Geometric Methods for Efficient Planar Swimming of Copepod Nauplii

Copepod nauplii are larval crustaceans with important ecological functions. Due to their small size, they experience an environment of low Reynolds number within their aquatic habitat. Here we provide a mathematical model of a swimming copepod nauplius with two legs moving in a plane. This model allows for both rotation and two-dimensional displacement by the periodic deformation of the swimmer’s body. The system is studied from the framework of optimal control theory, with a simple cost function designed to approximate the mechanical energy expended by the copepod. We find that this model is sufficiently realistic to recreate behavior similar to those of observed copepod nauplii, yet much of the mathematical analysis is tractable. In particular, we show that the system is controllable, but there exist singular configurations where the degree of non-holonomy is non-generic. We also partially characterize the abnormal extremals and provide explicit examples of families of abnormal curves. Finally, we numerically simulate normal extremals and observe some interesting and surprising phenomena.

Struktur Komunitas Plankton Perairan Payau di Kecamatan Wedung Kabupaten Demak

Aquaculture are highly prioritized by the government to support the economy. Products from the aquaculture sector is also targeted as a source of income to the Indonesian country. Aquaculture needs to improve to manage water quality, especially plankton to support natural food of the fish. This study aims to examines structure of plankton community in the brackish waters of the District Wedung and then examines the water quality with environmental quality standards of water the cultivation. Research was conducted in February-April 2015. The method used to analyze data that plankton with uses keanekargaman index (H ') and the perataan index ( e ). The results showed that the number of species (genera) plankton obtained during research in the waters of the District Wedung was 45 species, these types consist of 37 species of phytoplankton and zooplankton 8 types. The most common plankton species found in all the stations were Fragillaria sp, Synedra ulna, Oscillatoria formosa and Copepod nauplius. Index of species diversity that existed at the District Wedung moderate to high waters with a range from 1.69 to 2.91 therefore a complex community and stability of the ecosystem were moderate to high. The evennes index ranged from 0.63 to 0.85. Water quality based on the pH, salinity, Turbidity, N, P and organic materials are less good for the cultivation so that the necessary processing on the pond so that according to the criteria of the quality standards of water quality. Keywords: structure of plankton communities, brackish waters, District Wedung