

We show that Quantum Energy-Transport and Quantum Drift-Diffusion models can be derived through diffusion limits of a collisional Wigner equation. The collision operator relaxes to an equilibrium defined through the entropy minimization principle. Both models are shown to be entropic and exhibit fluxes which are related with the state variables through spatially non-local relations. Thanks to an � expansion of these models, � 2 perturbations of the Classical Energy-Transport and Drift-Diffusion models are found. In the Drift-Diffusion case, the quantum correction is the Bohm potential and the model is still entropic. In the Energy-Transport case however, the quantum correction is a rather complex expression and the model cannot be proven entropic.

Smooth Quantum Hydrodynamic model vs. NEMO Simulation of Resonant Tunneling Diodes

The smooth quantum hydrodynamic model is an extension of the classical hydrodynamic model for semiconductor devices which can handle in a mathematically rigorous way the discontinuities in the classical potential energy which occur at heterojunction barriers in quantum semiconductor devices. Smooth QHD model simulations of the current-voltage curves of resonant tunneling diodes are presented which exhibit negative differential resistance—the experimental signal for quantum resonance effects—and are compared with the experimentally verified current-voltage curves predicted by the simulator NEMO, which uses a non-equilibrium Green function method