Modeling migratory grazing of zooplankton on toxic and non-toxic phytoplankton

Migratory grazing of zooplankton between non-toxic phytoplankton (NTP) and toxic phytoplankton (TPP) is a realistic phenomena unexplored so far. The present article is a first step in this direction. A mathematical model of NTP–TPP-zooplankton with constant and variable zooplankton migration is proposed and analyzed. The asymptotic dynamics of the model system around the biologically feasible equilibria is explored through local stability analysis. The dynamics of the proposed system is explored and displayed for different combination of migratory parameters and toxin inhibition parameters. Our analysis suggests that the migratory grazing of zooplankton has a significant role in determining the dynamic stability and oscillation of phytoplankton zooplankton systems.

A high frequency boundary element method for scattering by a class of nonconvex obstacles

In this paper we propose and analyse a hybrid numerical-asymptotic boundary element method for the solution of problems of high frequency acoustic scattering by a class of sound-soft nonconvex polygons. The approximation space is enriched with carefully chosen oscillatory basis functions; these are selected via a study of the high frequency asymptotic behaviour of the solution. We demonstrate via a rigorous error analysis, supported by numerical examples, that to achieve any desired accuracy it is sufficient for the number of degrees of freedom to grow only in proportion to the logarithm of the frequency as the frequency increases, in contrast to the at least linear growth required by conventional methods. This appears to be the first such numerical analysis result for any problem of scattering by a nonconvex obstacle. Our analysis is based on new frequency-explicit bounds on the normal derivative of the solution on the boundary and on its analytic continuation into the complex plane.

Serial clustering of extratropical cyclones in a multi-model ensemble of historical and future simulations

This study has investigated serial (temporal) clustering of extra-tropical cyclones simulated by 17 climate models that participated in CMIP5. Clustering was estimated by calculating the dispersion (ratio of variance to mean) of 30 December-February counts of Atlantic storm tracks passing nearby each grid point. Results from single historical simulations of 1975-2005 were compared to those from historical ERA40 reanalyses from 1958-2001 ERA40 and single future model projections of 2069-2099 under the RCP4.5 climate change scenario. Models were generally able to capture the broad features in reanalyses reported previously: underdispersion/regularity (i.e. variance less than mean) in the western core of the Atlantic storm track surrounded by overdispersion/clustering (i.e. variance greater than mean) to the north and south and over western Europe. Regression of counts onto North Atlantic Oscillation (NAO) indices revealed that much of the overdispersion in the historical reanalyses and model simulations can be accounted for by NAO variability. Future changes in dispersion were generally found to be small and not consistent across models. The overdispersion statistic, for any 30 year sample, is prone to large amounts of sampling uncertainty that obscures the climate change signal. For example, the projected increase in dispersion for storm counts near London in the CNRMCM5 model is 0.1 compared to a standard deviation of 0.25. Projected changes in the mean and variance of NAO are insufficient to create changes in overdispersion that are discernible above natural sampling variations.

The sensitivity of convective aggregation to diabatic processes in idealized radiative-convective equilibrium simulations

Idealized explicit convection simulations of the Met Office Unified Model exhibit spontaneous self-aggregation in radiative-convective equilibrium, as seen in other models in previous studies. This self-aggregation is linked to feedbacks between radiation, surface fluxes, and convection, and the organization is intimately related to the evolution of the column water vapor field. Analysis of the budget of the spatial variance of column-integrated frozen moist static energy (MSE), following Wing and Emanuel [2014], reveals that the direct radiative feedback (including significant cloud longwave effects) is dominant in both the initial development of self-aggregation and the maintenance of an aggregated state. A low-level circulation at intermediate stages of aggregation does appear to transport MSE from drier to moister regions, but this circulation is mostly balanced by other advective effects of opposite sign and is forced by horizontal anomalies of convective heating (not radiation). Sensitivity studies with either fixed prescribed radiative cooling, fixed prescribed surface fluxes, or both do not show full self-aggregation from homogeneous initial conditions, though fixed surface fluxes do not disaggregate an initialized aggregated state. A sensitivity study in which rain evaporation is turned off shows more rapid self-aggregation, while a run with this change plus fixed radiative cooling still shows strong self-aggregation, supporting a “moisture memory” effect found in Muller and Bony [2015]. Interestingly, self-aggregation occurs even in simulations with sea surface temperatures (SSTs) of 295 K and 290 K, with direct radiative feedbacks dominating the budget of MSE variance, in contrast to results in some previous studies.

