Spinning Fluids in Relativistic Hydrodynamics

We study the well known propagation and constraint equations in General Relativity for the case where the matter source is an ideal Weyssenhoff fluid. Moreover we derive these equations for the Einstein-Cartan theory of gravitation for the same matter source. We discuss the different couplings of the matter content in detail in both theories and consider especially the behavior of the spin, angular and total angular momentum

Constitutive Theory in General Relativity and Einstein-Cartan Theory: Spin Balances, Energy-Momentum Balances and Weyssenhoff Fluid

It is shown, that the usually considered spin balances are too restrictive and only valid for pointlike particles. Furthermore, we will derive the full spin balance and discuss the Weyssenhoff-Fluid

Close-to-Fourier heat conduction equation for solids: motivation and symbolic-numerical analysis

Heat conduction close-to-Fourier means, that we look for a minimal extension of heat conduction theory using the usual Fourier expression of the heat flux density and modifying that of the internal energy as minimal as possible by choosing the minimal state space. Applying Liu's procedure results in the class of materials and a differential equation both belonging to the close-to-Fourier case of heat conduction. A symbolic-numerical computing method is applied to approximate the numerical solutions of 2 special heat conduction equations belonging to the close-to-Fourier class

Phoretic Motion of Spheroidal Particles Due To Self-Generated Solute Gradients

We study theoretically the phoretic motion of a spheroidal particle, which generates solute gradients in the surrounding unbounded solvent via chemical reactions active on its surface in a cap-like region centered at one of the poles of the particle. We derive, within the constraints of the mapping to classical diffusio-phoresis, an analytical expression for the phoretic velocity of such an object. This allows us to analyze in detail the dependence of the velocity on the aspect ratio of the polar and the equatorial diameters of the particle and on the fraction of the particle surface contributing to the chemical reaction. The particular cases of a sphere and of an approximation for a needle-like particle, which are the most common shapes employed in experimental realizations of such self-propelled objects, are obtained from the general solution in the limits that the aspect ratio approaches one or becomes very large, respectively.Comment: 18 pages, 5 figures, to appear in European Physical Journal

Issues dedicated to memory of the Professor Rastko Stojanović Spin axioms in relativistic continuum physics

J. Herrmann ∗ G. Rückner W. Muschik H. H. v.Borzeszkowski There is nothing so annnoying as a good example Mark Twain The 24 components of the relativistic spin tensor consist of 3+3 basic spin fields and 9 + 9 constitutive fields. Empirically only 3 basic spin fields and 9 constitutive fields are known. This empirem can be expressed by two spin axioms, one of them identifying 3 spin fields, and the other one 9 constitutive fields to each other. This identification by the spin axioms is materialindependent and does not mix basic spin fields with constitutive properties. The approaches to the Weyssenhoff fluid and the Dirac-electron fluid found in literature are discussed with regard to these spin axioms. The conjecture is formulated, that another reduction from 6 to 3 basic spin fields which does not obey the spin axioms introduces special material properties by not allowed mixing of constitutive and basic fields