Electrohydraulic extrusion of spherical bronze (CuSn6) micro samples

Conventional material testing strategies are time and cost intensive. In this paper, a new method for contactless high-speed testing of spherical micro samples by an electrohydraulic punch is introduced. The punch transfers the punching force incrementally to extrude the samples stepwise in dies with high aspect ratios. The sample’s material behavior is characterized by analyzing the deformation behavior between the extrusion steps and at different forming stages

On a class of invariant coframe operators with application to gravity

Let a differential 4D-manifold with a smooth coframe field be given. Consider the operators on it that are linear in the second order derivatives or quadratic in the first order derivatives of the coframe, both with coefficients that depend on the coframe variables. The paper exhibits the class of operators that are invariant under a general change of coordinates, and, also, invariant under the global SO(1,3)-transformation of the coframe. A general class of field equations is constructed. We display two subclasses in it. The subclass of field equations that are derivable from action principles by free variations and the subclass of field equations for which spherical-symmetric solutions, Minkowskian at infinity exist. Then, for the spherical-symmetric solutions, the resulting metric is computed. Invoking the Geodesic Postulate, we find all the equations that are experimentally (by the 3 classical tests) indistinguishable from Einstein field equations. This family includes, of course, also Einstein equations. Moreover, it is shown, explicitly, how to exhibit it. The basic tool employed in the paper is an invariant formulation reminiscent of Cartan's structural equations. The article sheds light on the possibilities and limitations of the coframe gravity. It may also serve as a general procedure to derive covariant field equations

Matrix theory of gravitation

A new classical theory of gravitation within the framework of general relativity is presented. It is based on a matrix formulation of four-dimensional Riemann-spaces and uses no artificial fields or adjustable parameters. The geometrical stress-energy tensor is derived from a matrix-trace Lagrangian, which is not equivalent to the curvature scalar R. To enable a direct comparison with the Einstein-theory a tetrad formalism is utilized, which shows similarities to teleparallel gravitation theories, but uses complex tetrads. Matrix theory might solve a 27-year-old, fundamental problem of those theories (sec. 4.1). For the standard test cases (PPN scheme, Schwarzschild-solution) no differences to the Einstein-theory are found. However, the matrix theory exhibits novel, interesting vacuum solutions.Comment: 24 page

An assessment of Evans' unified field theory I

Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. This geometry can be characterized by an orthonormal coframe theta and a (metric compatible) Lorentz connection Gamma. These two potentials yield the field strengths torsion T and curvature R. Evans tried to infuse electromagnetic properties into this geometrical framework by putting the coframe theta to be proportional to four extended electromagnetic potentials A; these are assumed to encompass the conventional Maxwellian potential in a suitable limit. The viable Einstein-Cartan(-Sciama-Kibble) theory of gravity was adopted by Evans to describe the gravitational sector of his theory. Including also the results of an accompanying paper by Obukhov and the author, we show that Evans' ansatz for electromagnetism is untenable beyond repair both from a geometrical as well as from a physical point of view. As a consequence, his unified theory is obsolete.Comment: 39 pages of latex, modified because of referee report, mistakes and typos removed, partly reformulated, taken care of M.W.Evans' rebutta