Resonant Wave Interactions in the Presence of a Diurnally Varying Heat Source

Resonant interactions among equatorial waves in the presence of a diurnally varying heat source are studied in the context of the diabatic version of the equatorial beta-plane primitive equations for a motionless, hydrostatic, horizontally homogeneous and stably stratified background atmosphere. The heat source is assumed to be periodic in time and of small amplitude [i.e., O(epsilon)] and is prescribed to roughly represent the typical heating associated with deep convection in the tropical atmosphere. In this context, using the asymptotic method of multiple time scales, the free linear Rossby, Kelvin, mixed Rossby-gravity, and inertio-gravity waves, as well as their vertical structures, are obtained as leading-order solutions. These waves are shown to interact resonantly in a triad configuration at the O(e) approximation, and the dynamics of these interactions have been studied in the presence of the forcing. It is shown that for the planetary-scale wave resonant triads composed of two first baroclinic equatorially trapped waves and one barotropic Rossby mode, the spectrum of the thermal forcing is such that only one of the triad components is resonant with the heat source. As a result, to illustrate the role of the diurnal forcing in these interactions in a simplified fashion, two kinds of triads have been analyzed. The first one refers to triads composed of a k = 0 first baroclinic geostrophic mode, which is resonant with the stationary component of the diurnal heat source, and two dispersive modes, namely, a mixed Rossby-gravity wave and a barotropic Rossby mode. The other class corresponds to triads composed of two first baroclinic inertio-gravity waves in which the highest-frequency wave resonates with a transient harmonic of the forcing. The integration of the asymptotic reduced equations for these selected resonant triads shows that the stationary component of the diurnal heat source acts as an ""accelerator"" for the energy exchanges between the two dispersive waves through the excitation of the catalyst geostrophic mode. On the other hand, since in the second class of triads the mode that resonates with the forcing is the most energetically active member because of the energy constraints imposed by the triad dynamics, the results show that the convective forcing in this case is responsible for a longer time scale modulation in the resonant interactions, generating a period doubling in the energy exchanges. The results suggest that the diurnal variation of tropical convection might play an important role in generating low-frequency fluctuations in the atmospheric circulation through resonant nonlinear interactions.

Effects of detectability on estimates of geographic range size in bignonieae

Extinction risk has not been evaluated for 96% of all described plant species. Given that the Global Strategy for Plant Conservation proposes preliminary conservation assessments of all described plant species by 2010, herbarium specimens (i.e., primary occurrence data) are increasingly being used to infer threat components from estimates of geographic range size. Nevertheless, estimates of range size based on herbarium data may be inaccurate due to collection bias associated with interspecific variation in detectability. We used data on 377 species of Bignonieae to test the hypothesis that there is a positive relationship between detectability and estimates of geographic range size derived from herbarium specimens. This relationship is expected if the proportion of the true geographic range size of a species that is documented by herbarium specimens is given by the product of the true geographic range size and the detectability of the species, assuming no relationship between true geographic range size and detectability. We developed 4 measures of detectability that can be estimated from herbarium data and examined the relationship between detectability and 2 types of estimates of geographic range size: area of occupancy and extent of occurrence. Our results from regressing estimates of extent of occurrence and area of occupancy on detectability across genera provided no support for this hypothesis. The same was true for regressions of estimated extent of occurrence on detectability across species within genera. Nevertheless, regressions of estimated area of occupancy on detectability across species within genera provided partial support for our hypothesis. We considered 3 possible explanations for this mixed outcome: violation of the assumption of no relationship between true geographic range size and detectability; the relationships between estimated geographic range size and detectability may be an artifact of a negative relationship between estimated area of occupancy and the sampling variance of detectability; detectability may have had 2 opposite effects on estimated species range sizes: one determines the proportion of the true range of a species documented by herbarium specimens and the other determines the distribution of true range size for the species actually observed with herbarium data. Our findings should help improve understanding of the potential biases incurred with the use of herbarium data.

