The Kummer tensor density in electrodynamics and in gravity

Guided by results in the premetric electrodynamics of local and linear media, we introduce on 4-dimensional spacetime the new abstract notion of a Kummer tensor density of rank four, ${\cal K}^{ijkl}$. This tensor density is, by definition, a cubic algebraic functional of a tensor density of rank four ${\cal T}^{ijkl}$, which is antisymmetric in its first two and its last two indices: ${\cal T}^{ijkl} = - {\cal T}^{jikl} = - {\cal T}^{ijlk}$. Thus, ${\cal K}\sim {\cal T}^3$, see Eq.(46). (i) If $\cal T$ is identified with the electromagnetic response tensor of local and linear media, the Kummer tensor density encompasses the generalized {\it Fresnel wave surfaces} for propagating light. In the reversible case, the wave surfaces turn out to be {\it Kummer surfaces} as defined in algebraic geometry (Bateman 1910). (ii) If $\cal T$ is identified with the {\it curvature} tensor $R^{ijkl}$ of a Riemann-Cartan spacetime, then ${\cal K}\sim R^3$ and, in the special case of general relativity, ${\cal K}$ reduces to the Kummer tensor of Zund (1969). This $\cal K$ is related to the {\it principal null directions} of the curvature. We discuss the properties of the general Kummer tensor density. In particular, we decompose $\cal K$ irreducibly under the 4-dimensional linear group $GL(4,R)$ and, subsequently, under the Lorentz group $SO(1,3)$.Comment: 54 pages, 6 figures, written in LaTex; improved version in accordance with the referee repor

Surface Curvature Differentially Regulates Stem Cell Migration and Differentiation via Altered Attachment Morphology and Nuclear Deformation

Signals from the microenvironment around a cell are known to influence cell behavior. Material properties, such as biochemical composition and substrate stiffness, are today accepted as significant regulators of stem cell fate. The knowledge of how cell behavior is influenced by 3D geometric cues is, however, strongly limited despite its potential relevance for the understanding of tissue regenerative processes and the design of biomaterials. Here, the role of surface curvature on the migratory and differentiation behavior of human mesenchymal stem cells (hMSCs) has been investigated on 3D surfaces with well-defined geometric features produced by stereolithography. Time lapse microscopy reveals a significant increase of cell migration speed on concave spherical compared to convex spherical structures and flat surfaces resulting from an upward-lift of the cell body due to cytoskeletal forces. On convex surfaces, cytoskeletal forces lead to substantial nuclear deformation, increase lamin-A levels and promote osteogenic differentiation. The findings of this study demonstrate a so far missing link between 3D surface curvature and hMSC behavior. This will not only help to better understand the role of extracellular matrix architecture in health and disease but also give new insights in how 3D geometries can be used as a cell-instructive material parameter in the field of biomaterial-guided tissue regeneration.Peer reviewe

Shear horizontal (SH) ultrasound wave propagation around smooth corners

Shear horizontal (SH) ultrasound guided waves are being used in an increasing number of non-destructive testing (NDT) applications. One advantage SH waves have over some wave types, is their ability to propagate around curved surfaces with little energy loss; to understand the geometries around which they could propagate, the wave reflection must be quantified. A 0.83 mm thick aluminium sheet was placed in a bending machine, and a shallow bend was introduced. Periodically-poled magnet (PPM) electromagnetic acoustic transducers (EMATs), for emission and reception of SH waves, were placed on the same side of the bend, so that reflected waves were received. Additional bending of the sheet demonstrated a clear relationship between bend angles and the reflected signal. Models suggest that the reflection is a linear superposition of the reflections from each bend segment, such that sharp turns lead to a larger peak-to-peak amplitude, in part due to increased phase coherence

A noncontact ultrasonic platform for structural inspection

Miniature robotic vehicles are receiving increasing attention for use in nondestructive testing (NDE) due to their attractiveness in terms of cost, safety, and their accessibility to areas where manual inspection is not practical. Conventional ultrasonic inspection requires the provision of a suitable coupling liquid between the probe and the structure under test. This necessitates either an on board reservoir or umbilical providing a constant flow of coupling fluid, neither of which are practical for a fleet of miniature robotic inspection vehicles. Air-coupled ultrasound offers the possibility of couplant-free ultrasonic inspection. This paper describes the sensing methodology, hardware platform and algorithms used to integrate an air-coupled ultrasonic inspection payload into a miniature robotic vehicle platform. The work takes account of the robot's inherent positional uncertainty when constructing an image of the test specimen from aggregated sensor measurements. This paper concludes with the results of an automatic inspection of a aluminium sample