The derivation of the Monge-Ampère (MA) equation, as it results from a variational principle involving grid displacement, is outlined in two dimensions (2D). This equation, a major element of Monge-Kantorovich (MK) optimization, is discussed both in the context of grid generation and grid adaptation. It is shown that grids which are generated by the MA equation also satisfy equations of an alte...

Abstract We study how three-dimensional linearized elasticity for thin plates can be approximated by a two-dimensional projection. The classical approach using formal asymptotic expansions in powers of the thickness in the Hellinger-Reissner formulation, only provides error estimates in the H1 norm for the displacements, assuming at least L2 regularity for the applied forces, plus additional re...

Stochastic transport of a two-dimensional (2D) dusty plasma liquid with a perpendicular magnetic field is studied. Superdiffusion is found to occur especially at higher magnetic fields with β of order unity. Here, β = ω(c)/ω(pd) is the ratio of the cyclotron and plasma frequencies for dust particles. The mean-square displacement MSD = 4D(α)t(α) is found to have an exponent α > 1, indicating sup...

A method for computing the 3D camera motion (the ego-motion) in a static scene is introduced, which is based on computing the 2D image motion of a single image region directly from image intensities. The computed image motion of this image region is used to register the images so that the detected image region appears stationary. The resulting displacement eld for the entire scene between the r...

The conventional generalized Hough transform (GHT) is useful for detecting or locating translated 2-dimensional (2D) object shapes. However, a weakness of the conventional GHT is that a brute force approach is usually required to handle shape scaling and rotation, resulting in the use of a 4D Hough counting space (HCS). A new version of the GHT, called scaleand orientation-invariant GHT (SOIGHT...

In this paper, a four-dimensional spatiotemporal shape context descriptor is introduced and used for human activity recognition in video. The spatiotemporal shape context is computed on silhouette points by binning the magnitude and direction of motion at every point with respect to given vertex, in addition to the binning of radial displacement and angular offset associated with the standard 2...

A two-dimensional (2D) solid lacks long-range positional order and is diffusive by means of the cooperative motion of particles. We find from molecular dynamics simulations of hard discs that 2D colloids in solid and hexatic phases show seemingly Fickian but strongly heterogeneous dynamics. Beyond translational relaxation time, the mean-square displacement is linear with time, t, implying that ...

We propose a $${\mathcal {C}}^0$$ interior penalty method (C0-IPM) for the computational modelling of flexoelectricity, with application also to strain gradient elasticity, as simplified case. Standard high-order finite element approximations, nodal basis, are considered. The proposed C0-IPM formulation involves second derivatives in elements, plus integrals on mesh faces (sides 2D), that impos...

A method for non-invasively estimating tissue temperatures using 2D diagnostic ultrasound imaging arrays is presented in this paper. It is based on a linear relationship between the apparent speckle pattern displacements and temperature, as seen on acquired A-lines when the sample is heated by external heating elds. The proportionality constant between speckle displacement and temperature is de...

MRI cardiac tagging has been established as the gold standard in assessing intramyocardial displacement and strain. Yet, despite the high imaging quality of cardiac MRI, tagging techniques are limited by low spatial and temporal resolution. It has been recently shown that axial displacement and strain could be estimated and utilizing Bscan ultrasonography [1]. We compared and correlated intramy...