We consider a system of random walks or directed polymers interacting with an environment which is random in space and time. Under minimal assumptions on the distribution of the environment, we prove that this system has diffusive behavior with probability one if d > 2 and fl < flo, where flo is defined in terms of the probability that the symmetric nearest neighbor random walk on the d-dimensi...

The random motion of a Brownian particle confined in some finite domain is considered. Quite generally, the relevant statistical properties involve infinite series, whose coefficients are related to the eigenvalues of the diffusion operator. Unfortunately, the latter depend on space dimensionality and on the particular shape of the domain, and an analytical expression is in most circumstances n...

Cardiac Magnetic Resonance images offer the opportunity to study the heart in detail. One of the main issues in its modelling is to create an accurate 3-D reconstruction of the left ventricle from 2-D views. A first step to achieve this goal is the correct registration among the different image planes due to patient movements. In this article, we present an accurate method to correct displaceme...

Joint errors are inevitable in robot manipulation. These uncertainties propagate to give rise to translational and orientational errors in the position and orientation of the robot end-effector. The displacement of the active vision head mounted on the robot endeffector produces distortion of the projected object on the image. Upon active visual inspection, the observed dimension of a mechanica...

The existing angular displacement measurement methods rely on the manufacturing precision of the fixedplate and moving-plate with high manufacturing cost, and it is difficult to overcome a static error and drift for the static measurement method. A kind of angular displacement measuring method based on correlation algorithm is presented with the characteristics of a low manufacturing cost, high...

In this paper, we propose upper and lower error bounding techniques for reduced order modelling applied to the computational homogenisation of random composites. The upper bound relies on the construction of a reduced model for the stress field. Upon ensuring that the reduced stress satisfies the equilibrium in the finite element sense, the desired bounding property is obtained. The lower bound...

This paper presents the basis of an adaptive mesh refinement technique aimed at reducing a local error, i.e. the error in a local quantity, which is defined as the integral of a stress or a displacement in a given subregion. Two pairs of dual solutions, one corresponding to the applied load and the other to the virtual action, dual of the local quantity, are used to bound the local error and to...

A common problem with modern numerical oceanographic models is spatial displacement, including misplacement and misshapenness of ocean circulation features. Traditional error metrics, such as least squares methods, are ineffective in many such cases; for example, only small errors in the location of a frontal pattern are translated to large differences in least squares of intensities. Such prob...