539 research outputs found
Complex singularities and PDEs
In this paper we give a review on the computational methods used to
characterize the complex singularities developed by some relevant PDEs. We
begin by reviewing the singularity tracking method based on the analysis of the
Fourier spectrum. We then introduce other methods generally used to detect the
hidden singularities. In particular we show some applications of the Pad\'e
approximation, of the Kida method, and of Borel-Polya method. We apply these
techniques to the study of the singularity formation of some nonlinear
dispersive and dissipative one dimensional PDE of the 2D Prandtl equation, of
the 2D KP equation, and to Navier-Stokes equation for high Reynolds number
incompressible flows in the case of interaction with rigid boundaries
Route to chaos in the weakly stratified Kolmogorov flow
We consider a two-dimensional fluid exposed to Kolmogorovâs forcing cos(ny) and heated from above. The stabilizing effects of temperature are taken into account using the Boussinesq approximation. The fluid with no temperature stratification has been widely studied and, although relying on strong simplifications, it is considered an important tool for the theoretical and experimental study of transition to turbulence. In this paper, we are interested in the set of transitions leading the temperature stratified fluid from the laminar solution [Uâcos(ny),0, T â y] to more complex states until the onset of chaotic states. We will consider Reynolds numbers 0 < Re †30, while the Richardson numbers shall be kept in the regime of weak stratifications (Ri †5 Ă 10 â3 ). We shall first review the non-stratified Kolmogorov flow and find a new period-tripling bifurcation as the precursor of chaotic states. Introducing the stabilizing temperature gradient, we shall observe that higher Re are required to trigger instabilities. More importantly, we shall see new states and phenomena: the newly discovered period-tripling bifurcation is supercritical or subcritical according to Ri; more period-tripling and doubling bifurcations may depart from this new state; strong enough stratifications trigger new regions of chaotic solutions and, on the drifting solution branch, non-chaotic bursting solutions
Complex singularity analysis for vortex layer flows
We study the evolution of a 2D vortex layer at high Reynolds number. Vortex layer flows are characterized by intense vorticity concentrated around a curve. In addition to their intrinsic interest, vortex layers are relevant configurations because they are regularizations of vortex sheets. In this paper, we consider vortex layers whose thickness is proportional to the square-root of the viscosity. We investigate the typical roll-up process, showing that crucial phases in the initial flow evolution are the formation of stagnation points and recirculation regions. Stretching and folding characterizes the following stage of the dynamics, and we relate these events to the growth of the palinstrophy. The formation of an inner vorticity core, with vorticity intensity growing to infinity for larger Reynolds number, is the final phase of the dynamics. We display the inner core's self-similar structure, with the scale factor depending on the Reynolds number. We reveal the presence of complex singularities in the solutions of Navier-Stokes equations; these singularities approach the real axis with increasing Reynolds number. The comparison between these singularities and the Birkhoff-Rott singularity seems to suggest that vortex layers, in the limit, behave differently from vortex sheets
Analysis of complex singularities in high-Reynolds-number Navier-Stokes solutions
Numerical solutions of the laminar Prandtl boundary-layer and Navier-Stokes
equations are considered for the case of the two-dimensional uniform flow past
an impulsively-started circular cylinder. We show how Prandtl's solution
develops a finite time separation singularity. On the other hand Navier-Stokes
solution is characterized by the presence of two kinds of viscous-inviscid
interactions that can be detected by the analysis of the enstrophy and of the
pressure gradient on the wall. Moreover we apply the complex singularity
tracking method to Prandtl and Navier-Stokes solutions and analyze the previous
interactions from a different perspective
Multidisciplinary Approach to Fused Maxillary central Incisors: a Case Report
Introduction: The fusion of permanent teeth is a development anomaly of dental hard tissue. It may require a hard
multidisciplinary approach with orthodontics, endodontics, surgery and prosthetics to solve aesthetic and functional
problems.
