Metric connections in projective differential geometry

We search for Riemannian metrics whose Levi-Civita connection belongs to a given projective class. Following Sinjukov and Mikes, we show that such metrics correspond precisely to suitably positive solutions of a certain projectively invariant finite-type linear system of partial differential equations. Prolonging this system, we may reformulate these equations as defining covariant constant sections of a certain vector bundle with connection. This vector bundle and its connection are derived from the Cartan connection of the underlying projective structure.Comment: 10 page

Industry 4.0 and sustainability: Towards conceptualization and theory

Both Industry 4.0 and sustainability have gained momentum in the academic, managerial and policy debate. Despite the relevance of the topics, the relation between Industry 4.0 and sustainability \u2013 revealed by many authors \u2013 is still unclear; literature is fragmented. This paper seeks to overcome this limit by developing a systematic literature review of 117 peer-reviewed journal articles. After descriptive and content analyses, the work presents a conceptualization and theoretical framework. The paper contributes to both theory and practice by advancing current understanding of Industry 4.0 and sustainability, especially the impact of Industry 4.0 technologies on sustainability practices and performance

Borehole climatology: a discussion based on contributions from climate modeling

Progress in understanding climate variability through the last millennium leans on simulation and reconstruction efforts. Exercises blending both approaches present a great potential for answering questions relevant both for the simulation and reconstruction of past climate, and depend on the specific peculiarities of proxies and methods involved in climate reconstructions, as well as on the realism and limitations of model simulations. This paper explores research specifically related to paleoclimate modeling and borehole climatology as a branch of climate reconstruction that has contributed significantly to our knowledge of the low frequency climate evolution during the last five centuries. The text flows around three main issues that group most of the interaction between model and geothermal efforts: the use of models as a validation tool for borehole climate reconstructions; comparison of geothermal information and model simulations as a means of either model validation or inference about past climate; and implications of the degree of realism on simulating subsurface climate on estimations of future climate change. The use of multi-centennial simulations as a surrogate reality for past climate suggests that within the simplified reality of climate models, methods and assumptions in borehole reconstructions deliver a consistent picture of past climate evolution at long time scales. Comparison of model simulations and borehole profiles indicate that borehole temperatures are responding to past external forcing and that more realism in the development of the soil model components in climate models is desirable. Such an improved degree of realism is important for the simulation of subsurface climate and air-ground interaction; results indicate it could also be crucial for simulating the adequate energy balance within climate change scenario experiments

Perturbation Theory for Metastable States of the Dirac Equation with Quadratic Vector Interaction

The spectral problem of the Dirac equation in an external quadratic vector potential is considered using the methods of the perturbation theory. The problem is singular and the perturbation series is asymptotic, so that the methods for dealing with divergent series must be used. Among these, the Distributional Borel Sum appears to be the most well suited tool to give answers and to describe the spectral properties of the system. A detailed investigation is made in one and in three space dimensions with a central potential. We present numerical results for the Dirac equation in one space dimension: these are obtained by determining the perturbation expansion and using the Pad\'e approximants for calculating the distributional Borel transform. A complete agreement is found with previous non-perturbative results obtained by the numerical solution of the singular boundary value problem and the determination of the density of the states from the continuous spectrum.Comment: 10 pages, 1 figur

Active Mass Under Pressure

After a historical introduction to Poisson's equation for Newtonian gravity, its analog for static gravitational fields in Einstein's theory is reviewed. It appears that the pressure contribution to the active mass density in Einstein's theory might also be noticeable at the Newtonian level. A form of its surprising appearance, first noticed by Richard Chase Tolman, was discussed half a century ago in the Hamburg Relativity Seminar and is resolved here.Comment: 28 pages, 4 figure

Conduction‐dominated heat transport of the annual temperature signal in soil

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95182/1/jgrb13727.pd

Comparison of observed and general circulation model derived continental subsurface heat flux in the Northern Hemisphere

Heat fluxes in the continental subsurface were estimated from general circulation model (GCM) simulations of the climate of the last millennium and compared to those obtained from subsurface geothermal data. Since GCMs have bottom boundary conditions (BBCs) that are less than 10 m deep and thus may be thermodynamically restricted in the continental subsurface, we used an idealized land surface model (LSM) with a very deep BBC to estimate the potential for realistic subsurface heat storage in the absence of bottom boundary constraints. Results indicate that there is good agreement between observed fluxes and GCM simulated fluxes for the 1780-1980 period when the GCM simulated temperatures are coupled to the LSM with deep BBC. These results emphasize the importance of placing a deep BBC in GCM soil components for the proper simulation of the overall continental heat budget. In addition, the agreement between the LSM surface fluxes and the borehole temperature reconstructed fluxes lends additional support to the overall quality of the GCM (ECHO-G) paleoclimatic simulations