We estimate the price elasticity of water demand with household-level data, structurally modeling the piecewise-linear budget constraints imposed by increasing block pricing. We develop a mathematical expression for the unconditional price elasticity of demand under increasing block prices and compare conditional and unconditional elasticities analytically and empirically. We test the hypothesi...

In this paper we obtain the constitutive equation for the second Piola-Kirchhoff stress tensor according to the linearized finite theory of elasticity for hyperelastic constrained materials. We show that in such a theory the three stress tensors (Cauchy stress tensor, first and second Piola-Kirchhoff stress tensor) differ by terms that are first order in the strain, while in classical linear th...

We propose a discontinuous Galerkin method for linear elasticity, based on discontinuous piecewise linear approximation of the displacements. We show optimal order a priori error estimates, uniform in the incompressible limit, and thus locking is avoided. The discontinuous Galerkin method is closely related to the non-conforming Crouzeix–Raviart (CR) element, which in fact is obtained when one ...

What relationship does (â, b̂) bear to (α, β) in the original model and can we hope to say anything reasonable having made this initial specification error? In Figure 1, we can examine a specific version of this situation in which (α, β) = (1, .5) and the variance of ui is quite small. Clearly we don’t do a very good job of estimating the curve represented by the observed points by the line indi...

We present a model for disordered 3D fiber networks to study their linear and nonlinear elasticity. In contrast to previous 2D models, these 3D networks with binary crosslinks are underconstrained with respect to fiber stretching elasticity, suggesting that bending may dominate their response. We find that such networks exhibit a bending-dominated elastic regime controlled by fiber length, as w...

We consider a variational antiplane lattice model and demonstrate that at zero temperature, there exist locally stable states containing screw dislocations, given conditions on the distance between the dislocations and on the distance between dislocations and the boundary of the crystal. In proving our results, we introduce approximate solutions which are taken from the theory of dislocations i...

The goal of this work is to construct and study hybrid and multiplicative two-level overlapping Schwarz algorithms with standard coarse spaces for the almost incompressible linear elasticity and Stokes systems, discretized by mixed finite and spectral element methods with discontinuous pressures. Two different approaches are considered to solve the resulting saddle point systems: a) a precondit...

In this work, the robustness of the fluid-structure interaction simulation with a nearly incompressible elasticity model from our previous work [Partitioned solvers for the fluid-structure interaction problems with a nearly incompressible elasticity model, Comput Visual Sci, 14:227-247, 2012] is improved. At each time step of the FSI simulation, using properly chosen elementwise stabilization p...

We present new rectangular mixed finite elements for linear elasticity. The approach is based on a modification of the Hellinger-Reissner functional in which the symmetry of the stress field is enforced weakly through the introduction of a Lagrange multiplier. The elements are analogues of the lowest order elements described in Arnold, Falk and Winther [ Mixed finite element methods for linear ...

The classical linear elasticity theory is based on the assumption that the size of the displacement gradient tensor is small. In many engineering applications, although the basic assumption is violated due to, e.g., corner singularities, the linear elasticity system is still used to approximate the reality. In this paper, we give a-posteriori error analysis for the eeect of the linearization on...