Relief influence on tree species richness in secondary forest fragments of Atlantic Forest, SE, Brazil

(Relief influence on tree species richness in secondary forest fragments of Atlantic Forest, SE, Brazil). The aim of this work was to explore the relationship between tree species richness and morphological characteristics of relief at the Ibiuna Plateau (SE Brazil). We sampled 61 plots of 0.30 ha, systematically established in 20 fragments of secondary forest (2-274 ha) and in three areas within a continuous secondary forest site, Morro Grande Reserve (9,400 ha). At each plot, 100 trees with diameter at breast height > 5 cm were sampled by the point centered quarter method, and total richness and richness per dispersal and succession class were obtained. The relief was characterized by the mean and variance of slope, elevation, aspect and slope location. There was no significant relationship between relief heterogeneity and tree species richness. Relief parameters generally did not affect tree richness, but elevation was particularly important especially in the continuous forest. Despite the limited range of altitudinal variation (150 m), species richness increases with elevation. The highest areas were also those with the largest forest cover and the lowest disturbance degree, which should contribute to the greater richness of those sites. Our results suggest an indirect influence of relief, due to the fact that deforestation is less intense in higher regions, rather than a direct influence of abiotic factors related to the altitudinal gradient.

Existence of pullback attractors for pullback asymptotically compact processes

This paper is concerned with the existence of pullback attractors for evolution processes. Our aim is to provide results that extend the following results for autonomous evolution processes (semigroups) (i) An autonomous evolution process which is bounded, dissipative and asymptotically compact has a global attractor. (ii) An autonomous evolution process which is bounded, point dissipative and asymptotically compact has a global attractor. The extension of such results requires the introduction of new concepts and brings up some important differences between the asymptotic properties of autonomous and non-autonomous evolution processes. An application to damped wave problem with non-autonomous damping is considered. (C) 2009 Elsevier Ltd. All rights reserved.

Positive solutions of the p-Laplacian involving a superlinear nonlinearity with zeros

Using a combination of several methods, such as variational methods. the sub and supersolutions method, comparison principles and a priori estimates. we study existence, multiplicity, and the behavior with respect to lambda of positive solutions of p-Laplace equations of the form -Delta(p)u = lambda h(x, u), where the nonlinear term has p-superlinear growth at infinity, is nonnegative, and satisfies h(x, a(x)) = 0 for a suitable positive function a. In order to manage the asymptotic behavior of the solutions we extend a result due to Redheffer and we establish a new Liouville-type theorem for the p-Laplacian operator, where the nonlinearity involved is superlinear, nonnegative, and has positive zeros. (C) 2009 Elsevier Inc. All rights reserved.

Dynamics in dumbbell domains III. Continuity of attractors

In this paper we conclude the analysis started in [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz, Dynamics in dumbbell domains I. Continuity of the set of equilibria, J. Differential Equations 231 (2006) 551-597] and continued in [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz, Dynamics in dumbbell domains II. The limiting problem, J. Differential Equations 247 (1) (2009) 174-202 (this issue)] concerning the behavior of the asymptotic dynamics of a dissipative reaction-diffusion equation in a dumbbell domain as the channel shrinks to a line segment. In [J.M. Arrieta, AN Carvalho. G. Lozada-Cruz, Dynamics in dumbbell domains I. Continuity of the set of equilibria, J. Differential Equations 231 (2006) 551-597], we have established an appropriate functional analytic framework to address this problem and we have shown the continuity of the set of equilibria. In [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz. Dynamics in dumbbell domains II. The limiting problem, J. Differential Equations 247 (1) (2009) 174-202 (this issue)], we have analyzed the behavior of the limiting problem. In this paper we show that the attractors are Upper semicontinuous and, moreover, if all equilibria of the limiting problem are hyperbolic, then they are lower semicontinuous and therefore, continuous. The continuity is obtained in L(p) and H(1) norms. (C) 2008 Elsevier Inc. All rights reserved.

