Dynamics of Conformal Maps for a Class of Non-Laplacian Growth Phenomena

Time-dependent conformal maps are used to model a class of growth phenomena limited by coupled non-Laplacian transport processes, such as nonlinear diffusion, advection, and electro-migration. Both continuous and stochastic dynamics are described by generalizing conformal-mapping techniques for viscous fingering and diffusion-limited aggregation, respectively. A general notion of time in stochastic growth is also introduced. The theory is applied to simulations of advection-diffusion-limited aggregation in a background potential flow. A universal crossover in morphology is observed from diffusion-limited to advection-limited fractal patterns with an associated crossover in the growth rate, controlled by a time-dependent effective Peclet number. Remarkably, the fractal dimension is not affected by advection, in spite of dramatic increases in anisotropy and growth rate, due to the persistence of diffusion limitation at small scales.Comment: 4 pages, 2 figures (six color plates

Quasi-Static Fractures in Disordered Media and Iterated Conformal Maps

We study the geometrical characteristic of quasi-static fractures in disordered media, using iterated conformal maps to determine the evolution of the fracture pattern. This method allows an efficient and accurate solution of the Lam\'e equations without resorting to lattice models. Typical fracture patterns exhibit increased ramification due to the increase of the stress at the tips. We find the roughness exponent of the experimentally relevant backbone of the fracture pattern; it crosses over from about 0.5 for small scales to about 0.75 for large scales, in excellent agreement with experiments. We propose that this cross-over reflects the increased ramification of the fracture pattern.Comment: submitted to Physical Review Letter

Quasi-Static Brittle Fracture in Inhomogeneous Media and Iterated Conformal Maps: Modes I, II and III

The method of iterated conformal maps is developed for quasi-static fracture of brittle materials, for all modes of fracture. Previous theory, that was relevant for mode III only, is extended here to mode I and II. The latter require solution of the bi-Laplace rather than the Laplace equation. For all cases we can consider quenched randomness in the brittle material itself, as well as randomness in the succession of fracture events. While mode III calls for the advance (in time) of one analytic function, mode I and II call for the advance of two analytic functions. This fundamental difference creates different stress distribution around the cracks. As a result the geometric characteristics of the cracks differ, putting mode III in a different class compared to modes I and II.Comment: submitted to PRE For a version with qualitatively better figures see: http://www.weizmann.ac.il/chemphys/ander

Recognition of COVID-19 with occupational origin: a comparison between European countries

Objectives This study aims to present an overview of the formal recognition of COVID-19 as occupational disease (OD) or injury (OI) across Europe. Methods A COVID-19 questionnaire was designed by a task group within COST-funded OMEGA-NET and sent to occupational health experts of 37 countries in WHO European region, with a last update in April 2022. Results The questionnaire was filled out by experts from 35 countries. There are large differences between national systems regarding the recognition of OD and OI: 40% of countries have a list system, 57% a mixed system and one country an open system. In most countries, COVID-19 can be recognised as an OD (57%). In four countries, COVID-19 can be recognised as OI (11%) and in seven countries as either OD or OI (20%). In two countries, there is no recognition possible to date. Thirty-two countries (91%) recognise COVID-19 as OD/OI among healthcare workers. Working in certain jobs is considered proof of occupational exposure in 25 countries, contact with a colleague with confirmed infection in 19 countries, and contact with clients with confirmed infection in 21 countries. In most countries (57%), a positive PCR test is considered proof of disease. The three most common compensation benefits for COVID-19 as OI/OD are disability pension, treatment and rehabilitation. Long COVID is included in 26 countries. Conclusions COVID-19 can be recognised as OD or OI in 94% of the European countries completing this survey, across different social security and embedded occupational health systems.This publication is based on work from COST Action CA16216 (OMEGA-NET), supported by COST (European Cooperation in Science and Technology)

The Average Shape of Transport-Limited Aggregates

We study the relation between stochastic and continuous transport-limited growth models, which generalize conformal-mapping formulations of diffusion-limited aggregation (DLA) and viscous fingering, respectively. We derive a nonlinear integro-differential equation for the asymptotic shape (average conformal map) of stochastic aggregates, whose mean-field approximation is the corresponding continuous equation, where the interface moves at its local expected velocity. Our equation accurately describes advection-diffusion-limited aggregation (ADLA), and, due to nonlinear averaging over fluctuations, the average ADLA cluster is similar, but not identical, to an exact solution of the mean-field dynamics. Similar results should apply to all models in our class, thus explaining the known discrepancies between average DLA clusters and viscous fingers in a channel geometry