Global Solutions for Two-Phase Complex Fluids with Quadratic Anchoring in Soft Matter Physics

We study a diffuse interface model describing the complex rheology and the interfacial dynamics during phase separation in a polar liquid-crystalline emulsion. More precisely, the physical systems comprises a two-phase mixture consisting in a polar liquid crystal immersed in a Newtonian fluid. Such composite material is a paradigmatic example of complex fluids arising in Soft Matter which exhibits multiscale interplay. Beyond the Ginzburg-Landau and Frank elastic energies for the concentration and the polarization, the free energy of the system is characterized by a quadratic anchoring term which tunes the orientation of the polarization at the interface. This leads to several quasi-linear nonlinear couplings in the resulting system describing the macroscopic dynamics. In this work, we establish the first mathematical results concerning the global dynamics of two-phase complex fluids with interfacial anchoring mechanism. First, we determine a set of sufficient conditions on the parameters of the system and the initial conditions which guarantee the existence of global weak solutions in two and three dimensions. Secondly, we show that weak solutions are unique and globally regular in the two dimensional case. Finally, we complement our analysis with some numerical simulations to display polarization and interfacial anchoring.Comment: 52 pages, 5 figure

Historic city and urban regeneration: towards a new centrality of Italian historic centers

El proceso actual de metropolización tiende a la homologación y trivialización de los paisajes culturales e identitarios que caracterizan la ciudad contemporánea, dispersando un patrimonio común de valores y significados. Este proceso está asociado con fenómenos de marginación que afectan las partes de planta más antigua, para lo cual, como demuestran las investigaciones más recientes, en comparación con los años en que las reformas urbanas sancionaron la obligación de conservación preservándolos en manera emblemática, la situación ha cambiado profundamente. Hoy los centros históricos están amenazados por problemas nuevos y antiguos, de manera generalizada pero divergente (turístificación/despoblación, musealización/construcciones ilegales, gentrificación/abandono), que adquieren características específicas de acuerdo con los contextos físicos y socioeconómicos de referencia (metrópolis, áreas internas, etc.) y que, por lo tanto, requieren habilidades cognitivas, de planificación y financiamiento nuevas y más actuales. En este contexto, surge la necesidad de asignar una posición prioritaria a la ciudad histórica dentro de las estrategias de regeneración urbana, reinterpretando el patrimonio cultural como un bien común, integrando conservación e innovación, revitalización socioeconómica y valorización sociocultural, a través del refuerzo de la armadura de la ciudad pública para restaurar la calidad urbana y lograr nuevas formas de bienestar e inclusión social. El texto trata una reflexión sobre los instrumentos destinados a contrastar procesos de marginación social y económica que tienen lugar en estos contextos, apoyando la reflexión con la ilustración de experiencias nacionales (Taranto y Palermo) que encuentran convergencia en la experimentación de enfoques integrados y métodos de proyecto multinivel y multiactoriales.The current metropolization process tends towards the homologation and trivialization of the cultural and identity landscapes that characterize the contemporary city, dispersing a common heritage of values and meanings. This process is associated with the marginalization phenomena that also affect the parts of the oldest plant, for which, as evidenced by the most recent research and experimentations, compared to the years in which effective urban reforms sanctioned the obligation of conservation - preserving them in a way emblematic on the international scene - the situation has profoundly changed. The historic city and, in particular, the historic centers, in fact, are today threatened by new and old issues - in a generalized but often divergent way (tourism/depopulation, abusiveness/museumization, gentrification/abandonment) - which acquire specific characteristics according to the physical and socio-economic contexts of reference (metropolis, internal areas, territories of diffusion, etc.) and which therefore require new and more current cognitive, planning and financing skills. In this context, emerges the need to assign a priority position to the historic city within urban regeneration strategies, reinterpreting cultural heritage as a common good, integrating conservation and innovation, socio-economic revitalization and socio-cultural enhancement, through the reinforcement of the armature of the public city to restore urban quality and achieve new forms of well-being and social inclusion. The contribution addresses a reflection on the tools aimed at contrasting the processes of social, economic and spatial marginalization taking place in these contexts, supporting the reflection with the illustration of national experiences (including Taranto and Palermo) that find convergence in the experimentation of integrated approaches and multilevel and multiactorial methods of planning

