In this paper, we present the exact solution of the Riemann problem for the nonlinear one-dimensional so-called shallow-water or Saint-Venant equations with friction proposed by SAVAGE and HUTTER to describe debris avalanches. This model is based on the depth-averaged thin layer approximation of granular flows over sloping beds and takes into account a Coulomb type friction law with a constant ...

We consider general nanotubes of atoms in R3 where each atom interacts with all others through a two-body potential. When there are no exterior forces, a particular family of nanotubes is the set of perfect nanotubes at the equilibrium. When exterior forces are applied on the nanotube, we compare the nanotube to nanotubes of the previous family. This quantitative comparison is formulated in our...

A new high-performance numerical model (Frehg) is developed to simulate water flow in shallow coastal wetlands. Frehg solves the 2D depth-integrated, hydrostatic, Navier–Stokes equations (i.e., shallow-water equations) surface domain and 3D variably-saturated Richards equation subsurface domain. The two domains are asynchronously coupled surface-subsurface exchange. applied evaluate sensitivity...

A layer-wise third order shear and normal deformable plate/shell theory (TSNDT) incorporating all geometric nonlinearities is used to study finite transient deformations of a curved laminated beam composed of a St. Venant–Kirchhoff material. In the TSNDT all displacement components of a point are expressed as 3rd order polynomials in the thickness coordinate in each layer while maintaining the ...

Within this work, we upscale the equations that describe pore-scale behaviour of nonlinear porous elastic composites, using asymptotic homogenization technique in order to derive macroscale effective governing equations. A hyperelastic composite can be thought as being comprised a matrix interacting with number subphases and percolated by fluid flowing pores (which is chosen Newtonian incompres...

In this article we study the so-called water tank system. system, behavior of contained in a 1-D is modelled by Saint-Venant equations, with scalar distributed control. It well-known that linearized systems around uniform steady-states are not controllable, uncontrollable part being infinite dimension. Here will focus on non-uniform steady states, corresponding to constant acceleration tank. We...

We solve the feedback stabilization problem for a tank, with friction, containing liquid modeled by viscous Saint-Venant system of Partial Differential Equations. A spill-free exponential is achieved, robustness to wall friction forces. Control Lyapunov Functional (CLF) methodology two different functionals employed. These determine specific parameterized sets which approximate state space. The...

An integrated approach to the design of an automatic control system for canals using a Linear Quadratic Gaussian regulator based on recursive least squares estimation was developed. The one-dimensional partial differential equations describing open channel flow (Saint-Venant) equations are linearized about an average operating condition of the canal. The concept of optimal control theory is app...

We consider multi-dimensional extensions of Maxwell’s seminal rheological equation for 1D viscoelastic flows. aim at a causal model compressible flows, defined by semi-group solutions given initial conditions, and such that perturbations propagate finite speed. propose symmetric hyperbolic system conservation laws contains the Upper-Convected Maxwell (UCM) as model. The is an extension polyconv...