We have developed a fully nonlocal model to describe the dynamic behavior of nematic liquid-crystal elastomers. The free energy, incorporating both elastic and nematic contributions, is a function of the material displacement vector and the orientational order parameter tensor. The free energy cost of spatial variations of these order parameters is taken into account through nonlocal interactio...

This work deals with the use of the conjugate gradient method in conjunction with an adjoint problem formulation for the simultaneous estimation of the spatially varying diffusion coefficient and of the source term distribution in a one-dimensional nonlinear diffusion problem. In the present approach, no a priori assumption is required regarding the functional form of the unknowns. This work ca...

Nonlocal gradient operators are basic elements of nonlocal vector calculus that play important roles in nonlocal modeling and analysis. In this work, we extend earlier analysis on nonlocal gradient operators. In particular, we study a nonlocal Dirichlet integral that is given by a quadratic energy functional based on nonlocal gradients. Our main finding, which differs from claims made in previo...

Steady state crack propagation produce substantial plastic strain gradients near the tip, which are accompanied by a high density of geometrically necessary dislocations and additional local strain hardening. Here, the objective is to study these gradient effects on Mode I toughness of a homogeneous rate-sensitive metal, using a higher order plasticity theory. Throughout, emphasis is on the tou...

An appealing property of the natural gradient is that it is invariant to arbitrary differentiable reparameterizations of the model. However, this invariance property requires infinitesimal steps and is lost in practical implementations with small but finite step sizes. In this paper, we study invariance properties from a combined perspective of Riemannian geometry and numerical differential equ...

Under the assumption of normally distributed returns, we analyze whether the Cumulative Prospect Theory of Tversky and Kahneman (1992) is consistent with the Capital Asset Pricing Model. We find that in every financial market equilibrium the Security Market Line Theorem holds. However, under the specific functional form suggested by Tversky and Kahneman (1992) financial market equilibria do not...

We describe an auto-encoder with multiplicative connections whose hidden variables encode products of pixel intensities. The model allows for efficient learning of image transformations and of higher-order structure within an image-patch. Modelling higher-order structure can be an effective way to improve recognition performance, as shown recently with a similar, probabilistic model of image co...