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

A community approach of pathogens and their arthropod vectors (ticks and fleas) in dogs of African Sub-Sahara

BACKGROUND : Arthropod-borne pathogens and their vectors are present throughout Africa. They have been wellstudied in livestock of sub-Saharan Africa, but poorly in companion animals. Given the socio-economic importance of companion animals, the African Small Companion Animal Network (AFSCAN), as part of the WSAVA Foundation, initiated a standardized multi-country surveillance study. METHODS : Macro-geographic variation in ectoparasite (ticks and fleas) and pathogen communities in dogs was assessed through molecular screening of approximately 100 infested dogs in each of six countries (Ghana, Kenya, Nigeria, Tanzania, Uganda and Namibia), both in rural and urban settings. The most important intrinsic and extrinsic risk factors within the subpopulation of infested dogs were evaluated. RESULTS : Despite the large macro-geographic variation in the dogs screened, there was no consistent difference between East and West Africa in terms of the diversity and numbers of ticks. The highest and lowest numbers of ticks were found in Nigeria and Namibia, respectively. Most often, there was a higher diversity of ticks in rural habitats than in urban habitats, although the highest diversity was observed in an urban Uganda setting. With the exception of Namibia, more fleas were collected in rural areas. We identified tick species (including Haemaphysalis spinulosa) as well as zoonotic pathogens (Coxiella burnetti, Trypanosoma spp.) that are not classically associated with companion animals. Rhipicephalus sanguineus was the most abundant tick, with a preference for urban areas. Exophilic ticks, such as Haemaphysalis spp., were more often found in rural areas. Several multi-host ticks occurred in urban areas. For R. sanguineus, housing conditions and additional pets were relevant factors in terms of infestation, while for a rural tick species (Haemaphysalis elliptica), free-roaming dogs were more often infested. Tick occurrence was associated to the use of endoparasiticide, but not to the use of ectoparasiticide. The most prevalent tick-borne pathogen was Hepatozoon canis followed by Ehrlichia canis. High levels of co-parasitism were observed in all countries and habitats. CONCLUSIONS : As dogs share a common environment with people, they have the potential to extend the network of pathogen transmission to humans. Our study will help epidemiologists to provide recommendations for surveillance and prevention of pathogens in dogs and humans.Additional file 1: Fig. S1. Overview of sampling times and average seasonal variation in precipitation and temperature. Table S1. Distribution of PCR signals allocated to an ectoparasite taxon (identification at genus level and more precise) in the infested dogs of urban and rural areas. Table S2. Distribution of co-infested dogs within the subpopulation of tick-infested dogs. Table S3. Co-infestations by different flea species (identification at genus level and lower). Table S4. Co-infections in dog blood. Table S5. Co-infections in dog ticks. Table S6. Co-infections in dog fleas. Table S7. Correlations with sero-prevalences. Table S8. Correlations with flea-borne pathogens.Additional file 2. Capture form.The Marie Sklodowska-Curie Actions, Bayer Animal Health GmbH, an Elanco Animal Health company, within the framework of the African Small Companion Animal Network (AFSCAN) program of the World Small Animal Veterinary Association (WASAVA) and supported by Idexx Laboratories and Clinvet International (Pty) Ltd.http://www.parasitesandvectors.comam2022Veterinary Tropical Disease

Increased GABAB receptor signaling in a rat model for schizophrenia

Contains fulltext : 167879.pdf (publisher's version ) (Open Access)Schizophrenia is a complex disorder that affects cognitive function and has been linked, both in patients and animal models, to dysfunction of the GABAergic system. However, the pathophysiological consequences of this dysfunction are not well understood. Here, we examined the GABAergic system in an animal model displaying schizophrenia-relevant features, the apomorphine-susceptible (APO-SUS) rat and its phenotypic counterpart, the apomorphine-unsusceptible (APO-UNSUS) rat at postnatal day 20-22. We found changes in the expression of the GABA-synthesizing enzyme GAD67 specifically in the prelimbic- but not the infralimbic region of the medial prefrontal cortex (mPFC), indicative of reduced inhibitory function in this region in APO-SUS rats. While we did not observe changes in basal synaptic transmission onto LII/III pyramidal cells in the mPFC of APO-SUS compared to APO-UNSUS rats, we report reduced paired-pulse ratios at longer inter-stimulus intervals. The GABAB receptor antagonist CGP 55845 abolished this reduction, indicating that the decreased paired-pulse ratio was caused by increased GABAB signaling. Consistently, we find an increased expression of the GABAB1 receptor subunit in APO-SUS rats. Our data provide physiological evidence for increased presynaptic GABAB signaling in the mPFC of APO-SUS rats, further supporting an important role for the GABAergic system in the pathophysiology of schizophrenia

Mathematical models for flame balls

Cette thèse est consacrée à l'étude de modèles mathématiques décrivant l'évolution de flammes en boules en présence d'un champ radiatif. Ces flammes ne sont observables qu'en microgravité et à faible nombre de Lewis. Les inconnues sont la température, la fraction massique du carburant et le rayon de la flamme sphérique. Le but de notre travail a été de modéliser le phénomène physique sous la forme d'un problème à frontière libre couplé à l'équation d'Eddington, puis d'étudier la stabilité des solutions au voisinage des états stationnaires, dont l'éxistence est prouvée en premier lieu. Danc ce but, nous linéarisons le problème à frontière libre, puis construisons une fonction d'Evans qui est analytique et dont les zéros sont les valeurs propres de l'opérateur linéarisé. Nous démontrons également des résultats d'instabilité en faisant appel à la théorie des problèmes paraboliques abstraits totalement non linéaires. Enfin on établit et analyse un modèle intégro-différentiel décrivant la dynamique en temps long du rayon de la flamme.BORDEAUX1-BU Sciences-Talence (335222101) / SudocSudocFranceNetherlandsFRN

Stability of the travelling wave in a 2D weakly nonlinear Stefan problem

We investigate the stability of the travelling wave (TW) solution in a 2D Stefan problem, a simplified version of a solid-liquid interface model. It is intended as a paradigm problem to present our method based on: (i) definition of a suitable linear one dimensional operator, (ii) projection with respect to the $x$ coordinate only; (iii) Lyapunov-Schmidt method. The main issue is that we are able to derive a parabolic equation for the corrugated front $\varphi$ near the TW as a solvability condition. This equation involves two linear pseudo-differential operators, one acting on $\varphi$, the other on $(\varphi_y)^2$ and clearly appears as a generalization of the Kuramoto-Sivashinsky equation related to turbulence phenomena in chemistry and combustion. A large part of the paper is devoted to study the properties of these operators in the context of functional spaces in the $y$ and $x,y$ coordinates with periodic boundary conditions. Technical results are deferred to the appendices

A General Approach to Stability in Free Boundary Problems

Every solution of a linear elliptic equation on a bounded domain may be considered as an equilibrium of a free boundary problem. The free boundary problem consists of the corresponding parabolic equation on a variable unknown domain with free boundary conditions prescribing both Dirichlet and Neumann data. We establish a rigorous stability analysis of such equilibria, including the construction of stable and unstable manifolds. For this purpose we transform the free boundary problem to a fully nonlinear and nonlocal parabolic problem on a fixed domain with fully nonlinear lateral boundary conditions and we develop the general theory for such problems. As an illustration we give two examples, the second being the focussing flame problem in combustion theory. AMS Subject Classification. 35K55, 35K65, 80A25. Key Words and Phrases. Free boundary problems, focussing selfsimilar solutions, linearisation, analytic semigroups, fully nonlinear equations, stable and unstable manifolds, saddle ..