We describe and analyze an approach to the pure Neumann problem of three-dimensional linearized elasticity, whose novelty consists in considering the strain tensor field as the sole unknown, instead of the displacement vector field as is customary. This approach leads to a well-posed quadratic minimization problem of a new type, constrained by a weak form of the classical Saint Venant compatibi...

Sunto. Si considera uno spazio omogeneo X = (X, d,m) di dimensione ν ≥ 1 e una forma di Dirichlet locale regolare in L (X,m) . Si dimostra che se una disuguaglianza di Poincaré vale su ogni pseudo-sfera B (x,R) di X , con costanti caratteristiche locali c0 (x) e c1 (r), allora si ricava una stima della funzione di Green da sopra e da sotto. Il principio tipo Saint-Venant viene ottenuto in termi...

This article is devoted to the proof of the hydrodynamical limit from kinetic equations (including BGK-like equations) to multidimensional isentropic gas dynamics. It is based on a relative entropy method; hence the derivation is valid only before shocks appear on the limit system solution. However, no a priori knowledge on high velocity distributions for kinetic functions is needed. The case o...

Using backstepping design, exponential stabilization of the linearized Saint-Venant–Exner (SVE) model of water dynamics in a sediment-filled canal with arbitrary values of canal bottom slope, friction, porosity, andwater–sediment interaction, is achieved. The linearized SVEmodel consists of two rightward convecting transport Partial Differential Equations (PDEs) and one leftward convecting tran...

We consider an elastic hollow sphere with midsurface radius R and thickness 2h which is subjected to two equal and opposite concentrated loads acting at the ends of a diameter. The three-dimensional linear elasticity solution to this problem consists of (i) a narrow Saint Venant component extending a distance of order O(h) from each load point, (ii) a wider “edge bending” component extending a ...

2014 We compute the high frequency elastic distortion of a columnar discotic single crystal submitted to a longitudinal dilation. The ends of the columns are assumed to be clamped and anchored perpendicularly to two infinitely rigid glass plates, on a width L. The local strain close to the plates relaxes to the homogeneous distortion of an unclamped sample on a characteristic length £ ~ (Lm)1/2...

Continental River Dynamics (CRD) is herein defined as modelling the flow dynamics in all channels of a continental-scale river basin using the physics-based Saint-Venant equations. At the boundary of hydraulics and hydrology, CRD requires significant collaborative efforts to make new progress. Six constraints and seven challenges are identified in the areas of dynamics, dimensionality, resoluti...

In this paper we apply the method proposed in our previous paper [Int. J. Solids Struct. 40(13–14) (2003) 3293] to quantitatively estimate the violation of Saint-Venant s principle in the problem of flexural vibration of a two-dimensional strip. A probabilistic approach is used to determine the relative magnitude of the penetrating stress state and the results of computations are presented as a...