A higher order semi-analytical method for the simulation of heat transfer in fields of geothermal boreholes is presented. The method uses the integration of the point heat source solution to evaluate borehole wall and ground temperatures. Instead of piecewise uniform heat extraction rate and borehole wall temperature along segments of discretized boreholes, the presented method considers polynomial variations of these quantities using the superposition of polynomial basis functions. Increasing the order of the polynomial basis function (by increasing the number of nodes per borehole segment) is shown to have a greater impact on the model accuracy than increasing the number of segments. The error on the g-function of a field of 8 inclined boreholes is less than 0.1 % using 2 segments of 11 nodes. The presented method enables the simulation of boreholes with curved trajectories. The results show an error of 10.3 % between the thermal response evaluated using the real measured trajectories of boreholes in a real installation and the thermal response evaluated using approximated straight trajectories.

The Gotay-Nester-Hinds method is used in this paper to study the Hamiltonian formulation of the Euclidean self-dual action. This action can be used to arrive at the complex Ashtekar formulation of general relativity or a real connection formulation for Euclidean general relativity. The main result of the paper is a derivation of the Ashtekar formulation for Euclidean gravity without using any gauge fixing. It is interesting to compare this derivation with the one corresponding to the Holst action. In particular it is worth noting that no "tertiary" constraints appear in the case considered in the present paper.

We examine relativistic diffusion through the frame and observer bundles associated with a Lorentzian manifold (M, g). Our focus is on spacetimes with a non-trivial isometry group, and we detail the conditions required to find symmetric solutions of the relativistic diffusion equation. Additionally, we analyze the conservation laws associated with the presence of Killing vector fields on (M, g) and their implications for the expressions of the geodesic spray and the vertical Laplacian on both the frame and the observer bundles. Finally, we present several relevant examples of symmetric spacetimes.