Remarks on formulating an adhesion problem using Euler’s elastica (draft)
نویسندگان
چکیده
Three formulations for the problem of an elastica adhering to a rigid surface are discussed and compared. These include stationary principles, the surface integral of Eshelby’s energy-momentum tensor, and the material (configurational) force balance. The configuration at static equilibrium is predicted in closed form for a pair of structures that arise in nanoand microscale applications. 2006 Elsevier Ltd. All rights reserved.
منابع مشابه
Supervised learning via Euler's Elastica models
This paper investigates the Euler’s elastica (EE) model for high-dimensional supervised learning problems in a function approximation framework. In 1744 Euler introduced the elastica energy for a 2D curve on modeling torsion-free thin elastic rods. Together with its degenerate form of total variation (TV), Euler’s elastica has been successfully applied to low-dimensional data processing such as...
متن کاملOn the Cauchy Problem for a Dynamical Euler’s Elastica
The dynamics for a thin, closed loop inextensible Euler’s elastica moving in three dimensions are considered. The equations of motion for the elastica include a wave equation involving fourth order spatial derivatives and a second order elliptic equation for its tension. A Hasimoto transformation is used to rewrite the equations in convenient coordinates for the space and time derivatives of th...
متن کاملA Fast Augmented Lagrangian Method for Euler’s Elastica Models
In this paper, a fast algorithm for Euler’s elastica functional is proposed, in which the Euler’s elastica functional is reformulated as a constrained minimization problem. Combining the augmented Lagrangian method and operator splitting techniques, the resulting saddle-point problem is solved by a serial of subproblems. To tackle the nonlinear constraints arising in the model, a novel fixed-po...
متن کاملA Fast Augmented Lagrangian Method for Euler's Elastica Model
In this paper, a fast algorithm for Euler’s elastica functional is proposed, in which the Euler’s elastica functional is reformulated as a constrained minimization problem. Combining the augmented Lagrangian method and operator splitting techniques, the resulting saddle-point problem is solved by a serial of subproblems. To tackle the nonlinear constraints arising in the model, a novel fixed-po...
متن کاملOn the moduli of a quantized elastica in P and KdV flows: Study of hyperelliptic curves as an extention of Euler’s perspective of elastica I
Quantization needs evaluation of all of states of a quantized object rather than its stationary states with respect to its energy. In this paper, we have investigated moduli Melas of a quantized elastica, a quantized loop on with an energy functional associated with the Schwarz derivative, on a Riemannian sphere P. Then we proved that its moduli is decomposed to equivalent classes determined by...
متن کامل