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 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

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

Modal Sosial Sebagai Suatu Aspek Dalam Rangka Pemberdayaan Masyarakat

Credit Union (CU) merupakan bagian dari Koperasi Simpan Pinjam, dimana CU bernaung dibawah Induk Koperasi Kredit (Inkopdit). Pada tahun 1852 dan 1864 koperasi ini kemudian dikembangkan oleh Herman Schulze Delitzsch dan Friedrich Wilhelm Raiffeisen menjadi Credit Union (CU).Pada tahun 1975 mulai diperkenalkan Credit Union ke Kalimantan Barat oleh CUCO Indonesia (Credit Union Counselling Office) yang berpusat di Jakarta. Penelitian ini merupakan penelitian deskriptif yang menggunakan pendekatan kualitatif bertujuan menjelaskan modal sosial sebagai suatu aspek dalam rangka pemberdayaan masyarakat di dalam Credit Union Bonaventura Tempat Pelayanan Ledo serta USAha mereka dalam memberdayakan para anggotanya. Penelitian ini dilaksanakan pada Credit Union Bonaventura Tempat Pelayanan Ledo, dengan waktu penelitian mulai bulan Januari 2017 sampai bulan Desember 2017. Populasi target penelitian adalah anggota, calon anggota, masyarakat umum, pengurus, dan manajemen Credit Union Bonaventura TP Ledo. Teknikdalammenentukansumber data primer atau informan adalah purposive sampling melalui key person