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

QCD in One Dimension at Nonzero Chemical Potential

Using an integration formula recently derived by Conrey, Farmer and Zirnbauer, we calculate the expectation value of the phase factor of the fermion determinant for the staggered lattice QCD action in one dimension. We show that the chemical potential can be absorbed into the quark masses; the theory is in the same chiral symmetry class as QCD in three dimensions at zero chemical potential. In the limit of a large number of colors and fixed number of lattice points, chiral symmetry is broken spontaneously, and our results are in agreement with expressions based on a chiral Lagrangian. In this limit, the eigenvalues of the Dirac operator are correlated according to random matrix theory for QCD in three dimensions. The discontinuity of the chiral condensate is due to an alternative to the Banks-Casher formula recently discovered for QCD in four dimensions at nonzero chemical potential. The effect of temperature on the average phase factor is discussed in a schematic random matrix model.Comment: Latex, 23 pages and 5 figures; Added two references and corrected several typo

Time-optimal control fields for quantum systems with multiple avoided crossings

We study time-optimal protocols for controlling quantum systems which show several avoided level crossings in their energy spectrum. The structure of the spectrum allows us to generate a robust guess which is time-optimal at each crossing. We correct the field applying optimal control techniques in order to find the minimal evolution or quantum speed limit (QSL) time. We investigate its dependence as a function of the system parameters and show that it gets proportionally smaller to the well-known two-level case as the dimension of the system increases. Working at the QSL, we study the control fields derived from the optimization procedure, and show that they present a very simple shape, which can be described by a few parameters. Based on this result, we propose a simple expression for the control field, and show that the full time-evolution of the control problem can be analytically solved.Comment: 11 pages, 7 figure

The use of LANDSAT data to monitor the urban growth of Sao Paulo Metropolitan area

Urban growth from 1977 to 1979 of the region between Billings and the Guarapiranga reservoir was mapped and the problematic urban areas identified using several LANDSAT products. Visual and automatic interpretation techniques were applied to the data. Computer compatible tapes of LANDSAT multispectral scanner data were analyzed through the maximum likelihood Gaussian algorithm. The feasibility of monitoring fast urban growth by remote sensing techniques for efficient urban planning and control is demonstrated

Preliminary analysis of the potential of LANDSAT imagery to study desertification

The use of LANDSAT imagery to define and delimit areas under process of desertification was investigated. Imagery for two different years (1973 and 1978) and two different seasons (dry and rainy seasons in 1976), were used to identify terrain morphology and vegetation cover. The analysis of LANDSAT interpretation, combined with geological and soil information obtained from published literature, allowed the identification of eleven ecological units which were classified corresponding to the degree of the Xique Xique region of Rio Sao Francisco

Quantum dissipative effects in graphene-like mirrors

We study quantum dissipative effects due to the accelerated motion of a single, imperfect, zero-width mirror. It is assumed that the microscopic degrees of freedom on the mirror are confined to it, like in plasma or graphene sheets. Therefore, the mirror is described by a vacuum polarization tensor $\Pi_{\alpha\beta}$ concentrated on a time-dependent surface. Under certain assumptions about the microscopic model for the mirror, we obtain a rather general expression for the Euclidean effective action, a functional of the time-dependent mirror's position, in terms of two invariants that characterize the tensor $\Pi_{\alpha\beta}$. The final result can be written in terms of the TE and TM reflection coefficients of the mirror, with qualitatively different contributions coming from them. We apply that general expression to derive the imaginary part of the `in-out' effective action, which measures dissipative effects induced by the mirror's motion, in different models, in particular for an accelerated graphene sheet.Comment: 8 pages, 2 figures. Minor changes, version to be published in Phys. Rev.

Anopheline salivary protein genes and gene families: an evolutionary overview after the whole genome sequence of sixteen Anopheles species

Background: Mosquito saliva is a complex cocktail whose pharmacological properties play an essential role in blood feeding by counteracting host physiological response to tissue injury. Moreover, vector borne pathogens are transmitted to vertebrates and exposed to their immune system in the context of mosquito saliva which, in virtue of its immunomodulatory properties, can modify the local environment at the feeding site and eventually affect pathogen transmission. In addition, the host antibody response to salivary proteins may be used to assess human exposure to mosquito vectors. Even though the role of quite a few mosquito salivary proteins has been clarified in the last decade, we still completely ignore the physiological role of many of them as well as the extent of their involvement in the complex interactions taking place between the mosquito vectors, the pathogens they transmit and the vertebrate host. The recent release of the genomes of 16 Anopheles species offered the opportunity to get insights into function and evolution of salivary protein families in anopheline mosquitoes. Results: Orthologues of fifty three Anopheles gambiae salivary proteins were retrieved and annotated from 18 additional anopheline species belonging to the three subgenera Cellia, Anopheles, and Nyssorhynchus. Our analysis included 824 full-length salivary proteins from 24 different families and allowed the identification of 79 novel salivary genes and re-annotation of 379 wrong predictions. The comparative, structural and phylogenetic analyses yielded an unprecedented view of the anopheline salivary repertoires and of their evolution over 100 million years of anopheline radiation shedding light on mechanisms and evolutionary forces that contributed shaping the anopheline sialomes. Conclusions: We provide here a comprehensive description, classification and evolutionary overview of the main anopheline salivary protein families and identify two novel candidate markers of human exposure to malaria vectors worldwide. This anopheline sialome catalogue, which is easily accessible as hyperlinked spreadsheet, is expected to be useful to the vector biology community and to improve the capacity to gain a deeper understanding of mosquito salivary proteins facilitating their possible exploitation for epidemiological and/or pathogen-vector-host interaction studies

How Phase Transitions induce classical behaviour

We continue the analysis of the onset of classical behaviour in a scalar field after a continuous phase transition, in which the system-field, the long wavelength order parameter of the model, interacts with an environment, of its own short-wavelength modes and other fields, neutral and charged, with which it is expected to interact. We compute the decoherence time for the system-field modes from the master equation and directly from the decoherence functional (with identical results). In simple circumstances the order parameter field is classical by the time the transition is complete.Comment: 10 pages, 1 figure: To be published in the International Journal of Theoretical Physics (2005) as part of the Proceedings of the "Peyresq Physics 9" meeting (2004) on "Micro and Macro structures of spacetime",ed. E. Verdague