Turbulence Enhancement of Coagulating Processes

We present and investigate the collision-coalescence process of particles in the presence of a fluid velocity field, examining the relationship between flow properties and enhanced coagulation. Our research focuses on two main aspects. Firstly, we propose a novel modeling approach for turbulent fluid at small scales, employing a Gaussian random field with non-trivial spatial covariance. Secondly, we derive rigorous partial differential equations (PDEs) and stochastic partial differential equations (SPDEs) from this model, capturing the physical characteristics of particles suspended in the fluid. From an Eulerian perspective, we analyze a kinetic particle system subjected to environmental transport noise. Specifically, we rigorously study a modified version of Smoluchowski’s coagulation equation, which incorporates velocity dependence akin to the Boltzmann equation. By utilizing techniques rooted in unbounded elliptic semigroup theory and weighted Sobolev space inequalities, we establish the existence and uniqueness of classical solutions for the case of a spatially homogeneous initial distribution. Moreover, from a Lagrangian viewpoint, we employ this particle system to gain insights into the collision rate at a steady state for particles uniformly distributed within a medium. Considering a particle-fluid model, we perform two scaling limits. The first limit, involving the number of particles, yields a stochastic Smoluchowski-type system, with the turbulent velocity field still governed by a noise stochastic process. The second scaling limit pertains to the parameters of the noise, specifically targeting the direction associated with small-scale turbulence. This limit leads to a deterministic equation with eddy dissipation in the velocity variable. We conduct numerical simulations of this equation system and demonstrate the influence of turbulence on rain formation. Our qualitative findings reveal a steady increase in coagulation efficiency with escalating turbulent kinetic energy of the fluid. Additionally, we observe a power-law decay over time and in relation to the turbulence parameter. Furthermore, we recover fundamental laws governing the collision rate and relative velocity of moving particles in the high Stokes number regime

Tax progressivity and self-employment dynamics

Analysis of the relationship between taxes and self-employment should acccount for the interplay between responses in self-employment and wage employment. To this end, we estimate a two-state multi-spell duration model which accounts for both observed and unobserved heterogeneity using a large longitudinal administrative dataset for Norway for 1993-2011. Our findings confirm theoretical predictions, and are robust to various changes to denitions and sample selections. A policy experiment simulating a flatter tax schedule in the year 2000, is found to encourage both entry into and exit from self-employment, with an increase of about 11.5 percent in net in ow into self-employment

Tax progressivity and self-employment dynamics

Analysis of the relationship between taxes and self-employment should account for the interplay between responses in self-employment and wage employment. We estimate a two-state multi-spell duration model which accounts for both observed and unobserved heterogeneity using a large longitudinal administrative dataset for Norway for 1993-2011. Our findings conform to theoretical predictions, and are robust to various changes to definitions and sample selections. A policy experiment simulating a flatter tax schedule in the year 2000,is found to encourage both entry into and exit from self-employment, with an increase of about 11.5 percent in net inflow into self-employment

Effect of Transport Noise on Kelvin-Helmholtz instability

The effect of transport noise on a 2D fluid may depend on the space-scale of the noise. We investigate numerically the dissipation properties of very small-scale transport noise. As a test problem we consider the Kelvin-Helmholtz instability and we compare the inviscid case, the viscous one, both without noise, and the inviscid case perturbed by transport noise. We observe a partial similarity with the viscous case, namely a delay of the instability.Comment: 22 pages, 22 figure

Turbulence enhancement of coagulation: the role of eddy diffusion in velocity

A Smoluchowski type model of coagulation in a turbulent fluid is given, first expressed by means of a stochastic model, then in a suitable scaling limit as a deterministic model with enhanced diffusion in the velocity component. A precise link between mean intensity of the turbulent velocity field and coagulation enhancement is obtained by numerical simulations.Comment: 8 pages, double column, 4 figures. Added appendix, more details on presented methods, added notations and kernel

Airborne Wind Energy Systems: A review of the technologies

Among novel technologies for producing electricity from renewable resources, a new class of wind energy converters has been conceived under the name of Airborne Wind Energy Systems (AWESs). This new generation of systems employs flying tethered wings or aircraft in order to reach winds blowing at atmosphere layers that are inaccessible by traditional wind turbines. Research on AWESs started in the mid seventies, with a rapid acceleration in the last decade. A number of systems based on radically different concepts have been analyzed and tested. Several prototypes have been developed all over the world and the results from early experiments are becoming available. This paper provides a review of the different technologies that have been conceived to harvest the energy of high-altitude winds, specifically including prototypes developed by universities and companies. A classification of such systems is proposed on the basis of their general layout and architecture. The focus is set on the hardware architecture of systems that have been demonstrated and tested in real scenarios. Promising solutions that are likely to be implemented in the close future are also considered

Epidemic Models as Scaling Limits of Individual Dynamics

Infection spread among individuals is modelled with a continuous time Markov chain, in which subject interactions depend on their distance in space. The well known SIR model and non local variants of the latter are then obtained as large scale limits of the individual based model in two different scaling regimes of the interaction.Comment: 22 page

The future of taxation in changing labour markets

This paper provides a first assessment of the fiscal and distributional consequences of the ongoing structural changes in the labour markets of EU member states, mostly driven by technological progress and ageing. The Cedefop 2020 Skills forecast (including the effects of COVID-19), population projections and the forecast on pension expenditures depict a scenario of an ageing population, an inverted U-shaped unemployment trend and potentially polarising labour markets in the EU till 2030, the latter mostly driven by a surge in high-skill occupations. We make use of the microsimulation model EUROMOD and reweighting techniques to analyse the fiscal and distributional impacts of these trends under a no-policy-change assumption. The results suggest that the macro trends will increase pressure on government budgets, however, we also show that the current tax-benefit systems have the capacity to counterbalance the increases in income inequality and poverty risks triggered by the expected future labour markets developments