A finite element implementation of the stress gradient theory

In this contribution, a finite element implementation of the stress gradient theory is proposed. The implementation relies on a reformulation of the governing set of partial differential equations in terms of one primary tensor-valued field variable of third order, the so-called generalised displacement field. Whereas the volumetric part of the generalised displacement field is closely related to the classic displacement field, the deviatoric part can be interpreted in terms of micro-displacements. The associated weak formulation moreover stipulates boundary conditions in terms of the normal projection of the generalised displacement field or of the (complete) stress tensor. A detailed study of representative boundary value problems of stress gradient elasticity shows the applicability of the proposed formulation. In particular, the finite element implementation is validated based on the analytical solutions for a cylindrical bar under tension and torsion derived by means of Bessel functions. In both tension and torsion cases, a smaller is softer size effect is evidenced in striking contrast to the corresponding strain gradient elasticity solutions.

Improving the GNSS-R Specular Reflection Point Positioning Accuracy Using the Gravity Field Normal Projection Reflection Reference Surface Combination Correction Method

Global Navigation Satellite System Reflectometry (GNSS-R) is of great significance for the extraction and research of precise information of sea surface topography. Improving measurement accuracy is necessary for realizing spaceborne GNSS-R sea surface altimetry application. The main error source of GNSS-R distance measurement is the error of the specular reflection point positioning, which directly affects the sea surface altimetry accuracy on the reference datum. There is an elevation error of several tens of meters between the reflection reference surface used by the existing specular reflection point geometric positioning methods and the sea surface elevation, which is importantly influenced by the earth’s gravity field. Therefore, the gravity field reflection reference surface correction is the key to improving the specular reflection point positioning accuracy. In this study, based on the correction of the GNSS-R reflection reference surface, research on improving the positioning accuracy of the specular reflection point is carried out. Firstly, in order to reduce the positioning error caused by the elevation difference between the reflection reference surface and the sea surface, the gravity field reflection reference surface correction method (GFRRSCM) which corrects the reflection reference surface from the WGS-84 ellipsoid to geoid is proposed, and the positioning accuracy is improved by 25.15 m. Secondly, the normal projection reflection reference surface correction method (NPRRSCM) is proposed to correct the specular reflection point determined by the GFRRSCM from the reflection reference plane of the radial to that of the normal. Additionally, in the process of solving the spatial geometric relationship of the reflection path, the approximate substitution error is reduced by directly solving the normal projection on the plane, and the positioning accuracy is further improved by 13.05 m towards the normal. Thirdly, based on the gravity field normal projection reflection reference surface combination correction method (GF-NPRRSCCM), the specular reflection point positioning accuracy is synthetically improved by 28.66 m.

An Optimal Matching Algorithm Based on Rough Localization and Exact Adjustment

Aiming at the problems on estimate of the initial transformation, matching precision and global optimization in matching, this paper presents a matching method, which is based on rough localization and exact adjustment. By means of rotation, translation and coincidence of the minimum bounding boxes of surface and measured points, rough localization is realized, which produces a good estimate for the follow-up iterative algorithm. The closest points that were calculated via the normal projection of the sample points then establish the correspondence between two objects. An iterative process is used in the exact adjustment to ensure the global optimization of match. For reducing the effect of bad points or local distortion, a maximum distance criterion is adopted to refine the transformation between objects. A computer simulation is given to demonstrate that the algorithm is steady and effective.

Differential Dissection of the Rat E16 Ventral Mesencephalon and Survival and Reinnervation of the 6-Ohda-Lesioned Striatum by a Subset of Aldehyde Dehydrogenase-Positive th Neurons

The retinoic acid-generating enzyme, aldehyde dehydrogenase (AHD), is expressed in a subpopulation of dopaminergic neurons found in the substantia nigra. Using AHD and tyrosine hydroxylase (TH) as immunohistochemical markers, we determined whether differential dissection of the embryonic (E16) ventral mesencephalon (VM) into its lateral and medial portions contributed equally to the number of TH cells surviving transplantation, if grafted AHD/TH neurons reinnervate the host striatum according to their normal projection patterns, and examined the functional recovery caused by the implanted cells as assessed by amphetamine-induced rotation in a 6-OHDA-lesioned model of Parkinson's disease. The embryonic tissue was transplanted as solid pieces injected via a 20-gauge lumbar puncture needle into the center of the deafferented striatum. Groups received either one complete ventral mesencephalic piece (VM), two medial pieces of ventral mesencephalic tissue (MVM), or two lateral pieces of ventral mesencephalic tissue (LVM). Both VM and MVM groups showed a significant decrease in amphetamine-induced rotation over time and, there was no difference in the degree of reduction observed between the two groups. Histological evaluation of the transplants revealed a much larger total number of surviving TH cells in grafts from the VM and MVM groups compared to the LVM group. Surviving AHD/TH neurons were found in all groups. Whereas TH staining of the transplanted striatum displayed a halo of graft-derived fibers all around the transplant and integration of these fibers into the host neuropil, AHD staining showed a preferential reinnervation of the dorsolateral striatum corresponding to the normal projection pattern of AHD/TH neurons. In summary, selective dissection of the embryonic ventral mesencephalon is possible, functional recovery as assessed by amphetamineinduced rotation in animals transplanted with MVM is similar to that seen in animals grafted with VM, and AHD/TH neurons have a selective reinnervation pattern in the PD transplantation paradigm. These findings may have implications for the grafting of fetal mesencephalic tissue in PD patients.