Population growth and persistence in a heterogeneous environment: the role of diffusion and advection

The spatio-temporal dynamics of a population present one of the most fascinating aspects and challenges for ecological modelling. In this article we review some simple mathematical models, based on one dimensional reaction-diffusion-advection equations, for the growth of a population on a heterogeneous habitat. Considering a number of models of increasing complexity we investigate the often contrary roles of advection and diffusion for the persistence of the population. When it is possible we demonstrate basic mathematical techniques and give the critical conditions providing the survival of a population, in simple systems and in more complex resource-consumer models which describe the dynamics of phytoplankton in a water column.Comment: Introductory review of simple conceptual models. 45 pages, 15 figures v2: minor change

Perturbation Analysis of Complete Synchronization in Networks of Phase Oscillators

The behavior of weakly coupled self-sustained oscillators can often be well described by phase equations. Here we use the paradigm of Kuramoto phase oscillators which are coupled in a network to calculate first and second order corrections to the frequency of the fully synchronized state for nonidentical oscillators. The topology of the underlying coupling network is reflected in the eigenvalues and eigenvectors of the network Laplacian which influence the synchronization frequency in a particular way. They characterize the importance of nodes in a network and the relations between them. Expected values for the synchronization frequency are obtained for oscillators with quenched random frequencies on a class of scale-free random networks and for a Erd\H{o}s-R\'enyi random network. We briefly discuss an application of the perturbation theory in the second order to network structural analysis.Comment: 19 pages, 1 figur

Perturbation Analysis of the Kuramoto Phase Diffusion Equation Subject to Quenched Frequency Disorder

The Kuramoto phase diffusion equation is a nonlinear partial differential equation which describes the spatio-temporal evolution of a phase variable in an oscillatory reaction diffusion system. Synchronization manifests itself in a stationary phase gradient where all phases throughout a system evolve with the same velocity, the synchronization frequency. The formation of concentric waves can be explained by local impurities of higher frequency which can entrain their surroundings. Concentric waves in synchronization also occur in heterogeneous systems, where the local frequencies are distributed randomly. We present a perturbation analysis of the synchronization frequency where the perturbation is given by the heterogeneity of natural frequencies in the system. The nonlinearity in form of dispersion, leads to an overall acceleration of the oscillation for which the expected value can be calculated from the second order perturbation terms. We apply the theory to simple topologies, like a line or the sphere, and deduce the dependence of the synchronization frequency on the size and the dimension of the oscillatory medium. We show that our theory can be extended to include rotating waves in a medium with periodic boundary conditions. By changing a system parameter the synchronized state may become quasi degenerate. We demonstrate how perturbation theory fails at such a critical point.Comment: 22 pages, 5 figure

Vertical distribution and composition of phytoplankton under the influence of an upper mixed layer

The vertical distribution of phytoplankton is of fundamental importance for the dynamics and structure of aquatic communities. Here, using an advection-reaction-diffusion model, we investigate the distribution and competition of phytoplankton species in a water column, in which inverse resource gradients of light and a nutrient can limit growth of the biomass. This problem poses a challenge for ecologists, as the location of a production layer is not fixed, but rather depends on many internal parameters and environmental factors. In particular, we study the influence of an upper mixed layer (UML) in this system and show that it leads to a variety of dynamic effects: (i) Our model predicts alternative density profiles with a maximum of biomass either within or below the UML, thereby the system may be bistable or the relaxation from an unstable state may require a long-lasting transition. (ii) Reduced mixing in the deep layer can induce oscillations of the biomass; we show that a UML can sustain these oscillations even if the diffusivity is less than the critical mixing for a sinking phytoplankton population. (iii) A UML can strongly modify the outcome of competition between different phytoplankton species, yielding bistability both in the spatial distribution and in the species composition. (iv) A light limited species can obtain a competitive advantage if the diffusivity in the deep layers is reduced below a critical value. This yields a subtle competitive exclusion effect, where the oscillatory states in the deep layers are displaced by steady solutions in the UML. Finally, we present a novel graphical approach for deducing the competition outcome and for the analysis of the role of a UML in aquatic systems.Comment: 20 pages, 8 figure

Quasi regular concentric waves in heterogeneous lattices of coupled oscillators

We study the pattern formation in a lattice of coupled phase oscillators with quenched disorder. In the synchronized regime concentric waves can arise, which are induced and increase in regularity by the disorder of the system. Maximal regularity is found at the edge of the synchronization regime. The emergence of the concentric waves is related to the symmetry breaking of the interaction function. An explanation of the numerically observed phenomena is given in a one-dimensional chain of coupled phase oscillators. Scaling properties, describing the target patterns are obtained.Comment: 4 pages, 3 figures, submitted to PR

Viking orbiter stereo imaging catalog

The extremely long mission of the two Viking Orbiter spacecraft produced a wealth of photos of surface features. Many of these photos can be used to form stereo images allowing the student of Mars to examine a subject in three dimensional. This catalog is a technical guide to the use of stereo coverage within the complex Viking imaging data set

Kajian Habitat Tumbuhan Obat Di Taman Wisata Alam Camplong

Study on Medical Plants Habitat in Taman Wisata Alam Camplong. The research aimed to find out the habitat condition of medical plants in Taman Wisata Alam Camplong covering, structure and composition of vegetation, as well as accentual and threat to the medical plants habitat. Collecting data of medical plants habitat covered habitat type, structural and composition of vegetation and accentual/threat to habitat of the plants. Those data were obtained through stocktaking and were analyzed using vegetation analysis. Samples were acquired at line plot of 20 x 1000 m. The line plot, hereinafter, was divided into smaller, depended on growth level and life model of the plants observed. Data of INP (Indeks Nilai Penting = Important Value Index) was to know type of dominant plant (Soerianegara and Indrawan, 1998). The results indicated that habitat type in the area of TWA Camplong included semi fall forest. The highest INP of tree was 42,4884 at taduk (Alstonia scholaris), while, the lowest INP was at papi (wild sandalwood), that is 0,8538. In level of pillar, the highest INP was 46,3083 at guava species, and the lowest was 2,4062 at haubiabnapa, tati'i, nangkelo. In the stake level, the highest INP was 40,8617 at bamboo and the lowest INP was 2,1032 at haumanikin. In seedling level, the highest INP was 90,4850 at kirinyu (Chromolena odorata); while, the lowest INP was at talas (INP = 0,9561)

Slower Speed and Stronger Coupling: Adaptive Mechanisms of Self-Organized Chaos Synchronization

We show that two initially weakly coupled chaotic systems can achieve self-organized synchronization by adaptively reducing their speed and/or enhancing the coupling strength. Explicit adaptive algorithms for speed-reduction and coupling-enhancement are provided. We apply these algorithms to the self-organized synchronization of two coupled Lorenz systems. It is found that after a long-time self-organized process, the two coupled chaotic systems can achieve synchronization with almost minimum required coupling-speed ratio.Comment: 4 pages, 5 figure

The Influence of Application System Quality Control in the Performance of Auditors (Empirical Studies) ABC Kap in South Jakarta in 2009 – 2013

This study has the objective to determine the effect the independence, professionalism, professional ethics and integrity of client understanding of the performance of the auditors on an empirical study of the public accounting firm ABC in South Jakarta. The method used in sampling is convenience sampling. The number of questionnaires distributed 150 questionnaires. However, the back and can be used for further analysis of 120 questionnaires. Analysis of the data is to use multiple linear regression coefficient of determination see, the value of F statistics and statistical t. Results of this study showed that the independence, professionalism and ethics of the profession positive effect on the performance of auditors while understanding client integrity negative effect on the performance of auditors