— Among all non-linear differential equations arising in Physics or in geometry, completely integrable systems are exceptional cases, at the concurrence of miraculous symmetry properties. This text proposes an introduction to this subject, through a list of examples (the sinh-Gordon, Toda, Korteweg-de Vries equations, the harmonic maps, the anti-self-dual connections on the four-dimensional spa...

This study investigates the impact of cross structures on flood occurrences in mountainous rivers. The governing equations open channel flow were formulated based Saint-Venant equations. was segmented, and a node equation established at each section’s connection point. An overflow model bridges weir dams also developed. physical simplified modeled using actual building data calculation requirem...

Hydraulic parameters, including bed shear stress, are challenging to calculate for flash floods. Applying theoretical equations strongly unsteady flows requires comprehensive and accurate flow data that difficult collect natural events. To empirically evaluate the extent which simpler calculations can reasonably predict stresses in rapidly changing hydrographs, determine how differ hydraulic bo...

Systems of Diierential-Algebraic Equations (DAE's) have been widely investigated, during the last twenty years, from a numerical point of view. The notion of index has shown to be eecient for the classiication of such systems with respect to the diiculties when trying to solve them with the standard discretization schemes. In this paper, our interest is in the study of formal (\structural") pro...

An isogeometric finite element formulation for geometrically and materially nonlinear Timoshenko beams is presented, which incorporates in-plane deformation of the cross-section described by two extensible director vectors. Since those directors belong to space ${\Bbb R}^3$, a configuration can be additively updated. The developed allows direct application three-dimensional constitutive equatio...