Accounting for exotic matter and the extreme radial tension in Morris–Thorne wormholes of embedding class one

The embedding of a curved spacetime in a higher-dimensional flat spacetime has continued to be a topic of interest in the general theory of relativity, as exemplified by the induced-matter theory. This paper deals with spacetimes of embedding class one, i.e., spacetimes that can be embedded in a five-dimensional flat spacetime. Einstein’s theory allows the fifth dimension to be either spacelike or timelike. By assuming the latter, this paper addresses two fundamental issues concerning Morris–Thorne wormholes, the origin of exotic matter and the frequently inexplicable enormous radial tension at the throat.

Analysis of Equibiaxial Tension Tests for Hyperelastic EAP Film

Equibiaxial tension tests for hyperelastic electroactive polymers (EAPs) are important means to obtain the mechanical properties. There are three main methods: equibiaxial planar tension, radial tension and bulge test. The finite element analysis software is used to model and analyze the influence of testing apparatus, specimen geometric parameters on the test results and accuracy. The results show that the uniformity of the deformation of the square film can be effectively improved by using single corner point fixed tension in equibiaxial planar tension test, and the force error also decreased; the number of the cuts and the size of punched holes should be appropriate in radial tension test of circular diaphragm specimen to avoid the material strength failure caused by excessive tension along the edge of transition arc between grips and excessive deformation of tensile belt between the cuts; in bulge test, the sampled deformation data should be near the spherical pole to obtain more accurate stress-strain relationship owing to contour error and non-uniform deformation, a certain range of model parameters will limit the scope of simulation analysis. This paper proposed research provides guidance for the design of equibiaxial tension test apparatus and method to obtain more accurate test results.

Cell-Scale Modeling to Probe Mechanobiology during Early Cortical Development

Background/Objective: During early cerebral cortex development, neurons form from proliferative glial cells near the ventricular (apical) surface, then migrate along radial glial scaffolds to the cortical surface. In species with wrinkled brains, the presence of basal radial glial cells (bRGCs), radial glial cells which have detached from the ventricular surface, is correlated to the process of gyrification. While mechanical forces are also involved in gyrus creation, the link between the mechanical and biological aspects of this process remains unelucidated. In this study, we hypothesized that radial tension may lead to the production of gyri via the intermediary creation of bRGCs. Methods: To test this hypothesis, the cell-level modeling software CX3D was used to simulate a system in which radial tension acts on radial glial cells (RGCs), facilitating the semi-stochastic production of bRGCs during the process of neocortex development. The outcome of this model was contrasted with a control case in which bRGCs were not allowed to form, and the two models were compared based upon the presence of neurons on the basal surface. Results: The production of bRGCs via tension corresponded to a significant increase in the presence of neurons on the pial surface, even if the total number of glial cells—and thus total number of neurons generated—remained constant. Additionally, the likelihood of neurons moving more basally was found to be significantly greater in the presence of bRGCs. Conclusion and Potential Impact: These results were interpreted to be indications of early gyrus formation. Thus, this study showed that bRGCs—and, ultimately, gyri—may arise from mechanical tension, indicating a possible link between the biological and mechanical explanations of gyrus formation. By providing an alternative lens through which to understand cortical folding, this may have implications for future lines of inquiry, which may expand our understanding of neuro-pathologies associated with misfolding, such as autism and epilepsy.

Stress amplification in three-dimensional narrow zones created by cavities

The paper is concerned with a particular case of stress amplification arising from the proximity of a spherical cavity to the boundary of a loaded elastic solid. The performed approximate analysis yields distributions of stresses and displacements in the narrow region formed between a spherical cavity and the faces of a thin flat layer subjected to a far field uniform radial tension. The narrow region is modelled as a circular plate of non-uniform thickness undergoing coupled membrane and flexural deformation. Series solutions are obtained for both membrane forces and bending moments leading to estimates for the stress concentration factor at minimum thickness. These predictions are found consistent with those obtained from both the exact analytical solution and finite element modelling of the problem. Cross-validated results from the two latter methods also provide trends for the stress amplification due to the narrowness of the region.