Rigorous derivation of the Kuramoto-Sivashinsky equation in a 2D weakly nonlinear Stefan problem

In this paper we are interested in a rigorous derivation of the Kuramoto-Sivashinsky equation (K--S) in a Free Boundary Problem. As a paradigm, we consider a two-dimensional Stefan problem in a strip, a simplified version of a solid-liquid interface model. Near the instability threshold, we introduce a small parameter $\varepsilon$ and define rescaled variables accordingly. At fixed $\varepsilon$, our method is based on: definition of a suitable linear 1D operator, projection with respect to the longitudinal coordinate only, Lyapunov-Schmidt method. As a solvability condition, we derive a self-consistent parabolic equation for the front. We prove that, starting from the same configuration, the latter remains close to the solution of K--S on a fixed time interval, uniformly in $\varepsilon$ sufficiently small

Modeling fungal hypha tip growth via viscous sheet approximation

In this paper we present a new model for single-celled, non-branching hypha tip growth. The growth mechanism of hypha cells consists of transport of cell wall building material to the cell wall and subsequent incorporation of this material in the wall as it arrives. To model the transport of cell wall building material to the cell wall we follow Bartnicki-Garcia et al in assuming that the cell wall building material is transported in straight lines by an isotropic point source. To model the dynamics of the cell wall, including its growth by new material, we use the approach of Campas and Mahadevan, which assumes that the cell wall is a thin viscous sheet sustained by a pressure difference. Furthermore, we include a novel equation which models the hardening of the cell wall as it ages. We present numerical results which give evidence that our model can describe tip growth, and briefly discuss validation aspects

Mechanophysiological study on the lateral line of the ruff

This thesis describes the results of a study on the lateral line of the ruff. The lateral line organ is an organ, found in aquatic amphibians and fishes, used to detect water motions. The elementary detection units are neurornasts: groups of hair cells (depending on the species and the location of the neuromast from about ten to about ten thousand) and supporting cells, covered by a translucent structure, the so-called cupula. The mechanotransduction - the conversion of a mechanical signal into an electrical one - takes place in the hair cells. Tilting of the "hairs" (cilia), caused by cupular motion, results in a change of the spike rate in the afferent nerve fibre, which has a synapse at the basal end of the hair cell. The cupula couples the surrounding fluid to the hair bundles. (zie Summary

Universality of cauliflower-like fronts: from nanoscale thin films to macroscopic plants

Chemical vapor deposition (CVD) is a widely used technique to grow solid materials with accurate control of layer thickness and composition. Under mass-transport-limited conditions, the surface of thin films thus produced grows in an unstable fashion, developing a typical motif that resembles the familiar surface of a cauliflower plant. Through experiments on CVD production of amorphous hydrogenated carbon films leading to cauliflower-like fronts, we provide a quantitative assessment of a continuum description of CVD interface growth. As a result, we identify non-locality, non-conservation and randomness as the main general mechanisms controlling the formation of these ubiquitous shapes.We also show that the surfaces of actual cauliflower plants and combustion fronts obey the same scaling laws, proving the validity of the theory over seven orders of magnitude in length scales. Thus, a theoretical justification is provided, which had remained elusive so far, for the remarkable similarity between the textures of surfaces found for systems that differ widely in physical nature and typical scales.Publicad

PICU mortality of children with cancer admitted to pediatric intensive care unit : a systematic review and meta-analysis

Background: Outcomes for children diagnosed with cancer have improved dramatically over the past 20 years. However, although 40% of pediatric cancer patients require at least one intensive care admission throughout their disease course, PICU outcomes and resource utilization by this population have not been rigorously studied in this specific group. Methods: Using a systematic strategy, we searched Medline, Embase, and CINAHL databases for articles describing PICU mortality of pediatric cancer patients admitted to PICU. Two investigators independently applied eligibility criteria, assessed data quality, and extracted data. We pooled PICU mortality estimates using random-effects models and examined mortality trends over time using meta-regression models. Results: Out of 1218 identified manuscripts, 31 studies were included covering 16,853 PICU admissions with the majority being retrospective in nature. Overall pooled weighted mortality was 27.8% (95% confidence interval (CI), 23.7-31.9%). Mortality decreased slightly over time when post-operative patients were excluded. The use of mechanical ventilation (odds ratio (OR): 18.49 [95% CI 13.79-24.78], p < 0.001), inotropic support (OR: 14.05 [95% CI 9.16-21.57], p < 0.001), or continuous renal replacement therapy (OR: 3.24 [95% CI 1.31-8.04], p = 0.01) was significantly associated with PICU mortality. Conclusions: PICU mortality rates of pediatric cancer patients are far higher when compared to current mortality rates of the general PICU population. PICU mortality has remained relatively unchanged over the past decades, a slight decrease was only seen when post-operative patients were excluded. This compared infavorably with the improved mortality seen in adults with cancer admitted to ICU, where research-led improvements have led to the paradigm of unlimited, aggressive ICU management without any limitations on resuscitations status, for a time-limited trial