Thermodynamics of traversable wormholes in f(R,T) gravity

In this paper, we discuss thermodynamics for spherically symmetric and static traversable wormholes which include Morris–Thorne wormholes and charged wormholes in the background of [Formula: see text] gravity. The local coordinates have been used to find trapping horizons of these objects and generalized surface gravity has been worked out on the trapping horizons. The expression for the unified first law has also been derived from the gradient of Misner–Sharp energy with the help of gravitational field equations and from this law the first law of wormhole dynamics has been obtained. We have done this analysis for the simplest case of [Formula: see text] gravity where [Formula: see text], [Formula: see text] and [Formula: see text] being the traces of the Ricci and stress–energy tensors. Also, we have extended these thermodynamic results to non-minimal curvature-matter coupling.

Black hole solutions and Euler equation in Rastall and generalized Rastall theories of gravity

Focusing on the special case of generalized Rastall theory, as a subclass of the non-minimal curvature-matter coupling theories in which the field equations are mathematically similar to the Einstein field equations in the presence of cosmological constant, we find two classes of black hole (BH) solutions including (i) conformally flat solutions and (ii) non-singular BHs. Accepting the mass function definition and by using the entropy contents of the solutions along with thermodynamic definitions of temperature and pressure, we study the validity of Euler equation on the corresponding horizons. Our results show that the thermodynamic pressure, meeting the Euler equation, is not always equal to the pressure components appeared in the gravitational field equations and satisfies the first law of thermodynamics, a result which in fact depends on the presumed energy definition. The requirements of having solutions with equal thermodynamic and Hawking temperatures are also studied. Additionally, we study the conformally flat BHs in the Rastall framework. The consequences of employing generalized Misner–Sharp mass in studying the validity of the Euler equation are also addressed.

How and to What Extent Does Topography Control the Results of Soil Function Assessment: A Case Study From the Alps in South Tyrol (Italy)

Soil function assessments (SFA) are becoming increasingly important as a tool to integrate soil-related issues in decision-making processes in order to maintain soil quality. We present the SEPP (Soil Evaluation for Planning Procedures) tool, which calculates a level of fulfillment for 14 soil functions based on the information generally collected in soil pit descriptions. By using a statistical modeling approach based on support vector machine classification, we investigate how and to what extent topography, as representated by local terrain parameters and landform classes computed with the GRASS GIS tool r.geomorphon algorithm, controls soil parameters and hence the output of the SEPP tool. A feature selection procedure is applied which highlights those topographic attributes best suited for modeling the various soil function fulfillment levels. By evaluating the model for each soil function using cross-validation we show that the prediction accuracy varies from function to function. While some terrain attributes are directly implemented in the SFA algorithms of SEPP, others are implemented indirectly due to the link between topography and land use. Minimal curvature and slope were found to be first indicators of function fulfillment level for a number of soil functions.

Gravitational collapse in f(R) theories of gravity with non-minimal coupling

The purpose of this paper is to discuss the perfect fluid gravitational collapse in modified f(R) metric gravity theories with non-minimal curvature coupled to matter. For this inference, we investigate the effects on self-gravitating implosion with spherically symmetric non-static geometry in the presence of extra force [Formula: see text], that express the cosmic expansion with dark source constraints. Matching conditions are given in which we have taken the insertion of non-static interior and static exterior regions along with cosmological constant. We have investigated the apparent horizons with effective results and along with their physical interpretation. It is analyzed that the extra component of dark source material reduces the gravitating implosion, hence slowing the rate of collapse. This study also reflects the contribution towards the perfect fluid for the generalization in f(R) gravity with zero coupling constant [Formula: see text].

Neuron Net for Forming Optimal Smooth Trajectories Based on Bezier Splines

In this paper, the problem of planning smooth trajectories of mechatronic objects on the basis of Bezier splines of the third order with a minimal curvature is solved. Using such trajectories provides the maximal speed of movement for mechatronic objects. The neuron net, which approximates the function of the optimal selection of spline parameters is proposed to solve this problem. The advantage of the proposed approach is its lack of computational complexity, which allows its use in most on-board computers in real time.