Entropy Identity and Material-Independent Equilibrium Conditions in Relativistic Thermodynamics

On the basis of the balance equations for energy-momentum, spin, particle and entropy density, an approach is considered which represents a comparatively general framework for special- and general-relativistic continuum thermodynamics. In the first part of the paper, a general entropy density 4-vector, containing particle, energy-momentum, and spin density contributions, is introduced which makes it possible, firstly, to judge special assumptions for the entropy density 4-vector made by other authors with respect to their generality and validity and, secondly, to determine entropy supply and entropy production. Using this entropy density 4-vector, in the second part, material-independent equilibrium conditions are discussed. While in literature, at least if one works in the theory of irreversible thermodynamics assuming a Riemann space-time structure, generally thermodynamic equilibrium is determined by introducing a variety of conditions by hand, the present approach proceeds as follows: For a comparatively wide class of space-time geometries the necessary equilibrium conditions of vanishing entropy supply and entropy production are exploited and, afterwards, supplementary conditions are assumed which are motivated by the requirement that thermodynamic equilibrium quantities have to be determined uniquely.Comment: Research Paper, 30 page

A soil column study to evaluate treatment of trace elements from saline industrial wastewater

Citation: Paredez, J. M., Mladenov, N., Galkaduwa, M. B., Hettiarachchi, G. M., Kluitenberg, G. J., & Hutchinson, S. L. (2017). A soil column study to evaluate treatment of trace elements from saline industrial wastewater. Water Science and Technology. https://doi.org/10.2166/wst.2017.413Industrial wastewater from the flue gas desulfurization (FGD) process is characterized by the presence of trace elements of concern, such as selenium (Se) and boron (B) and relatively high salinity. To simulate treatment that FGD wastewater undergoes during transport through soils in subsurface treatment systems, a column study (140-d duration) was conducted with native Kansas soil and saline FGD wastewater, containing high Se and B concentrations (170 ?g/L Se and 5.3 mg/L B) and negligible arsenic (As) concentration (?1.2 ?g/L As). Se, B, and As, and dissolved organic carbon concentrations and organic matter spectroscopic properties were measured in the influent and outflow. Influent Se concentrations were reduced by only ?half in all treatments, and results suggest that Se sorption was inhibited by high salinity of the FGD wastewater. By contrast, relative concentrations (C/Co) of B in the outflow were typically 150 ?g/L in the treatment with labile organic carbon addition) suggest that soils not previously known to be geogenic arsenic sources have the potential to release As to groundwater in the presence of high salinity wastewater and under reducing conditions

On the Cheeger inequality in Carnot-Carath\'eodory spaces

We generalize the Cheeger inequality, a lower bound on the first nontrivial eigenvalue of a Laplacian, to the case of geometric sub-Laplacians on rank-varying Carnot-Carath\'eodory spaces and we describe a concrete method to lower bound the Cheeger constant. The proof is geometric, and works for Dirichlet, Neumann and mixed boundary conditions. One of the main technical tools in the proof is a generalization of Courant's nodal domain theorem, which is proven from scratch for Neumann and mixed boundary conditions. Carnot groups and the Baouendi-Grushin cylinder are treated as examples.Comment: Updates v2: - Added a proof of Courant's theorem which does not use (S), improving the main result - Added Section 6 on methods for obtaining lower bounds for the Cheeger constant - Minor readability improvements Updates v3: Fixed some typo

On the Cheeger Inequality in Carnot-Carathéodory Spaces

We generalize the Cheeger inequality, a lower bound on the first nontrivial eigenvalue of a Laplacian, to the case of geometric sub-Laplacians on rank-varying Carnot-Carathéodory spaces and we describe a concrete method to lower bound the Cheeger constant. The proof is geometric, and works for Dirichlet, Neumann and mixed boundary conditions. One of the main technical tools in the proof is a generalization of Courant’s nodal domain theorem, which is proven from scratch for Neumann and mixed boundary conditions. Carnot groups and the Baouendi-Grushin cylinder are treated as examples.</p