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 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

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

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

Thermography as a method to detect dental anxiety in oral surgery

(1) Background: the aim of this study was to evaluate if dental anxiety can be measured objectively using thermal infrared imaging. (2) Methods: Patients referred to the Department of Oral Surgery of the University of Naples Federico II and requiring dental extractions were consecutively enrolled in the study. Face thermal distribution images of the patients were acquired before and during their first clinical examination using infrared thermal cameras. The data were analyzed in relation to five regions of interest (ROI) of the patient’s face (nose, ear, forehead, zygoma, chin). The differences in the temperatures assessed between the two measurements for each ROI were evaluated by using paired T‐test. The Pearson correlation and linear regression were performed to evaluate the association between differences in temperatures and Modified Dental Anxiety Scale (MDAS) questionnaire score, age, and gender; (3) results: sixty participants were enrolled in the study (28 males and 32 females; mean age 57.4 year‐old; age range 18–80 year‐old). Only for nose and ear zone there was a statistically significant difference between measurements at baseline and visit. Correlation between the thermal imaging measurements and the scores of the MDAS questionnaire was found for nose and ear, but not for all of the other regions. (4) Conclusions: the study demonstrated a potential use of thermal infrared imaging to measure dental anxiety

On the role of the bay of Algeciras in the exchange across the Strait of Gibraltar.

Política de acceso abierto tomada de: https://v2.sherpa.ac.uk/id/publication/35864The role that the Algeciras Bay, a medium size embayment located in the eastern part of the Strait of Gibraltar, may have on the water exchange through the Strait and on other physical properties of the area has been numerically investigated using different configurations of a numerical model. Three domains have been considered, the present configuration with the Bay and two other configurations in which the Bay is suppressed either by filling the embayment, which produces a longer Strait, or by removing the Gibraltar Rock and isthmus, which gives rise to a shorter Strait. Only little modifications are produced in the mean properties, the shorter Strait increasing very slightly the mean exchange and diminishing the cross-section averaged salinity of the inflow. The spatial pattern of semidiurnal tidal ellipses is changed in the vicinity of the Bay, but other properties such as the minimum amplitude of semidiurnal M2 transport that occurs off the Bay in the Strait and that could be related to the present configuration, remain unaltered. It is speculated that the main consequence of suppressing the Bay relates to the export of primary production, as it acts out as a buffer of water with residence times long enough to sustain high levels of productivity

Coupling palaeobiology and geochemistry from the Holocene of the southern Adriatic Sea (Gulf of Manfredonia, Italy): Shelf facies patterns and eutrophication trends

The combined use of the meiofauna (benthic foraminifers and ostracods) and geochemical data from three cores, recovered in distinct bathymetric sectors of the southern Adriatic shelf (Apulia, SE Italy), provides new insights on the relationships between shallow-marine environments, sediment fluxes and eutrophication trends over the last ~7000 years. The stratigraphic distribution of meiofauna assemblages allows distinguishing a variety of facies associations, accumulated at proximal (Manfredonia Gulf), intermediate and distal shelf sectors. Spatial-temporal facies trajectories mainly reflect changes in fluxes of fine-grained, inorganic and organic particles at the seafloor. Major palaeoenvironmental shifts are paralleled by stratigraphic variations of Cr-Ni values, which represent effective provenance tracers for the Adriatic region. The correlation between the meiofauna content and trace-metal concentrations documents the link between the type of substrate (organic matter-OM and grain-size) and sediment provenance along the bathymetric profile and through time. After 6000 yr B.P., the gulf, partly sheltered by the Gargano Promontory, experienced the first increase in OM fluxes (transition from open-bay to prodelta). This turnaround occurred under the progressive change in sediment supply from southern Apennine source-rocks, poor in trace metals, to a mixed contribution including northern sources, enriched in chromium and nickel (mafic/ultramafic rocks of the Po River catchment) via the SSE-directed longshore drift. Alongside, prodelta clays in lateral transition to mud-belt deposits accumulated in the adjacent open shelf under the steady influence of the longshore drift. Finally, since ~2000 yr B.P. a pervasive subaqueous delta system developed across the study area in response to increased sediment load by Po + Apennine rivers, likely induced by enhanced anthropic pressure during Roman times. This study highlights the key role played by the sediment routing system, coastal morphology and human land-use on shelf facies patterns and eutrophication trends, even in areas hundreds of km away from the main fluvial mouths

Cytokine-induced instabilities in a reaction–diffusion-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 reaction–diffusion-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 Balò 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