An extension of the concept of gradient semigroups which is stable under perturbation

In this article we introduce the concept of a gradient-like nonlinear semigroup as an intermediate concept between a gradient nonlinear semigroup (those possessing a Lyapunov function, see [J.K. Hale, Asymptotic Behavior of Dissipative Systems, Math. Surveys Monogr., vol. 25, Amer. Math. Soc., 1989]) and a nonlinear semigroup possessing a gradient-like attractor. We prove that a perturbation of a gradient-like nonlinear semigroup remains a gradient-like nonlinear semigroup. Moreover, for non-autonomous dynamical systems we introduce the concept of a gradient-like evolution process and prove that a non-autonomous perturbation of a gradient-like nonlinear semigroup is a gradient-like evolution process. For gradient-like nonlinear semigroups and evolution processes, we prove continuity, characterization and (pullback and forwards) exponential attraction of their attractors under perturbation extending the results of [A.N. Carvalho, J.A. Langa, J.C. Robinson, A. Suarez, Characterization of non-autonomous attractors of a perturbed gradient system, J. Differential Equations 236 (2007) 570-603] on characterization and of [A.V. Babin, M.I. Vishik, Attractors in Evolutionary Equations, Stud. Math. Appl.. vol. 25, North-Holland, Amsterdam, 1992] on exponential attraction. (C) 2009 Elsevier Inc. All rights reserved.

On the dominance of roots of characteristic equations for neutral functional differential equations

We present a sufficient condition for a zero of a function that arises typically as the characteristic equation of a linear functional differential equations of neutral type, to be simple and dominant. This knowledge is useful in order to derive the asymptotic behaviour of solutions of such equations. A simple characteristic equation, arisen from the study of delay equations with small delay, is analyzed in greater detail. (C) 2009 Elsevier Inc. All rights reserved.

Polarization and Spectral Shift of Benzophenone in Supercritical Water

Monte Carlo simulation and quantum mechanics calculations based on the INDO/CIS and TD-DFT methods were utilized to study the solvatochromic shift of benzophenone when changing the environment from normal water to supercritical (P = 340.2 atm and T = 673 K) condition. Solute polarization increases the dipole moment of benzophenone, compared to gas phase, by 88 and 35% in normal and supercritical conditions, giving the in-solvent dipole value of 5.8 and 4.2 D, respectively. The average number of solute-solvent hydrogen bonds was analyzed, and a large decrease of 2.3 in normal water to only 0.8 in the supercritical environment was found. By using these polarized models of benzophenone in the two different conditions of water, we performed MC simulations to generate statistically uncorrelated configurations of the solute surrounded by the solvent molecules and subsequent quantum mechanics calculations on these configurations. When changing from normal to supercritical water environment, INDO/CIS calculations explicitly considering all valence electrons of the 235 solvent water molecules resulted in a solvatochromic shift of 1425 cm(-1) for the most intense transition of benzophenone, that is, slightly underestimated in comparison with the experimentally inferred result of 1700 cm(-1). TD-B3LYP/6-311+G(2d,p) calculations on the same configurations but with benzophenone electrostatically embedded in the 320 water molecules resulted in a solvatochromic shift of 1715 cm(-1) for this transition, in very good agreement with the experimental result. When using the unpolarized model of the benzophenone, this calculated solvatochromic shift was only 640 cm(-1). Additional calculations were also made by using BHandHLYP/6-311+G(2d,p) to analyze the effect of the asymptotic decay of the exchange functional. This study indicates that, contrary to the general expectation, there is a sizable solute polarization even in the low-density regime of supercritical condition and that the inclusion of this polarization is important for a reliable description of the spectral shifts considered here.

The stochastic nature of predator-prey cycles

We study by numerical simulations the time correlation function of a stochastic lattice model describing the dynamics of coexistence of two interacting biological species that present time cycles in the number of species individuals. Its asymptotic behavior is shown to decrease in time as a sinusoidal exponential function from which we extract the dominant eigenvalue of the evolution operator related to the stochastic dynamics showing that it is complex with the imaginary part being the frequency of the population cycles. The transition from the oscillatory to the nonoscillatory behavior occurs when the asymptotic behavior of the time correlation function becomes a pure exponential, that is, when the real part of the complex eigenvalue equals a real eigenvalue. We also show that the amplitude of the undamped oscillations increases with the square root of the area of the habitat as ordinary random fluctuations. (C) 2009 Elsevier B.V. All rights reserved.

Borel-Leroy summability of a nonpolynomial potential

We investigate the perturbation series for the spectrum of a class of Schrodinger operators with potential V = 1/2 x(2) + g(m-1)x(2m)/(1 + alpha gx(2)) which generalize particular cases investigated in the literature in connection with models in laser theory and quantum field theory of particles and fields. It is proved that the series obey a modified strong asymptotic condition of order (m - 1) and have an order (m - 1) strong asymptotic series in g which are shown to be summable in the sense of Borel-Leroy method.