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...

In recent years, total variation (TV) and Euler’s elastica (EE) have been successfully applied to image processing tasks such as denoising and inpainting. This paper investigates how to extend TV and EE to the supervised learning settings on high dimensional data. The supervised learning problem can be formulated as an energy functional minimization under Tikhonov regularization scheme, where t...

As expressed in the Gestalt law of good continuation, human perception tends to associate stimuli that form smooth continuations. Contextual modulation in primary visual cortex, in the form of association fields, is believed to play an important role in this process. Yet a unified and principled account of the good continuation law on the neural level is lacking. In this study we introduce a po...

In a study of the peripheral arteries of foetuses it was found that focal areas of intimal thickening and of splitting of the internal elastica had developed, the thickening being similar to that found in the coronary arteries. Characteristically the thickenings were found in the mouths of branches and in those vessels subject to pulsation. It is believed that they are physiological in nature a...

Soft robots are notoriously hard to control. This is partly due the scarcity of models and simulators able capture their complex continuum mechanics, resulting in a lack control methodologies that take full advantage body compliance. Currently available methods either too computational demanding or overly simplistic physical assumptions, leading paucity simulation resources for developing such ...

A rod covering a fixed span is loaded at the middle with a transverse force, such that with increasing load a progressive deflection occurs. After a certain initial deflection, a phenomenon is observed where two points of the rod come in contact with each other. This is defined as the 'dripping point' and is when 'self-encapsulation' of the elastic rod occurs. Dripping seems at a first glance t...

A new nonlinear model for large deflections of a beam is proposed. It comprises the Euler-Bernoulli boundary value problem for the deflection and a nonlinear integral condition. When bending does not alter the beam length, this condition guarantees that the deflected beam has the original length and fixes the horizontal displacement of the free end. The numerical results are in good agreement w...

We prove a result concerning the approximation of the elastica functional with a sequence of second order functionals, under radial symmetry assumptions. This theorem is strictly related to a conjecture of De Giorgi [8].

A coordinate-free Lie-group formulation for generating ensembles of DNA conformations in solution is presented. In this formulation, stochastic differential equations define sample paths on the Euclidean motion group. The ensemble of these paths exhibits the same behavior as solutions of the Fokker-Planck equation for the stochastically forced elastica. Longer chains for which the effects of ex...

In this paper, we consider the L2-gradient flow for modified p-elastic energy defined on planar closed curves. We formulate a notion of weak solution and prove existence global-in-time solutions with p≥2 initial curves in space via minimizing movements. Moreover, unique to p=2 obtain their subconvergence an elastica as t→∞. Nous nous penchons sur le flot de gradient L2 l'équation p-élastique mo...