Turing pattern formation in the Brusselator system with nonlinear diffusion

In this work we investigate the effect of density dependent nonlinear diffusion on pattern formation in the Brusselator system. Through linear stability analysis of the basic solution we determine the Turing and the oscillatory instability boundaries. A comparison with the classical linear diffusion shows how nonlinear diffusion favors the occurrence of Turing pattern formation. We study the process of pattern formation both in 1D and 2D spatial domains. Through a weakly nonlinear multiple scales analysis we derive the equations for the amplitude of the stationary patterns. The analysis of the amplitude equations shows the occurrence of a number of different phenomena, including stable supercritical and subcritical Turing patterns with multiple branches of stable solutions leading to hysteresis. Moreover we consider traveling patterning waves: when the domain size is large, the pattern forms sequentially and traveling wavefronts are the precursors to patterning. We derive the Ginzburg-Landau equation and describe the traveling front enveloping a pattern which invades the domain. We show the emergence of radially symmetric target patterns, and through a matching procedure we construct the outer amplitude equation and the inner core solution.Comment: Physical Review E, 201

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

On the stability and convergence of a semi-discrete discontinuous Galerkin scheme to the kinetic Cucker–Smale model

We study analytical properties of a semi-discrete discontinuous Galerkin (DG) scheme for the kinetic Cucker–Smale (CS) equation. The kinetic CS equation appears in the mean-field limit of the particle CS model and it corresponds to the dissipative Vlasov type equation approximating the large particle CS system. For this proposed DG scheme, we show that it exhibits analytical properties such as the conservation of mass, L2 -stability and convergence to the sufficiently regular solution, as the mesh-size tends to zero. In particular, we verify that the convergence rate of the DG numerical solution to the sufficiently regular kinetic solution is dependent on the Sobolev regularity of the kinetic soluiton. We also present several numerical simulations for low-dimensional cases

Route to chaos in the weakly stratified Kolmogorov flow

We consider a two-dimensional fluid exposed to Kolmogorov’s 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 [U∝cos(ny),0, T ∝ 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 × 10 −3 ). 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

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

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

COMPORTAMENTO AD ALTA PRESSIONE DI TRASDUTTORI PIEZOELETTRICI PER APPLICAZIONI DI GEOFISICA SPERIMENTALE

L’investigazione del comportamento acustico di campioni di roccia implica l’uso di trasduttori piezoelettrici [Spinelli et al., 2009], sia in uso attivo (eccitazione e rilevazione) che passivo (rilevazione delle onde elastiche generate da fenomeni di fratturazione). In alcuni casi vengono imposte elevate pressioni per simulare le condizioni di sconfinamento del campione di roccia in profondità, utilizzando un liquido o un gas. La natura dei trasduttori piezoelettrici suggerisce che essi non debbano soffrire molto in ambienti in cui la variazioni di pressione o la pressione di esercizio sia un elemento non trascurabile e possono essere utilizzati in tali condizioni senza particolari precauzioni con evidenti vantaggi nella semplificazione del set-up sperimentale. Questa nota è la descrizione delle misure condotte per caratterizzare dei trasduttori piezoelettrici, nell’intervallo di pressione di interesse (0 - 1000 atm), da utilizzare per scopi sperimentali nell’ambito del progetto europeo ERC Starting Grant Project GLASS InteGrated Laboratories to investigate the mechanics of ASeismic vs. Seismic faulting. Per fare ciò due trasduttori sono stati incollati direttamente tra loro in modo da realizzare un quadripolo, con una porta d’ingresso e una di uscita, e ne è stata rilevata la caratteristica ingresso – uscita al variare della frequenza. Per il rilevamento delle caratteristiche elettriche sono stati usati differenti strumenti di misura: un generatore di segnali, un oscilloscopio e un analizzatore di reti vettoriale. Per imporre sui campioni una pressione controllata è stato allestito un apparato meccanico dedicato, formato da un insieme pistone-cilindro all’interno del quale viene alloggiata la coppia di trasduttori incollati. Nel cilindro viene inserito olio (adeguatamente incomprimibile ed elettricamente isolante) come vettore di pressione; la spinta sul pistone viene esercitata attraverso una pressa idraulica. Una particolare cura è stata posta nella costruzione del passacavo a tenuta per alte pressioni. Nei paragrafi che seguono verranno dapprima descritti i trasduttori usati per gli esperimenti e l’apparato meccanico, quindi si passerà alla presentazione delle misure effettuate in varie condizioni e con i vari strumenti

Usefulness of regional right ventricular and right atrial strain for prediction of early and late right ventricular failure following a left ventricular assist device implant: A machine learning approach

Background: Identifying candidates for left ventricular assist device surgery at risk of right ventricular failure remains difficult. The aim was to identify the most accurate predictors of right ventricular failure among clinical, biological, and imaging markers, assessed by agreement of different supervised machine learning algorithms. Methods: Seventy-four patients, referred to HeartWare left ventricular assist device since 2010 in two Italian centers, were recruited. Biomarkers, right ventricular standard, and strain echocardiography, as well as cath-lab measures, were compared among patients who did not develop right ventricular failure (N = 56), those with acute–right ventricular failure (N = 8, 11%) or chronic–right ventricular failure (N = 10, 14%). Logistic regression, penalized logistic regression, linear support vector machines, and naïve Bayes algorithms with leave-one-out validation were used to evaluate the efficiency of any combination of three collected variables in an “all-subsets” approach. Results: Michigan risk score combined with central venous pressure assessed invasively and apical longitudinal systolic strain of the right ventricular–free wall were the most significant predictors of acute–right ventricular failure (maximum receiver operating characteristic–area under the curve = 0.95, 95% confidence interval = 0.91–1.00, by the naïve Bayes), while the right ventricular–free wall systolic strain of the middle segment, right atrial strain (QRS-synced), and tricuspid annular plane systolic excursion were the most significant predictors of Chronic-RVF (receiver operating characteristic–area under the curve = 0.97, 95% confidence interval = 0.91–1.00, according to naïve Bayes). Conclusion: Apical right ventricular strain as well as right atrial strain provides complementary information, both critical to predict acute–right ventricular failure and chronic–right ventricular failure, respectively

The New AIS-INGV Ionosonde at Italian Antarctic Observatory

The Italian Ionospheric Antarctic Observatory of Terra Nova Bay (74.70S, 164.11E) was recently equipped with the AIS-INGV ionosonde developed at the Istituto Nazionale di Geofisica e Vulcanologia (INGV), Rome, (Italy). This paper aims to describe briefly which are the main characteristics of the instrument and show the good quality and reliability of the recorded ionograms

Opuntia cladodes as functional ingredient in durum wheat bread: rheological, sensory, and chemical characterization

Cladodes are considered by-products of Opuntia ficus-indica cultivation. Their addition as source of antioxidants to durum wheat breads could have effects on preventing cardiovascular diseases, cancers, and inflammation. The inclusion of 0-5-10-15% cladodes, harvested in three different locations, on quality and antioxidant properties of fortified durum wheat breads has been evaluated. The enrichment with 10% of cladodes resulted in an increase in the content of total phenolics (14.8 vs 2.7 mg GAE/100 g of control bread), a decrease of IC50 (3.28 vs 49.7 mg/ml of control bread), good rheological characteristics of loaves and largely positive evaluation by panel test. Fortification with 15% of cladodes caused an increase in the resistance to the mixture with a reduction of dough extensibility. In addition, the evaluation of different populations of Opuntia gave information about the valorization of the crop and could be a strategy to increase bioactive compounds in durum wheat breads