Related papers: Low Energy Clamped Planar Elastica
In this paper we find curves minimizing the elastic energy among curves whose length is fixed and whose ends are pinned. Applying the shooting method, we can identify all critical points explicitly and determine which curve is the global…
In this letter we propose the use of physics techniques for entropy determination on constrained parameter optimization problems. The main feature of such techniques, the construction of an unbiased walk on energy space, suggests their use…
In this paper we address the challenging problem of designing globally convergent estimators for the parameters of nonlinear systems containing a non-separable exponential nonlinearity. This class of terms appears in many practical…
We derive error estimates for a linear-quadratic elliptic distributed optimal control problem with pointwise control constraints that can be applied to standard finite element methods and multiscale finite element methods.
A discretization scheme for variable coefficient elliptic PDEs in the plane is presented. The scheme is based on high-order Gaussian quadratures and is designed for problems with smooth solutions, such as scattering problems involving soft…
This article considers a model problem of elastoplasticity with linearly kinematic hardening and presents hp-finite element discretizations of two equivalent weak formulations each having their respective advantages. A mixed variational…
In the context of global/goal-oriented error estimation applied to computational mechanics, the need to obtain reliable and guaranteed bounds on the discretization error has motivated the use of residual error estimators. These estimators…
We derive an expression of the core traction contribution to the dislocation elastic energy within linear anisotropic elasticity theory using the sextic formalism. With this contribution, the elastic energy is a state variable consistent…
This study proposes a novel spatial discretization procedure for the compressible Euler equations which guarantees entropy conservation at a discrete level when an arbitrary equation of state is assumed. The proposed method, based on a…
In [Bonito et al., J. Comput. Phys. (2022)], a local discontinuous Galerkin method was proposed for approximating the large bending of prestrained plates, and in [Bonito et al., IMA J. Numer. Anal. (2023)] the numerical properties of this…
A shape sensitive, variational approach for the matching of surfaces considered as thin elastic shells is investigated. The elasticity functional to be minimized takes into account two different types of nonlinear energies: a membrane…
An error control technique aimed to assess the quality of smoothed finite element approximations is presented in this paper. Finite element techniques based on strain smoothing appeared in 2007 were shown to provide significant advantages…
Intermittent renewable energy resources like wind and solar pose great uncertainty of multiple time scales, from minutes to years, on the design and operation of power systems. Energy system optimization models have been developed to find…
We analyze a semi-explicit time discretization scheme of first order for poro\-elasticity with nonlinear permeability provided that the elasticity model and the flow equation are only weakly coupled. The approach leads to a decoupling of…
Recent developments in statistical mechanics have allowed the estimation of equilibrium free energies from the statistics of work measurements during processes that drive the system out of equilibrium. Here a different class of processes is…
We present a novel approach to probe elastic properties of polyelectrolyte multilayer microcapsules. The method is based on measurements of the capsule load-deformation curves with the atomic force microscope. The experiment suggests that…
We analyze the wave equation in mixed form, with periodic and/or Dirichlet homogeneous boundary conditions, and nonconstant coefficients that depend on the spatial variable. For the discretization, the weak form of the second equation is…
We minimize elastic energies on framed curves which penalize both curvature and torsion. We also discuss critical points using the infinite dimensional version of the Lagrange multipliers' method. Finally, some examples arising from the…
The energy level spacing distribution of a tight-binding hamiltonian is monitored across the mobility edge for a fixed disorder strength. Any mixing of extended and localized levels is avoided in the configurational averages, thus…
In this paper we consider the convergence analysis of adaptive finite element method for elliptic optimal control problems with pointwise control constraints. We use variational discretization concept to discretize the control variable and…