Global Production Increased by Spatial Heterogeneity in a Population Dynamics Model

Spatial and temporal heterogeneity are often described as important factors having a strong impact on biodiversity. The effect of heterogeneity is in most cases analyzed by the response of biotic interactions such as competition of predation. It may also modify intrinsic population properties such as growth rate. Most of the studies are theoretic since it is often difficult to manipulate spatial heterogeneity in practice. Despite the large number of studies dealing with this topics, it is still difficult to understand how the heterogeneity affects populations dynamics. On the basis of a very simple model, this paper aims to explicitly provide a simple mechanism which can explain why spatial heterogeneity may be a favorable factor for production.We consider a two patch model and a logistic growth is assumed on each patch. A general condition on the migration rates and the local subpopulation growth rates is provided under which the total carrying capacity is higher than the sum of the local carrying capacities, which is not intuitive. As we illustrate, this result is robust under stochastic perturbations

Aggregation methods in dynamical systems and applications in population and community dynamics

Approximate aggregation techniques allow one to transform a complex system involving many coupled variables into a simpler reduced model with a lesser number of global variables in such a way that the dynamics of the former can be approximated by that of the latter. In ecology, as a paradigmatic example, we are faced with modelling complex systems involving many variables corresponding to various interacting organization levels. This review is devoted to approximate aggregation methods that are based on the existence of different time scales, which is the case in many real systems as ecological ones where the different organization levels (individual, population, community and ecosystem) possess a different characteristic time scale. Two main goals of variables aggregation are dealt with in this work. The first one is to reduce the dimension of the mathematical model to be handled analytically and the second one is to understand how different organization levels interact and which properties of a given level emerge at other levels. The review is organized in three sections devoted to aggregation methods associated to different mathematical formalisms: ordinary differential equations, infinite-dimensional evolution equations and difference equations

A new composition-sensitive parameter for Ultra-High Energy Cosmic Rays

A new family of parameters intended for composition studies in cosmic ray surface array detectors is proposed. The application of this technique to different array layout designs has been analyzed. The parameters make exclusive use of surface data combining the information from the total signal at each triggered detector and the array geometry. They are sensitive to the combined effects of the different muon and electromagnetic components on the lateral distribution function of proton and iron initiated showers at any given primary energy. Analytical and numerical studies have been performed in order to assess the reliability, stability and optimization of these parameters. Experimental uncertainties, the underestimation of the muon component in the shower simulation codes, intrinsic fluctuations and reconstruction errors are considered and discussed in a quantitative way. The potential discrimination power of these parameters, under realistic experimental conditions, is compared on a simplified, albeit quantitative way, with that expected from other surface and fluorescence estimators.Comment: 27 pages, 17 figures. Submitted to a refereed journa

Elements Discrimination in the Study of Super-Heavy Elements using an Ionization Chamber

Dedicated ionization chamber was built and installed to measure the energy loss of very heavy nuclei at 2.7 MeV/u produced in fusion reactions in inverse kinematics (beam of 208Pb). After going through the ionization chamber, products of reactions on 12C, 18O targets are implanted in a Si detector. Their identification through their alpha decay chain is ambiguous when their half-life is short. After calibration with Pb and Th nuclei, the ionization chamber signal allowed us to resolve these ambiguities. In the search for rare super-heavy nuclei produced in fusion reactions in inverse or symmetric kinematics, such a chamber will provide direct information on the nuclear charge of each implanted nucleus.Comment: submitted to NIMA, 10 pages+4 figures, Latex, uses elsart.cls and grahpic

Response of CsI(Tl) scintillators over a large range in energy and atomic number of ions (Part I): recombination and delta -- electrons

A simple formalism describing the light response of CsI(Tl) to heavy ions, which quantifies the luminescence and the quenching in terms of the competition between radiative transitions following the carrier trapping at the Tl activator sites and the electron-hole recombination, is proposed. The effect of the delta rays on the scintillation efficiency is for the first time quantitatively included in a fully consistent way. The light output expression depends on four parameters determined by a procedure of global fit to experimental data.Comment: 28 pages, 6 figures, submitted to Nucl. Inst. Meth.

