Self-similar solutions for a fractional thin film equation governing hydraulic fractures

In this paper, self-similar solutions for a fractional thin film equation governing hydraulic fractures are constructed. One of the boundary conditions, which accounts for the energy required to break the rock, involves the toughness coefficient $K\geq 0$. Mathematically, this condition plays the same role as the contact angle condition in the thin film equation. We consider two situations: The zero toughness ($K=0$) and the finite toughness $K\in(0,\infty)$ cases. In the first case, we prove the existence of self-similar solutions with constant mass. In the second case, we prove that for all K\textgreater{}0 there exists an injection rate for the fluid such that self-similar solutions exist

Electrified thin films: Global existence of non-negative solutions

To appear in Annales de l'IHP, analyse non-linéaire. Minor modifications after reading proofs.International audienceWe consider an equation modeling the evolution of a viscous liquid thin film wetting a horizontal solid substrate destabilized by an electric field normal to the substrate. The effects of the electric field are modeled by a lower order non-local term. We introduce the good functional analysis framework to study this equation on a bounded domain and prove the existence of weak solutions defined globally in time for general initial data (with finite energy)

Détection de la FI de signaux à variations de phase sinusoïdales et faible indice de modulation par une technique basée sur le principe du maximum de vraisemblance : Application à la mesure de la vitesse particulaire acoustique

- La mesure de la vitesse particulaire acoustique par vélocimétrie laser à effet doppler (VLD) nécessite une démodulation de signaux à variation de fréquence sinusoïdale. La gamme d'amplitude et de fréquence étant étendue en acoustique, l'indice de modulation des signaux recueillis peut atteindre des valeurs faibles. Cette étude présente la comparaison de 2 méthodes basées sur le principe du maximum de vraisemblance pour estimer la FI de signaux dont l'indice de modulation est de l'ordre de 10-2. L'influence des paramètres de chaque méthode sur la précision d'estimation est mis en évidence

The neural correlates of highly iconic structures and topographic discourse in French Sign Language as observed in six hearing native signers

International audience"Highly iconic" structures in Sign Language enable a narrator to act, switch characters, describe objects, or report actions in four-dimensions. This group of linguistic structures has no real spoken-language equivalent. Topographical descriptions are also achieved in a sign-language specific manner via the use of signing-space and spatial-classifier signs. We used functional magnetic resonance imaging (fMRI) to compare the neural correlates of topographic discourse and highly iconic structures in French Sign Language (LSF) in six hearing native signers, children of deaf adults (CODAs), and six LSF-naïve monolinguals. LSF materials consisted of videos of a lecture excerpt signed without spatially organized discourse or highly iconic structures (Lect LSF), a tale signed using highly iconic structures (Tale LSF), and a topographical description using a diagrammatic format and spatial-classifier signs (Topo LSF). We also presented texts in spoken French (Lect French, Tale French, Topo French) to all participants. With both languages, the Topo texts activated several different regions that are involved in mental navigation and spatial working memory. No specific correlate of LSF spatial discourse was evidenced. The same regions were more activated during Tale LSF than Lect LSF in CODAs, but not in monolinguals, in line with the presence of signing-space structure in both conditions. Motion processing areas and parts of the fusiform gyrus and precuneus were more active during Tale LSF in CODAs; no such effect was observed with French or in LSF-naïve monolinguals. These effects may be associated with perspective-taking and acting during personal transfers

A common neural system is activated in hearing non-signers to process French Sign language and spoken French

International audienceWe used functional magnetic resonance imaging to investigate the areas activated by signed narratives in non-signing subjects naïve to sign language (SL) and compared it to the activation obtained when hearing speech in their mother tongue. A subset of left hemisphere (LH) language areas activated when participants watched an audiovisual narrative in their mother tongue was activated when they observed a signed narrative. The inferior frontal (IFG) and precentral (Prec) gyri, the posterior parts of the planum temporale (pPT) and of the superior temporal sulcus (pSTS), and the occipito-temporal junction (OTJ) were activated by both languages. The activity of these regions was not related to the presence of communicative intent because no such changes were observed when the non-signers watched a muted video of a spoken narrative. Recruitment was also not triggered by the linguistic structure of SL, because the areas, except pPT, were not activated when subjects listened to an unknown spoken language. The comparison of brain reactivity for spoken and sign languages shows that SL has a special status in the brain compared to speech; in contrast to unknown oral language, the neural correlates of SL overlap LH speech comprehension areas in non-signers. These results support the idea that strong relationships exist between areas involved in human action observation and language, suggesting that the observation of hand gestures have shaped the lexico-semantic language areas as proposed by the motor theory of speech. As a whole, the present results support the theory of a gestural origin of language