A variational principle is used to derive a new radiation boundary condition for the two-dimensional wave equation. This boundary condition is obtained from an expression for the local energy flux velocity on the boundary in normal direction. The wellposedness of the wave equation with this boundary condition is analyzed by investigating the energy of the system. Results obtained with this (non...

We propose a convex variational approach to space-time reconstruction which estimates surface normal information and integrates it into the photoconsistency estimation as well as into an anisotropic spatio-temporal total variation regularization. As such the proposed method generalizes the works [4], [5]. Although [4] already studied anisotropic regularization they did not estimate normals but ...

Quasi-Normal Modes are used to characterize transmission resonances in 1D optical defect cavities and the related field approximations. We specialize to resonances inside the bandgap of the periodic multilayer mirrors that enclose the defect cavities. Using a template with the most relevant QNMs a variational principle permits to represent the field and the spectral transmission close to resona...

We analyze coupled optical defect cavities realized in finite one-dimensional Photonic Crystals. Viewing these as open systems where waves are permitted to leave the structures, one obtains eigenvalue problems for complex frequencies (eigenvalues) and Quasi-Normal-Modes (eigenfunctions). Single defect structures (photonic crystal atoms) can be viewed as elementary building blocks for multiple-d...

We present a unified computational framework which properly implements the smoothness constraint to generate descriptions in terms of surfaces, regions, curves, and labelled junctions, from sparse, noisy, binary data in 2-D or 3-D. Each input site can be a point, a point with an associated tangent direction, a point with an associated normal direction, or any combination of the above. The metho...

New principles are introduced for the formulation of dynamic problems in viscoelasticity for the most general case of anisotropy. One is a variational principle derived from irreversible thermodynamics. The other a correspondence principle between viscoelasticity and elasticity. Applications to the mmics of viscoelastic plates and rods are developed as examples. The variational principles are a...

In this paper, a high-precision eigenmode-computation analysis of arbitrary azimuthal mode numbers in periodic disc-loaded structure based on variational method will be discussed. It allows for rounding the edge of a disk hole without any approximation in shape treatment and calculates the modes exactly synchronous to the beam. It converges much faster than the mesh-based computer code. Good ag...

In this paper we consider the analogue of the Courant nodal domain theorem for the nonlinear eigenvalue problem for the p-Laplacian. In particular we prove that if uln is an eigenfunction associated with the nth variational eigenvalue, ln, then uln has at most 2n−2 nodal domains. Also, if uln has n+k nodal domains, then there is another eigenfunction with at most n−k nodal domains. © 2002 Elsev...

We provide an index formula for solutions of variational inequality problems defined by a continuously differentiable function F over a convex set M represented by a finite number of inequality constraints. Our index formula can be applied when the solutions are non-singular and possibly degenerate, as long as they also satisfy the injective normal map (INM) property, which is implied by strong...

We establish two global bounds measuring the distance from any vector to the solution set of the co-coercive variational inequality. To prove our results, we use the fact that the co-coercivity condition is sufficient for the (strong) monotonicity of (perturbed) fixed point and normal maps associated with variational inequalities.