Case presentation: A 20-year-old Caucasian man presented to our Department to solve a dental anomaly of his
upper central incisors. An oral investigation revealed the fusion of his maxillary central incisors and dyschromia of
right central incisor. Vitality pulp tests were negative for lateral upper incisors and left central incisor. Radiographic
examinations showed a fused tooth with two separate pulp chambers, two distinct roots and two separate root
canals. There were also periapical lesions of central incisors and right lateral incisor, so he underwent endodontic
treatment. Six months later, OPT examination revealed persistence of the periapical radiolucency, so endodontic
surgery was performed, which included exeresis of the lesion, an apicoectomy and retrograde obturation with a
reinforced zinc oxide-eugenol cement (SuperEBA) Complete healing of the lesion was obtained six months
postoperatively. Fused teeth crowns were separated and orthodontic appliances were put in place. When correct
teeth position was achieved (after nine months), the anterior teeth were prosthetically rehabilitated.
Conclusion: Many treatment options have been proposed in the literature to solve cases of dental fusion. The best
treatment plan depends on the nature of the anomaly, its location, the morphology of the pulp chamber
and root canal system, the subgingival extent of the separation line, and the patient compliance. Following
an analysis of radiographical and clinical data, it was possible to solve our patientâs dental anomaly with a
multidisciplinary approach
Cytokine-induced instabilities in a reactionâdiffusion-chemotaxis model of Multiple Sclerosis: Bifurcation analysis and well-posedness
In this paper, we develop a model for the evolution of the Multiple Sclerosis pathology that considers the modulatory influence of cytokines on the activation rate of macrophages. Our starting point is the reactionâdiffusion-chemotaxis model proposed in 4, and we modify the macrophage activation mechanism. What triggers the immune cells into an active state is still debated in the medical literature. In this paper, we explore the hypothesis, e.g., Lassmann, (2018), that cytokines mediate the activation mechanism. Our primary focus is on the rigorous analysis of instabilities responsible for the formation of demyelinating lesions and on the qualitative properties of the solution. Through a weakly nonlinear analysis, we characterize the chemotaxis-driven Turing instability and construct the stationary patterns that emerge from this instability. Using biologically relevant parameter values, we show that the asymptotic solutions of our model system reproduce the concentric demyelinating rings, confluent plaques, and preactive lesions observed in BaloÌ sclerosis and type III Multiple Sclerosis. Furthermore, we explore the initiation and progression of demyelinated plaques through extensive numerical simulations on two-dimensional domains. Our findings reveal that the alternative scenario proposed here results in a less aggressive pathology characterized by reduced inflammation levels and significantly slower disease progression. Under the appropriate regularity conditions on the initial data, we prove the existence of a unique global solution to our proposed system. This study provides insights into the role of cytokines in the pathogenesis of Multiple Sclerosis, shedding light on the disease's dynamics and offering potential avenues for therapeutic interventions
Ecopharmacology: Deliberated or casual dispersion of pharmaceutical principles, phytosanitary, personal health care and veterinary products in environment needs a multivariate analysis or expert systems for the control, the measure and the remediation
.The increasing human and animal use and abuse of drugs as well as of personalhealthcare and gross domestic products, involve disposal and waste problems and, as a consequence, affect the environmental condition. Actually most of the active principles are complex synthesised organic molecules that react, inside human or animal body, by specific biochemical reactions that in no case can reach a 100% yield and produce residues that could be more noxious of the starting compounds. Just reading the indication sheet accompanying any drugs, it is easy to state that no drug can be considered healthy, so, their use constitutes a serious pollution source. The full awareness of this relatively new environmental problem let many researchers to face it from different point of view. Current studies are considering the sources of these substances in the environment, the effects on human health as well as on the flora and fauna species, the recalcitrance and possible degradation methods, analytical techniques able to determine them and their metabolites even at low concentrations and in complex matrices. Literature on the subject continuously increases and a comparison of all data became more and more difficult both for a single drug and for different ones based on the same or different active principles. This is a typical case in which chemometrics can extract a full information in the easier way, so the design of a European database coupled to suitable expertsystem software should be strongly suggested
