Hamilton-Pontryagin Principle for Incompressible Ideal Fluids

2011 ◽  
Author(s):  
Hiroaki Yoshimura ◽  
François Gay-Balmaz ◽  
Jiachun Li ◽  
Song Fu
Keyword(s):  
Pontryagin Principle ◽  
Ideal Fluids

scholarly journals Hamiltonian Aspects of Three-Layer Stratified Fluids

2021 ◽  
Vol 31 (4) ◽  
Author(s):  
R. Camassa ◽  
G. Falqui ◽  
G. Ortenzi ◽  
M. Pedroni ◽  
T. T. Vu Ho
Keyword(s):  
Hamiltonian Structure ◽  
Linear Equations ◽  
Hamiltonian Formalism ◽  
Reduction Process ◽  
Ideal Fluids ◽  
Upper Lid ◽  
Stratification Structure ◽  
Special Solutions ◽  
Dispersionless Limit ◽  
Unbounded Fluid

AbstractThe theory of three-layer density-stratified ideal fluids is examined with a view toward its generalization to the n-layer case. The focus is on structural properties, especially for the case of a rigid upper lid constraint. We show that the long-wave dispersionless limit is a system of quasi-linear equations that do not admit Riemann invariants. We equip the layer-averaged one-dimensional model with a natural Hamiltonian structure, obtained with a suitable reduction process from the continuous density stratification structure of the full two-dimensional equations proposed by Benjamin. For a laterally unbounded fluid between horizontal rigid boundaries, the paradox about the non-conservation of horizontal total momentum is revisited, and it is shown that the pressure imbalances causing it can be intensified by three-layer setups with respect to their two-layer counterparts. The generator of the x-translational symmetry in the n-layer setup is also identified by the appropriate Hamiltonian formalism. The Boussinesq limit and a family of special solutions recently introduced by de Melo Viríssimo and Milewski are also discussed.

scholarly journals Euler equations for incompressible ideal fluids

2007 ◽  
Vol 62 (3) ◽  
pp. 409-451 ◽  
Author(s):  
Claude Bardos ◽  
Edriss Titi
Keyword(s):  
Euler Equations ◽  
Ideal Fluids

scholarly journals KENDALI OPTIMAL PERTUMBUHAN POPULASI ECENG GONDOK DENGAN IKAN GRASS CRAP DAN PEMANENAN

2019 ◽  
Vol 20 (2) ◽  
pp. 132-141
Author(s):  
Fitroh Resmi ◽  
Settings Aris Alfan ◽  
Slamet Ifandi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Grass Carp ◽  
Water Hyacinth ◽  
Aquatic Plant ◽  
Pontryagin Principle ◽  
Paddy Irrigation ◽  
Irrigation Channels ◽  
Natural Predator ◽  
Predator System

Water hyacinth is a wild aquatic plant that grows quickly. The growth of water hyacinth need to be controled to prevent the flood and not to disturb paddy irrigation channels. Grass carp as herbivorous fish is used as natural predator to reduce the population of water hyacinth. The interaction between water hyacinth and grass carp is modeled using the prey-predator system. In this model there are harvest factors and predation factors using Holling type III. The optimal control problem is applied to minimize the mass of water hyacinth and harvest efforts of water hyacinth and maximize the mass of grass carp. The solution uses the Pontryagin Principle. The result is the harvesting of water hyacinth and the grass carp can minimize the water hyacinth biomass at the end of time. Eceng gondok merupakan tanaman liar di perairan yang tumbuh dengan cepat. Pertumbuhannya perlu dikendalikan agar tidak menyebabkan banjir dan tidak mengganggu saluran irigasi persawahan. Ikan grass carp sebagai ikan herbivora digunakan sebagai predator alami untuk mengurangi populasi eceng gondok. Hubungan antara eceng gondok dan ikan grass carp dimodelkan dengan menggunakan sistem prey-predator. Pada model ini terdapat faktor pemanenan dan faktor predasi menggunakan Holling tipe III. Masalah kendali optimal diterapkan dengan tujuan untuk meminimumkan massa eceng gondok dan usaha pemanenan eceng gondok serta memaksimumkan massa ikan grass carp. Penyelesaiannya menggunakan Prinsip Pontryagin. Hasilnya dengan adanya usaha pemanenan eceng gondok dan pengadaan ikan grass carp dapat meminimumkan biomassa eceng gondok di waktu akhir.

Multi-reservoir design using Pontryagin principle

2002 ◽  
Vol 25 (6) ◽  
pp. 677-687 ◽  
Author(s):  
Hirad Mousavi ◽  
A.S. Ramamurthy
Keyword(s):  
Pontryagin Principle ◽  
Reservoir Design

Bernoulli’s Equation (Mechanics of Ideal Fluids)

2016 ◽  
pp. 89-97
Author(s):  
Hajime Akimoto ◽  
Yoshinari Anoda ◽  
Kazuyuki Takase ◽  
Hiroyuki Yoshida ◽  
Hidesada Tamai
Keyword(s):  
Bernoulli’S Equation ◽  
Ideal Fluids
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