Sessile droplet with negative line tension

Abstract: We study the local stability of a sessile droplet with non-vanishing line tension along the contact line, where three phases are in equilibrium. We confirm Widom\u27s results (B. Widom, Line tension and the shape of a sessile drop. J. Chem. Phys. 99 (1995), 2803-2806.) on the local stability of a droplet with positive line tension in a larger class of perturbations. When the line tension is negative, although equilibria would be unstable against modes that make the contact line wigglier and wigglier, the length over which the oscillations of destabilizing modes are effective can become too short compared ti the natural cut-off length given by the ratio between the line and the surface tensions of the droplet. Thus, provided that the line tension strength is not too large, conditionally stable equilibria exist, even when the line tension is negative

Constant-angle surfaces in liquid crystals

We discuss some properties of surfaces in R3 whose unit normal has constant angle with an assigned direction field. The constant angle condition can be rewritten as an Hamilton-Jacobi equation correlating the surface and the direction field. We focus on examples motivated by the physics of interfaces in liquid crystals and of layered fluids, and discuss the properties of the constant-angle surfaces when the direction field is singular along a line (disclination) or at a point (hedgehog defect

Le acque sotterranee del Gargano: risorse idriche integrative e di emergenza

II presente lavoro intende caratterizzare ii rapporto tra alimentazione della falda idrica sotterranea del Gargano e ii prelievo dai pozzi, gli efflussi dalle sorgenti e l’esistenza di risorse idriche sotterranee ulteriormente utilizzabili. L’area, di circa 2.000 km2, è stata discretizzata in un reticolo a maglie quadrate di 4 km2, per ciascuna delle quali è stata stimata la litologia affiorante prevalente, la quota e la pendenza media. Caratterizzato nel dettaglio ii regime termopluviometrico vigente nel Gargano, si è proceduto, per ogni celia, al calcolo delle grandezze termopluviometriche e alla definizione del bilancio idrologico. Sono state raccolte tutte le informazioni disponibili relative alle portate sorgive e ai pozzi al fine di una stima, ad oggi possibile soltanto in difetto, degli efflussi sorgivi e degli emungimenti. Al fine di meglio quantificare le portate sorgive, è stato definito un bilancio idrologico semplificato del lago di Varano. Ii metodo utilizzato è stato positivamente validato su un piccolo acquifero campione del Gargano, l’acquifero carbonatico e superficiale di Vico-Ischitella. In termini medi, dei circa 37 m3/s di precipitazioni meteoriche si stima che non meno di 8,12 m3/s finiscano per alimentare l’unità idrogeologica del Gargano. Si è stimato che non meno di 3,4 m3/s alimentino sorgenti, pan al 42 % dell’infiltrazione, mentre almeno 0,53 m3/s, pan al 7%, viene prelevato dai pozzi. Ii 50 % dell’alimentazione del Gargano dà vita ad una risorsa idrica sotterranea ii cui recapito finale non è ad oggi noto. Trattasi di non meno di 4 m3/s che si versa- no a mare senza che si abbiano notizie certe sull’ubicazione e la reale portata, anche approssimata, di tali sorgenti. La notevole entità delle portate in gioco e la buona qualità delle acque sotterranee del Gargano impongono di considerare tale acquifero profondo come una fonte per l’utilizzazione razionale e sostenibile di risorse idriche integrative e di emergenza

Landau-De Gennes theory of nematic liquid\ud crystals: the Oseen-Frank limit and beyond

We study global minimizers of a continuum Landau-De Gennes energy functional for nematic liquid crystals, in three-dimensional domains, subject to uniaxial boundary conditions. We analyze the physically relevant limit of small elastic constant and show that global minimizers converge strongly, in W 1,2 , to a global minimizer predicted by the Oseen-Frank theory for uniaxial nematic liquid crystals with constant order parameter. Moreover, the convergence is uniform in the interior of the domain, away from the singularities of the limiting Oseen-Frank global minimizer. We obtain results on the rate of convergence of the eigenvalues and the regularity of the eigenvectors of the Landau-De Gennes global minimizer.\ud \ud \ud We also study the interplay between biaxiality and uniaxiality in Landau-De Gennes global energy minimizers and obtain estimates for various related quantities such as the biaxiality parameter and the size of admissible strongly biaxial regions

CARATTERI IDROGEOLOGICI DELLE SORGENTI CIRCOSTANTI IL LAGO DI LESINA (GARGANO)

Si studia il contributo alla Laguna di Lesina proveniente da tre principali sorgenti alimentate dal vasto acquifero carsico del Gargano. Con un approccio idrologico-statistico si determina l'estensione dell'area di alimentazione delle sorgenti

Parity Breaking in Nematic Tactoids

We theoretically investigate under what conditions the director field in a spindle-shaped nematic droplet or tactoid obtains a twisted, parity-broken structure. By minimizing the sum of the bulk elastic and surface energies, we show that a twisted director field is stable if the twist and bend elastic constants are small enough compared to the splay elastic constant, but only if the droplet volume is larger than some minimum value. We furthermore show that the transition from an untwisted to a twisted director-field structure is a sharp function of the various control parameters. We predict that suspensions of rigid, rod-like particles cannot support droplets with a parity broken structure, whereas they could possibly occur in those of semi-flexible, worm-like particles.Comment: 20 pages, 9 figures, submitted to Journal of Physics: Condensed Matte

Celery (Apium graveolens L.) Performances as Subjected to Different Sources of Protein Hydrolysates

The vegetable production sector is currently fronting several issues mainly connected to the increasing demand of high quality food produced in accordance with sustainable horticultural technologies. The application of biostimulants, particularly protein hydrolysates (PHs), might be favorable to optimize water and mineral uptake and plant utilization and to increase both production performance and quality feature of vegetable crops. The present study was carried out on celery plants grown in a tunnel to appraise the influence of two PHs, a plant-derived PH (P-PH), obtained from soy extract and an animal PH (A-PH), derived from hydrolyzed animal epithelium (waste from bovine tanneries) on yield, yield components (head height, root collar diameter, and number of stalks), mineral composition, nutritional and functional features, as well as the economic profitability of PHs applications. Fresh weight in A-PH and P-PH treated plants was 8.3% and 38.2% higher, respectively than in untreated control plants. However, no significant difference was found between A-PH treated plants and control plants in terms of fresh weight. Head height significantly increased by 5.5% and 16.3% in A-PH and P-PH treated plants, respectively compared with untreated control (p ≤ 0.05). N content was inferior in PHs treated plants than in untreated control. Conversely, K and Mg content was higher in A-PH and P-PH treated plants as compared to the untreated ones. Furthermore, A-PH and P-PH improved ascorbic acid content by 8.2% and 8.7%, respectively compared with the non-treated control (p ≤ 0.001). Our results confirmed, also, that PHs application is an eco-friendly technique to improve total phenolic content in celery plants. In support of this, our findings revealed that animal or plants PH applications increased total phenolics by 36.9% and 20.8%, respectively compared with untreated plants (p ≤ 0.001)