Quasicrystals can carry, in addition to the classical phonon displacement field, a phason displacement field, which requires a generalized theory of elasticity. In this paper, the third-order strain invariants (including phason strain) of icosahedral quasicrystals are determined. They are connected with 20 independent third-order elastic constants. By means of non-linear elasticity, phason stra...

During in-situ mechanical tests performed on polycrystalline materials in a scanning electron microscope, crystal orientation maps may be recorded at different stages of deformation from electron backscattered diffraction (EBSD). The present study introduces a novel correlation technique that exploits the crystallographic orientation field as a surface pattern to measure crystal motions. Introd...

We present a unified statistical framework for analyzing temporally varying brain morphology using the 3D displacement vector field from a nonlinear deformation required to register a subject's brain to an atlas brain. The unification comes from a single model for structural change, rather than two separate models, one for displacement and one for volume changes. The displacement velocity field...

We present a stochastic approach for ion transport at the mesoscopic level. The description takes into account the self-consistent electric field generated by the fixed and mobile charges as well as the discrete nature of these latter. As an application we study the noise in the ion transport process, including the effect of the displacement current generated by the fluctuating electric field. ...

Two-dimensional linear elasticity problems are approximately solved by a mixed finite-element method based on Raviart-Thomas-Nedelec spaces; maximum-norm error estimates of optimal rate and almost optimal regularity are derived for the displacement field, and of optimal regularity and almost optimal rate for the stress tensor. The superconvergence of the approximate displacement field to the L2...

We present a Bayesian multimodality non-rigid image registration method. Since the likelihood is unknown in the general multimodality setting, we use a density estimator as a drop in replacement to the true likelihood. The prior is a standard small deformation penalty on the displacement field. Since mutual information-based methods are in widespread use for multimodality registration, we attem...

In this paper the possibility of applying the Trefftz-method to thick and thin shells is discussed. A mixed variational formulation is used in which the assumed strain and stress functions are derived from the three-dimensional solution representation for the displacement field. For the construction of the linearly independent Trefftz trial functions both the Neuber/Papkovich solution represent...

Aim. Alzheimer's disease (AD) is a chronic neurodegenerative disease. Recently, computer scientists have developed various methods for early detection based on computer vision and machine learning techniques. Method. In this study, we proposed a novel AD detection method by displacement field (DF) estimation between a normal brain and an AD brain. The DF was treated as the AD-related features, ...

In this work a periodic crystal with point defects is described in the framework of linear-response theory for broken-symmetry states using correlation functions and Zwanzig-Mori equations. The main results are microscopic expressions for the elastic constants and for the coarse-grained density, point-defect density, and displacement field, which are valid in real crystals, where vacancies and ...