Asymptotic behaviour for a class of non-monotone delay differential systems with applications

The paper concerns a class of $n$-dimensional non-autonomous delay differential equations obtained by adding a non-monotone delayed perturbation to a linear homogeneous cooperative system of ordinary differential equations. This family covers a wide set of models used in structured population dynamics. By exploiting the stability and the monotone character of the linear ODE, we establish sufficient conditions for both the extinction of all the populations and the permanence of the system. In the case of DDEs with autonomous coefficients (but possible time-varying delays), sharp results are obtained, even in the case of a reducible community matrix. As a sub-product, our results improve some criteria for autonomous systems published in recent literature. As an important illustration, the extinction, persistence and permanence of a non-autonomous Nicholson system with patch structure and multiple time-dependent delays are analysed.Comment: 26 pages, J Dyn Diff Equat (2017

A model for Faraday pilot waves over variable topography

Couder and Fort discovered that droplets walking on a vibrating bath possess certain features previously thought to be exclusive to quantum systems. These millimetric droplets synchronize with their Faraday wavefield, creating a macroscopic pilot-wave system. In this paper we exploit the fact that the waves generated are nearly monochromatic and propose a hydrodynamic model capable of quantitatively capturing the interaction between bouncing drops and a variable topography. We show that our reduced model is able to reproduce some important experiments involving the drop-topography interaction, such as non-specular reflection and single-slit diffraction

Harmonic density interpolation methods for high-order evaluation of Laplace layer potentials in 2D and 3D

We present an effective harmonic density interpolation method for the numerical evaluation of singular and nearly singular Laplace boundary integral operators and layer potentials in two and three spatial dimensions. The method relies on the use of Green's third identity and local Taylor-like interpolations of density functions in terms of harmonic polynomials. The proposed technique effectively regularizes the singularities present in boundary integral operators and layer potentials, and recasts the latter in terms of integrands that are bounded or even more regular, depending on the order of the density interpolation. The resulting boundary integrals can then be easily, accurately, and inexpensively evaluated by means of standard quadrature rules. A variety of numerical examples demonstrate the effectiveness of the technique when used in conjunction with the classical trapezoidal rule (to integrate over smooth curves) in two-dimensions, and with a Chebyshev-type quadrature rule (to integrate over surfaces given as unions of non-overlapping quadrilateral patches) in three-dimensions

Parametric Competition in non-autonomous Hamiltonian Systems

In this work we use the formalism of chord functions (\emph{i.e.} characteristic functions) to analytically solve quadratic non-autonomous Hamiltonians coupled to a reservoir composed by an infinity set of oscillators, with Gaussian initial state. We analytically obtain a solution for the characteristic function under dissipation, and therefore for the determinant of the covariance matrix and the von Neumann entropy, where the latter is the physical quantity of interest. We study in details two examples that are known to show dynamical squeezing and instability effects: the inverted harmonic oscillator and an oscillator with time dependent frequency. We show that it will appear in both cases a clear competition between instability and dissipation. If the dissipation is small when compared to the instability, the squeezing generation is dominant and one can see an increasing in the von Neumann entropy. When the dissipation is large enough, the dynamical squeezing generation in one of the quadratures is retained, thence the growth in the von Neumann entropy is contained

Theory of weakly nonlinear self sustained detonations

We propose a theory of weakly nonlinear multi-dimensional self sustained detonations based on asymptotic analysis of the reactive compressible Navier-Stokes equations. We show that these equations can be reduced to a model consisting of a forced, unsteady, small disturbance, transonic equation and a rate equation for the heat release. In one spatial dimension, the model simplifies to a forced Burgers equation. Through analysis, numerical calculations and comparison with the reactive Euler equations, the model is demonstrated to capture such essential dynamical characteristics of detonations as the steady-state structure, the linear stability spectrum, the period-doubling sequence of bifurcations and chaos in one-dimensional detonations and cellular structures in multi- dimensional detonations

Interband polarized absorption in InP polytypic superlattices

Recent advances in growth techniques have allowed the fabrication of semiconductor nanostructures with mixed wurtzite/zinc-blende crystal phases. Although the optical characterization of these polytypic structures is well eported in the literature, a deeper theoretical understanding of how crystal phase mixing and quantum confinement change the output linear light polarization is still needed. In this paper, we theoretically investigate the mixing effects of wurtzite and zinc-blende phases on the interband absorption and in the degree of light polarization of an InP polytypic superlattice. We use a single 8$\times$8 k$\cdot$p Hamiltonian that describes both crystal phases. Quantum confinement is investigated by changing the size of the polytypic unit cell. We also include the optical confinement effect due to the dielectric mismatch between the superlattice and the vaccum and we show it to be necessary to match experimental results. Our calculations for large wurtzite concentrations and small quantum confinement explain the optical trends of recent photoluminescence excitation measurements. Furthermore, we find a high sensitivity to zinc-blende concentrations in the degree of linear polarization. This sensitivity can be reduced by increasing quantum confinement. In conclusion, our theoretical analysis provides an explanation for optical trends in InP polytypic superlattices, and shows that the interplay of crystal phase mixing and quantum confinement is an area worth exploring for light polarization engineering.Comment: 9 pages, 6 figures and 1 tabl

Analytical treatment of stabilization

We present a summarizing account of a series of investigations whose central topic is to address the question whether atomic stabilization exists in an analytical way. We provide new aspects on several issues of the matter in the theoretical context when the dynamics is described by the Stark Hamiltonian. The main outcome of these studies is that the governing parameters for this phenomenon are the total classical momentum transfer and the total classical displacement. Whenever these two quantities vanish, asymptotically weak stabilization does exist. For all other situations we did not find any evidence for stabilization. We found no evidence that strong stabilization might occur. Our results agree qualitatively with the existing experimental findings

Relationships between nutrient composition of flowers and fruit quality in orange trees grown in calcareous soil

To determine if flower nutrient composition can be used to predict fruit quality, a field experiment was conducted over three seasons (1996-1999) in a commercial orange orchard (Citrus sinensis (L.) Osbeck cv. 'Valencia Late', budded on Troyer citrange rootstock) established on a calcareous soil in southern Portugal. Flowers were collected from 20 trees during full bloom in April and their nutrient composition determined, and fruits were harvested the following March and their quality evaluated. Patterns of covariation in flower nutrient concentrations and in fruit quality variables were evaluated by principal component analysis. Regression models relating fruit quality variables to flower nutrient composition were developed by stepwise selection procedures. The predictive power of the regression models was evaluated with an independent data set. Nutrient composition of flowers at full bloom could be used to predict the fruit quality variables fresh fruit mass and maturation index in the following year. Magnesium, Ca and Zn concentrations measured in flowers were related to fruit fresh mass estimations and N, P, Mg and Fe concentrations were related to fruit maturation index. We also established reference values for the nutrient composition of flowers based on measurements made in trees that produced large (> 76 mm in diameter) fruit.info:eu-repo/semantics/publishedVersio