The Aronson-Bénilan Estimate in Lebesgue Spaces

In a celebrated three-pages long paper in 1979, Aronson and Bénilan obtained a remarkable estimate on second order derivatives for the solution of the porous media equation. Since its publication, the theory of porous medium flow has expanded relentlessly with applications including thermodynamics, gas flow, ground water flow as well as ecological population dynamics. The purpose of this paper is to clarify the use of recent extensions of the Aronson and Bénilan estimate in L p spaces, of some modifications and improvements, as well as to show certain limitations of their strategy

Gingival overgrowth caused by Olmesartan Medoxomil: Observational study

Objective: Olmesartan Medoxomil is a type 1 receptor antagonist an antagonist of type 1 receptor (AT1) of angiotensin II (A-II) that inhibits numerous actions of A-II in the renin-angiotensin-aldosterone system (RAAS). A-II is a significant and multifunctional peptide involved in the pathophysiology of blood hypertension and for this reason it represents the main target in several classes of drugs used to treat and control arterial hypertension, such as angiotensin converting enzyme inhibitors (ACE-i), angiotensin receptor blockers (ARB) and renin direct inhibitors. The aim of the study is to evaluate whether the two drugs that have as an active principle Olmesartan Medoxomil, with and without the diuretic hydrochlorothiazide, are able to determine gingival overgrowth. Study Design: 108 subjects were examined and divided into three groups: G1, subjects treated with Olmesartan Medoxomil and hydrochlorothiazide (n=60); G2, subjects received only Olmesartan Medoxomil (n=24); G3, control group without pharmacological therapies (n=24). The plaque index (IP) and the gingival overgrowth index (OI) were recorded, considering the vertical and horizontal components. Results: Vertical overgrowth averaged between 0.17 \ub1 0.15 (G3) and 0.34 \ub1 0.26 (G2) showing statistically significant differences (p <0.05) compared to the other groups. Horizontal overgrowth ranged from 0.18 \ub1 0.26 (G3) to 0.49 \ub1 0.35 (G2) showing statistically significant differences (p <0.05). Conclusions: antihypertensive agents as Olmesartan Medoxomil may result in mild gingival overgrowth in the upper and lower frontal dental elements not related to other etiological factors

Volumetric analysis of gingival crevicular fluid and peri-implant sulcus fluid in healthy and diseased sites: A cross-sectional split-mouth pilot study

Background: Researchers have recently drawn attention to the analysis of gingival crevicular fluid (GCF) and peri-implant sulcus fluid (PISF) for the implementation of the diagnosis of periodontal and peri-implant disease. Nevertheless, the measurements of volume and biomarkers concentration can be critically biased when data collected from studies with parallel group design are compared, given the technical difficulties, methodological variables, as well as the variability of crevicular fluid characteristics among different individuals. Objective: The aim of the present study was to assess the GCF and PISF volumes in healthy and diseased sites belonging to the same patient. Method: Ten patients presenting a periodontally healthy tooth, a tooth with periodontitis, an implant with healthy peri-implant tissues and an implant with peri-implantitis were enrolled. Samples of GCF and PISF were collected from each site of interest and their volume measured with a Periotron 8000 device. Non-parametric statistical analysis was performed to test the significance of the differences in GCF and PISF volumes between i) sites of teeth and dental implants with the same condition of health or disease and ii) healthy and diseased sites of both teeth and dental implants subgroups. The correlation between probing pocket depth (PPD) and fluid production was also tested (p<0.05). Results: Healthy periodontal and peri-implant tissues produced comparable amounts of fluid that was significantly lower than in diseased sites (p<0.05). In the presence of diagnosed disease, the volumes of GCF and PISF were similar, too. The correlation between PPD and fluid production was significant only in healthy sites (PPD/GCF, \u3c1=0.890, p<0.001; PPD/PISF, \u3c1=0.810; p<0.005). Conclusion: The periodontal and peri-implant tissues behaved similarly in terms of fluid production in condition of both health and active disease