BCS-BEC crossover in a trapped Fermi super-fluid using a density-functional equation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Universal scaling in a trapped Fermi super-fluid in the BCS-unitarity crossover

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Superfluid Bose-Fermi mixture from weak coupling to unitarity

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Self-trapping of a Fermi superfluid in a double-well potential in the Bose-Einstein-condensate-unitarity crossover

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Stability of neutral functional differential equations in terms of measures

In this paper we investigate the relationships between different concepts of stability in measure for the solutions of an autonomous or periodic neutral functional differential equation.

The role of habitat heterogeneity for the functional response of the spider Nesticodes rufipes (Araneae : Theridiidae) to houseflies

We investigated whether or not different degrees of refuge for prey influence the characteristic of functional response exhibited by the spider Nesticodes rufipes on Musca domestica, comparing the inherent ability of N. rufipes to kill individual houseflies in such environments at two distinct time intervals. To investigate these questions, two artificial habitats were elaborated in the laboratory. For 168 h of predator-prey interaction, logistic regression analyses revealed a type 11 functional response, and a significant decrease in prey capture in the highest prey density was observed when habitat complexity was increased. Data from habitat 1 (less complex) presented a greater coefficient of determination than those from habitat 2 (more complex), indicating a higher variation of predation of the latter. For a 24 h period of predator-prey interaction, spiders killed significantly fewer prey in habitat 2 than in habitat 1. Although prey capture did not enable data to fit properly in the random predator equation in this case, predation data from habitat 2 presented a higher variation than data from habitat 1, corroborating results from 168 h of interaction. The high variability observed on data from habitat 2 (more complex habitat) is an interesting result because it reinforces the importance of refuge in promoting spatial heterogeneity, which can affect the extent of predator-prey interactions.

Consequences of refuge for the functional response of Dermestes ater (Coleoptera : Dermestidae) to Musca domestica (Diptera : Muscidae)

It is well known that a predator has the potential to regulate a prey population only if the predator responds to increases in prey density and inflicts greater mortality rates. Predators may cause such density-dependent mortality depending on the nature of the functional and numerical responses. Yet, few studies have examined the relationship between the addition of refuges and the characteristic of functional response fits. We investigated whether addition of a refuge changed the type of functional response exhibited by Dermestes ater on Musca domestica, comparing the inherent ability of D. ater to kill houseflies in the absence and in the presence of refuge. An additional laboratory experiment was also carried out to assess handling and searching times exhibited by D. ater. Logistic regression analyses revealed a type III functional response for predator-prey interaction without refuge, and results were described by the random predator equation. The mean number of prey killed did not differ between experimental habitats, indicating that the addition of refuge did not inhibit predation. However, predators that interacted with prey without refuge spent less time searching for prey at higher densities, increasing predatory interaction. We concluded that this interaction may be weak, because data from experiments with refuge fitted poorly to models. However, the high variability and the nonsignificance of the data from the experiment with refuge show the importance of refuge for promoting spatial heterogeneity, which may prevent prey extinction.

Some results on stability of retarded functional differential equations using dichotomic map techniques

This paper deals with the study of the stability of nonautonomous retarded functional differential equations using the theory of dichotomic maps. After some preliminaries, we prove the theorems on simple and asymptotic stability. Some examples are given to illustrate the application of the method. Main results about asymptotic stability of the equation x′(t) = -b(t)x(t - r) and of its nonlinear generalization x′(t) = b(t) f (x(t - r)) are established. © 1998 Kluwer Academic Publishers.

On exponential stability of functional differential equations with variable impulse perturbations

We consider a class of functional differential equations subject to perturbations, which vary in time, and we study the exponential stability of solutions of these equations using the theory of generalized ordinary differential equations and Lyapunov functionals. We introduce the concept of variational exponential stability for generalized ordinary differential equations and we develop the theory in this direction by establishing conditions for the trivial solutions of generalized ordinary differential equations to be exponentially stable. Then, we apply the results to get corresponding ones for impulsive functional differential equations. We also present an example of a delay differential equation with Perron integrable right-hand side where we apply our result.

On a class of abstract neutral functional differential equations

By using the theory of semigroups of growth α, we discuss the existence of mild solutions for a class of abstract neutral functional differential equations. A concrete application to partial neutral functional differential equations is considered.