Platelet-rich plasma counteracts detrimental effect of high-glucose concentrations on mesenchymal stem cells from Bichat fat pad
Diabetic patients display increased risk of periodontitis and failure in bone augmentation procedures. Mesenchymal stem cells (MSCs) and platelet-rich plasma (PRP) represent a relevant advantage in tissue repair process and regenerative medicine. We isolated MSCs from Bichat's buccal fat pad (BFP) and measured the effects of glucose and PRP on cell number and osteogenic differentiation potential. Cells were cultured in the presence of 5.5-mM glucose (low glucose [LG]) or 25-mM glucose (high glucose [HG]). BFPâMSC number was significantly lower when cells were cultured in HG compared with those in LG. Following osteogenic differentiation procedures, calcium accumulation, alkaline phosphatase activity, and expression of osteogenic markers were significantly lower in HG compared with LG. Exposure of BFPâMSC to PRP significantly increased cell number and osteogenic differentiation potential, reaching comparable levels in LG and in HG. Thus, high-glucose concentrations impair BFPâMSC growth and osteogenic differentiation. However, these detrimental effects are largely counteracted by PRP
Provenance and sediment dispersal in the Po-Adriatic source-to-sink system unraveled by bulk-sediment geochemistry and its linkage to catchment geology
The Po-Adriatic region offers an excellent case for reconstructing sediment provenance and transport pathways of a multi-sourced sediment-routing system. Through a comprehensive set of ~1,400 geochemical data, a model for provenance and sediment flux was built based on distinct compositional fingerprints of 53 fluvial systems and their comparison to coastal, shelf and deep-marine sediments. Geochemically unique catchment lithologies (mafic/ultramafic rocks, limestones and dolostones) were used as end-members to assess exclusive source-rock signatures. Following calibration with sedimentary facies, selected key elements and element ratios poorly sensitive to particle size (Ni/Cr, MgO, Ni/Al2O3, Cr/V, Ca/Al2O3 and Ce/V) were adopted as provenance indicators. The high-Ni and high-Cr source-rock signature of mafic/ultramafic rocks widely exposed in the Po River watershed and along the Albanian Dinarides contrasts markedly with the high-Ca (and locally high-Mg) geochemical composition of Eastern Alpine, Apennine, and Eastern Adriatic (Montenegro, Croatia, Slovenia) river catchments, which are, instead, carbonate-rich and virtually ophiolite-free. Relatively high Ce values from Apulian river samples serve as a key marker for a minor, but very distinct sediment provenance from southern Apennine alkaline volcanic rocks.
Despite along-shore mixing and dilution with sediment sourced from other river catchments, the geochemical signature of Adriatic shelf muds primarily reflects composition of sediment eroded from the contiguous continental areas. Chromium-rich and nickel-rich detritus generated in mafic and ultramafic complexes of the Western Alps and conveyed through the Po River into the Adriatic Sea records a geochemical signal that can be traced downstream as long as 1000 km, from the Alpine zone of sediment production to the area of final deposition, offshore Apulia.
While longitudinal dispersion linked to the general cyclonic, counter-clockwise Adriatic circulation is prevailing along the Western Adriatic Sea, conspicuous detrital input from transversal pathways to the deep sea is revealed across the Eastern Adriatic shelf using heavy metals as provenance tracers. Estimates of fluvial sediment loads and compositional fingerprinting of fluvial, coastal and shelf sediments indicate that previously neglected ophiolite-rich successions of Albania represent a major sediment-conveyor to the offshore sinks (Southern Adriatic Deep and Mid-Adriatic Deep) through significant cross-shore and NNW-directed sediment transport in the Eastern Adriatic Sea. A cut-off value of the Ni/Cr ratio targeted around 0.8 represents an effective tool for the differentiation in marine sediments of Ni-rich (serpentine-rich) ophiolite detritus of Albanian origin from mafic/ultramafic sources of Alpine affinity. High trace-metal contents found within the Adriatic deep basin are mostly of natural origin and only minimally reflect metal contamination
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