Cross-diffusion driven instability in a predator-prey system with cross-diffusion

In this work we investigate the process of pattern formation induced by nonlinear diffusion in a reaction-diffusion system with Lotka-Volterra predator-prey kinetics. We show that the cross-diffusion term is responsible of the destabilizing mechanism that leads to the emergence of spatial patterns. Near marginal stability we perform a weakly nonlinear analysis to predict the amplitude and the form of the pattern, deriving the Stuart-Landau amplitude equations. Moreover, in a large portion of the subcritical zone, numerical simulations show the emergence of oscillating patterns, which cannot be predicted by the weakly nonlinear analysis. Finally when the pattern invades the domain as a travelling wavefront, we derive the Ginzburg-Landau amplitude equation which is able to describe the shape and the speed of the wave.Comment: 15 pages, 5 figure

Zero viscosity limit of the Oseen equations in a channel

Oseen equations in the channel are considered. We give an explicit solution formula in terms of the inverse heat operators and of projection operators. This solution formula is used for the analysis of the behavior of the Oseen equations in the zero viscosity limit. We prove that the solution of Oseen equations converges in W1,2 to the solution of the linearized Euler equations outside the boundary layer and to the solution of the linearized Prandtl equations inside the boundary layer. © 2001 Society for Industrial and Applied Mathematics

Well-posedness of the boundary layer equations

We consider the mild solutions of the Prandtl equations on the half space. Requiring analyticity only with respect to the tangential variable, we prove the short time existence and the uniqueness of the solution in the proper function space. The proof is achieved applying the abstract Cauchy-Kowalewski theorem to the boundary layer equations once the convection-diffusion operator is explicitly inverted. This improves the result of [M. Sammartino and R. E. Caflisch, Comm. Math. Phys., 192 (1998), pp. 433-461], as we do not require analyticity of the data with respect to the normal variable

Asymptotic analysis of the linearized Navier-Stokes equation on an exterior circular domain: Explicit solution and the zero viscosity limit

In this paper we study and derive explicit formulas for the linearized Navier-Stokes equations on an exterior circular domain in space dimension two. Through an explicit construction, the solution is decomposed into an inviscid solution, a boundary layer solution and a corrector. Bounds on these solutions are given, in the appropriate Sobolev spaces, in terms of the norms of the initial and boundary data. The correction term is shown to be of the same order of magnitude as the square root of the viscosity. Copyright © 2001 by Marcel Dekker, Inc

Cytoreduction and HIPEC in the treatment of "unconventional" secondary peritoneal carcinomatosis

BACKGROUND: Peritoneal metastasis (PM) is considered a terminal and incurable disease. In the last 30 years, cytoreductive surgery (CRS) and hyperthermic intraperitoneal chemotherapy (HIPEC) radically changed the therapeutic approach for these patients and is regarded as the standard of care for pseudomyxoma peritonei from appendiceal cancer and peritoneal mesotheliomas. Improved survival has also been reported in treating PM from ovarian, gastric, and colorectal cancers. However, PM often seriously complicates the clinical course of patients with other primary digestive and non-digestive cancers. There is increasing literature evidence that helped to identify not only the primary tumors for which CRS and HIPEC showed a survival advantage but also the patients who may benefit form this treatment modality for the potential lethal complications. Our goal is to report our experience with cytoreduction and HIPEC in patients with PM from rare or unusual primary tumors, discussing possible "unconventional" indications, outcome, and the peculiar issues related to each tumor. METHODS: From a series of 253 consecutive patients with a diagnosis of peritoneal carcinomatosis and treated by CRS and HIPEC, we selected only those with secondary peritoneal carcinomatosis from rare or unusual primary tumors, excluding pseudomyxoma peritonei, peritoneal mesotheliomas, ovarian, gastric, and colorectal cancers. Complications and adverse effects were graded from 0 to 5 according to the WHO Common Toxicity Criteria for Adverse Events (CTCAE). Survival was expressed as mean and median. RESULTS: We admitted and treated by CRS and HIPEC 28 patients with secondary peritoneal carcinomatosis from rare or unusual primary tumors. Morbidity and mortality rates were in line with those reported for similar procedures. Median survival for the study group was 56 months, and 5-year overall survival reached 40.3 %, with a difference between patients with no (CC0) and minimal (CC1) residual disease (52.3 vs. 25.7), not reaching statistical significance. Ten patients are alive disease-free, and eight are alive with disease. CONCLUSIONS: Cytoreduction and HIPEC should not be excluded "a priori" for the treatment of peritoneal metastases from unconventional primary tumors. This combined therapeutic approach, performed in an experienced center, is safe and can provide a survival benefit over conventional palliative treatments

Characterization of Rome’s rainwater in the early of 2018 aiming to find correlations between chemical-physical parameters and sources of pollution: a statistical study

Analysis of rainwater in historical cities plays a key role to save ancient monuments from atmospheric agents. In this study we sampled the Rome’s rainwater from February to July of 2018 and we analysed them to determine their chemical and physical parameters: pH, redox potential, conductivity, temperature, and the concentration of the main inorganic ions (Na+, K+, Ca++, Mg++, F−, Cl−, NO3−, SO4−−). The volume of the daily fallen rainwater, the speed and direction of the wind in the sampling site were also collected. In order to find a correlation between all the above data we used the Principal Component Analysis (PCA). Results evidenced that there aren’t authentic “acid rains” as the minimum pH value that we found is 5.2. In some cases high concentrations of nitrates and sulphates were found with maximum values of 12.4 ppm and 18.7 ppm respectively. We also found no correlation between the rainwater’s composition and the seasonal period; on the contrary, the speed and direction of the wind, especially when coming from the sea or industrial country near Rome, play a noticeable role on the rainwater composition. [Figure not available: see fulltext.] © 2020, The Author(s)

Wavefront invasion for a chemotaxis model of Multiple Sclerosis

In this work we study wavefront propagation for a chemotaxis reaction-diffusion system describing the demyelination in Multiple Sclerosis. Through a weakly non linear analysis, we obtain the Ginzburg–Landau equation governing the evolution of the amplitude of the pattern. We validate the analytical findings through numerical simulations. We show the existence of traveling wavefronts connecting two different steady solutions of the equations. The proposed model reproduces the progression of the disease as a wave: for values of the chemotactic parameter below threshold, the wave leaves behind a homogeneous plaque of apoptotic oligodendrocytes. For values of the chemotactic coefficient above threshold, the model reproduces the formation of propagating concentric rings of demyelinated zones, typical of Baló’s sclerosis