20 research outputs found
Weak and strong solutions of equations of compressible magnetohydrodynamics
International audienceThis article proposes a review of the analysis of the system of magnetohydrodynamics (MHD). First, we give an account of the modelling asumptions. Then, the results of existence of weak solutions, using the notion of renormalized solutions. Then, existence of strong solutions in the neighbourhood of equilibrium states is reviewed, in particular with the method of Kawashima and Shizuta. Finally, the special case of dimension one is highlighted : the use of Lagrangian coordinates gives a simpler system, which is solved by standard techniques
Multilevel Selection in Models of Prebiotic Evolution II: A Direct Comparison of Compartmentalization and Spatial Self-Organization
Multilevel selection has been indicated as an essential factor for the evolution of complexity in interacting RNA-like replicator systems. There are two types of multilevel selection mechanisms: implicit and explicit. For implicit multilevel selection, spatial self-organization of replicator populations has been suggested, which leads to higher level selection among emergent mesoscopic spatial patterns (traveling waves). For explicit multilevel selection, compartmentalization of replicators by vesicles has been suggested, which leads to higher level evolutionary dynamics among explicitly imposed mesoscopic entities (protocells). Historically, these mechanisms have been given separate consideration for the interests on its own. Here, we make a direct comparison between spatial self-organization and compartmentalization in simulated RNA-like replicator systems. Firstly, we show that both mechanisms achieve the macroscopic stability of a replicator system through the evolutionary dynamics on mesoscopic entities that counteract that of microscopic entities. Secondly, we show that a striking difference exists between the two mechanisms regarding their possible influence on the long-term evolutionary dynamics, which happens under an emergent trade-off situation arising from the multilevel selection. The difference is explained in terms of the difference in the stability between self-organized mesoscopic entities and externally imposed mesoscopic entities. Thirdly, we show that a sharp transition happens in the long-term evolutionary dynamics of the compartmentalized system as a function of replicator mutation rate. Fourthly, the results imply that spatial self-organization can allow the evolution of stable folding in parasitic replicators without any specific functionality in the folding itself. Finally, the results are discussed in relation to the experimental synthesis of chemical Darwinian systems and to the multilevel selection theory of evolutionary biology in general. To conclude, novel evolutionary directions can emerge through interactions between the evolutionary dynamics on multiple levels of organization. Different multilevel selection mechanisms can produce a difference in the long-term evolutionary trend of identical microscopic entities
A new sediment contact assay to assess particle-bound pollutants using zebrafish (danio rerio) embryos
Dynamics of a Laterally Evolving Community of Ribozyme-Like Agents as Studied with a Rule-Based Computing System
Discrete and continuum models for the evolutionary and spatial dynamics of cancer:a very short introduction through two case studies
We give a very short introduction to discrete and continuum models for the
evolutionary and spatial dynamics of cancer through two case studies: a model
for the evolutionary dynamics of cancer cells under cytotoxic therapy and a
model for the mechanical interaction between healthy and cancer cells during
tumour growth. First we develop the discrete models, whereby the dynamics of
single cells are described through a set of rules that result in branching
random walks. Then we present the corresponding continuum models, which are
formulated in terms of non-local and nonlinear partial differential equations,
and we summarise the key properties of their solutions. Finally, we carry out
numerical simulations of the discrete models and we construct numerical
solutions of the corresponding continuum models. The biological implications of
the results obtained are briefly discussed.Comment: 21 pages, 5 figures, BIOMAT2019 (19th International Symposium on
Mathematical and Computational Biology