In this paper, the theory of abstract splines is applied to the variational refinement of (periodic) curves that meet data to within convex sets in IR. The analysis is relevant to each level of refinement (the limit curves are not considered here). The curves are characterized by an application of a separation theorem for multiple convex sets, and represented as the solution of an equation invo...

The dynamic response of component bolted joints often plays a significant role in the overall behavior of a structural system. Accurate finite element simulation of these problems requires proper treatment of the interface conditions. We present a formulation carefully suited to these problems that incorporates discontinuous Galerkin (DG) treatment locally at the interface. The present work is ...

Article history: Received 26 March 2014 Received in revised form 25 September 2014 Accepted 27 September 2014 Available online 15 October 2014

Variational integrators [1] are geometric integrators that are symplectic, momentum-preserving and have an excellent long-time energy behavior. This means that energy (for conservative systems) or the energy rate (for systems with external forces) is on average preserved in the discrete solution even for large step sizes, i.e., there is no numerical energy dissipation or generation. Variational...

We propose a variational method to solve all three estimation problems for nonlinear stochastic dynamical systems: prediction, filtering, and smoothing. Our new approach is based upon a proper choice of cost function, termed the effective action. We show that this functional of time-histories is the unique statistically well-founded cost function to determine most probable histories within empi...

We consider a variational problem for the two-dimensional (2D) Heisenberg and XY models, using a trial state which is constructed as a 2D product of local weights. Variational energy is calculated by use of the the corner transfer matrix renormalization group (CTMRG) method, and its upper bound is surveyed. The variational approach is a way of applying the density matrix renormalization group m...

Many edge detection techniques exhibit scale-dependent distortion of edges. We develop two ideas, which may also be of independent interest, to produce sharp edge localization at all scales. The first is approximation of the functional associated with the variational formulation via epi-convergence, replacing the edge set with a function. We provide a fast algorithm for minimizing the approxima...

We present a class of constitutive updates for general viscoplastic solids including such aspects of material behavior as nite elastic and plastic deformations, non-Newtonian viscosity, rate-sensitivity and arbitrary ow and hardening rules. The distinguishing characteristic of the proposed constitutive updates is that, by construction, the corresponding incremental stress-strain relations deriv...