Fragmentation in Peripheral Heavy-Ion Collisions: from Neck Emission to Spectator Decays

Invariant cross sections of intermediate mass fragments in peripheral collisions of Au on Au at incident energies between 40 and 150 AMeV have been measured with the 4-pi multi-detector INDRA. The maximum of the fragment production is located near mid-rapidity at the lower energies and moves gradually towards the projectile and target rapidities as the energy is increased. Schematic calculations within an extended Goldhaber model suggest that the observed cross-section distributions and their evolution with energy are predominantly the result of the clustering requirement for the emerging fragments and of their Coulomb repulsion from the projectile and target residues. The quantitative comparison with transverse energy spectra and fragment charge distributions emphasizes the role of hard scattered nucleons in the fragmentation process.Comment: 5 pages, 5 eps figures, RevTeX4, submitted to Phys. Lett.

Multifragmentation process for different mass asymmetry in the entrance channel around the Fermi energy

The influence of the entrance channel asymmetry upon the fragmentation process is addressed by studying heavy-ion induced reactions around the Fermi energy. The data have been recorded with the INDRA 4pi array. An event selection method called the Principal Component Analysis is presented and discussed. It is applied for the selection of central events and furthermore to multifragmentation of single source events. The selected subsets of data are compared to the Statistical Multifragmentation Model (SMM) to check the equilibrium hypothesis and get the source characteristics. Experimental comparisons show the evidence of a decoupling between thermal and compresional (radial flow) degrees of freedom in such nuclear systems.Comment: 28 pages, 15 figures, article sumitted to Nuclear Physics

Multifragmentation in Xe(50A MeV)+Sn Confrontation of theory and data

We compare in detail central collisions Xe(50A MeV) + Sn, recently measured by the INDRA collaboration, with the Quantum Molecular Dynamics (QMD) model in order to identify the reaction mechanism which leads to multifragmentation. We find that QMD describes the data quite well, in the projectile/target region as well as in the midrapidity zone where also statistical models can be and have been employed. The agreement between QMD and data allows to use this dynamical model to investigate the reaction in detail. We arrive at the following observations: a) the in medium nucleon nucleon cross section is not significantly different from the free cross section, b) even the most central collisions have a binary character, c) most of the fragments are produced in the central collisions and d) the simulations as well as the data show a strong attractive in-plane flow resembling deep inelastic collisions e) at midrapidity the results from QMD and those from statistical model calculations agree for almost all observables with the exception of ${d^2 \sigma \over dZdE}$. This renders it difficult to extract the reaction mechanism from midrapidity fragments only. According to the simulations the reaction shows a very early formation of fragments, even in central collisions, which pass through the reaction zone without being destroyed. The final transverse momentum of the fragments is very close to the initial one and due to the Fermi motion. A heating up of the systems is not observed and hence a thermal origin of the spectra cannot be confirmed.Comment: figures 1 and 2 changed (no more ps -errors

Effect of the intermediate velocity emissions on the quasi-projectile properties for the Ar+Ni system at 95 A.MeV

The quasi-projectile (QP) properties are investigated in the Ar+Ni collisions at 95 A.MeV taking into account the intermediate velocity emission. Indeed, in this reaction, between 52 and 95 A.MeV bombarding energies, the number of particles emitted in the intermediate velocity region is related to the overlap volume between projectile and target. Mean transverse energies of these particles are found particularly high. In this context, the mass of the QP decreases linearly with the impact parameter from peripheral to central collisions whereas its excitation energy increases up to 8 A.MeV. These results are compared to previous analyses assuming a pure binary scenario

Multifragmentation of a very heavy nuclear system (I): Selection of single-source events

A sample of `single-source' events, compatible with the multifragmentation of very heavy fused systems, are isolated among well-measured 155Gd+natU 36AMeV reactions by examining the evolution of the kinematics of fragments with Z>=5 as a function of the dissipated energy and loss of memory of the entrance channel. Single-source events are found to be the result of very central collisions. Such central collisions may also lead to multiple fragment emission due to the decay of excited projectile- and target-like nuclei and so-called `neck' emission, and for this reason the isolation of single-source events is very difficult. Event-selection criteria based on centrality of collisions, or on the isotropy of the emitted fragments in each event, are found to be inefficient to separate the two mechanisms, unless they take into account the redistribution of fragments' kinetic energies into directions perpendicular to the beam axis. The selected events are good candidates to look for bulk effects in the multifragmentation process.Comment: 39 pages including 15 figures; submitted to Nucl. Phys.