Turing Instability and Pattern Formation in an Activator-Inhibitor System with Nonlinear Diffusion

In this work we study the effect of density dependent nonlinear diffusion on pattern formation in the Lengyel--Epstein system. Via the linear stability analysis we determine both the Turing and the Hopf instability boundaries and we show how nonlinear diffusion intensifies the tendency to pattern formation; %favors the mechanism of pattern formation with respect to the classical linear diffusion case; in particular, unlike the case of classical linear diffusion, the Turing instability can occur even when diffusion of the inhibitor is significantly slower than activator's one. In the Turing pattern region we perform the WNL multiple scales analysis to derive the equations for the amplitude of the stationary pattern, both in the supercritical and in the subcritical case. Moreover, we compute the complex Ginzburg-Landau equation in the vicinity of the Hopf bifurcation point as it gives a slow spatio-temporal modulation of the phase and amplitude of the homogeneous oscillatory solution.Comment: Accepted for publication in Acta Applicandae Mathematica

Pattern formation driven by cross--diffusion in a 2D domain

In this work we investigate the process of pattern formation in a two dimensional domain for a reaction-diffusion system with nonlinear diffusion terms and the competitive Lotka-Volterra kinetics. The linear stability analysis shows that cross-diffusion, through Turing bifurcation, is the key mechanism for the formation of spatial patterns. We show that the bifurcation can be regular, degenerate non-resonant and resonant. We use multiple scales expansions to derive the amplitude equations appropriate for each case and show that the system supports patterns like rolls, squares, mixed-mode patterns, supersquares, hexagonal patterns

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

On the effects of strong ionization in medium-order harmonic generation

Strong ionization of the gas medium has significant effects in the process of medium-order harmonic generation. The combined effect of neutral atom depletion and defocusing of the pump beam due to the intensity-dependent density of free electrons, significantly modifies the conversion characteristics and efficiency. For moderate harmonic orders, the yield is optimized for well-defined values of the pump laser intensity that do not depend on the order or on the focusing geometry, but only on the ionization potential of the gas. In particular focusing conditions, the ionization-induced defocusing can effectively guide the pump beam along channels of optimum intensity, thus enhancing the overall conversion efficiency. We demonstrate that a very simple model is able to reproduce all our experimental results in a surprisingly good way

Complete NNLO QCD Analysis of B -> X_s l^+ l^- and Higher Order Electroweak Effects

We complete the next-to-next-to-leading order QCD calculation of the branching ratio for B -> X_s l^+ l^- including recent results for the three-loop anomalous dimension matrix and two-loop matrix elements. These new contributions modify the branching ratio in the low-q^2 region, BR_ll, by about +1% and -4%, respectively. We furthermore discuss the appropriate normalization of the electromagnetic coupling alpha and calculate the dominant higher order electroweak effects, showing that, due to accidental cancellations, they change BR_ll by only -1.5% if alpha(mu) is normalized at mu = O(m_b), while they shift it by about -8.5% if one uses a high scale normalization mu = O(M_W). The position of the zero of the forward-backward asymmetry, q_0^2, is changed by around +2%. After introducing a few additional improvements in order to reduce the theoretical error, we perform a comprehensive study of the uncertainty. We obtain BR_ll(1 GeV^2 <= q^2 <= 6 GeV^2) = (1.57 +- 0.16) x 10^-6 and q_0^2 = (3.76 +- 0.33) GeV^2 and note that the part of the uncertainty due to the b-quark mass can be easily reduced.Comment: 26 pages, 7 figures; v5: corrected normalisation in Eq. (5), numerical results unchange

Recent developments in radiative B decays

We report on recent theoretical progress in radiative B decays. We focus on a calculation of logarithmically enhanced QED corrections to the branching ratio and forward-backward asymmetry in the inclusive rare decay anti-B --> X(s) l+ l-, and present the results of a detailed phenomenological analysis. We also report on the calculation of NNLO QCD corrections to the inclusive decay anti-B --> X(s) gamma. As far as exclusive modes are concerned we consider transversity amplitudes and the impact of right-handed currents in the exclusive anti-B --> K^* l+ l- decay. Finally, we state results for exclusive B --> V gamma decays, notably the time-dependent CP-asymmetry in the exclusive B --> K^* gamma decay and its potential to serve as a so-called ``null test'' of the Standard Model, and the extraction of CKM and unitarity triangle parameters from B --> (rho,omega) gamma and B --> K^* gamma decays.Comment: 5 pages, 2 figures. Accepted for publication in the proceedings of International Europhysics Conference on High Energy Physics (EPS-HEP2007), Manchester, England, 19-25 Jul 200

Excitable FitzHugh-Nagumo model with cross-diffusion: long-range activation instabilities

In this paper, we shall study a spatially extended version of the FitzHugh-Nagumo model, where one describes the motion of the species through cross-diffusion. The motivation comes from modeling biological species where reciprocal interaction influences spatial movement. We shall focus our analysis on the excitable regime of the system. In this case, we shall see how cross-diffusion terms can destabilize uniform equilibrium, allowing for the formation of close-to-equilibrium patterns; the species are out-of-phase spatially distributed, namely high concentration areas of one species correspond to a low density of the other (cross-Turing patterns). Moreover, depending on the magnitude of the inhibitor’s cross-diffusion, the pattern’s development can proceed in either case of the inhibitor/activator diffusivity ratio being higher or smaller than unity. This allows for spatial segregation of the species in both cases of short-range activation/long-range inhibition or long-range activation/short-range inhibition

Excitable FitzHugh-Nagumo model with cross-diffusion: close and far-from-equilibrium coherent structures

In this paper, we shall study the formation of stationary patterns for a reaction-diffusion system in which the FitzHugh-Nagumo (FHN) kinetics, in its excitable regime, is coupled to linear cross-diffusion terms. In (Gambino et al. in Excitable Fitzhugh-Nagumo model with cross-diffusion: long-range activation instabilities, 2023), we proved that the model supports the emergence of cross-Turing patterns, i.e., close-to-equilibrium structures occurring as an effect of cross-diffusion. Here, we shall construct the crossTuring patterns close to equilibrium on 1-D and 2-D rectangular domains. Through this analysis, we shall show that the species are out-of-phase spatially distributed and derivethe amplitude equations that govern the pattern dynamics close to criticality. Moreover, we shall classify the bifurcation in the parameter space, distinguishing between super-and sub-critical transitions. In the final part of the paper, we shall numerically investigate the impact of the cross-diffusion terms on large-amplitude pulse-like solutions existing outside the cross-Turing regime, showing their emergence also in the case of lateral activation and short-range inhibition

I Quaderni di Careggi- Fifth issue- Landscape Observatories

Having regard to Recommendation CM/Rec (2008)3 on the Guidelines for the implementation of the European Landscape Convention, “landscape observatories, centers and institutes” are one of the main instruments for the implementation of landscape policies (II.3.3). They facilitate the collection and exchange of information and study protocols between states and local communities. This issue of the Quaderni di Careggi presents an international overview of the activities of landscape observatories, a reflection on their mission and effectiveness with regard to the ELC objectives, and a reflection on the relationships between the different subjects, thanks to the participation of institutional bodies, public officials as well as researchers and representatives of civil society. It reflects part of the scientific contributions which will be presented during the V Careggi Seminar (Florence, 27-28th June 2013)