Scalar potential

About: Scalar potential is a research topic. Over the lifetime, 3642 publications have been published within this topic receiving 78868 citations. The topic is also known as: potential.

Essential self-adjointness for semi-bounded magnetic Schr\"odinger operators on non-compact manifolds

Abstract: We prove essential self-adjointness for semi-bounded below magnetic Schrodinger operators on complete Riemannian manifolds with a given positive smooth measure which is fixed independently of the metric. Some singularities of the scalar potential are allowed. This is an extension of the Povzner--Wienholtz--Simader theorem. The proof uses the scheme of Wienholtz but requires a refined invariant integration by parts technique, as well as a use of a family of cut-off functions which are constructed by a non-trivial smoothing procedure due to Karcher.

Constant-roll Inflation in $F(R)$ Gravity

Abstract: We propose the study of constant-roll inflation in $F(R)$ gravity. We use two different approaches, one that relates an $F(R)$ gravity to well known scalar models of constant-roll and a second that examines directly the constant-roll condition in $F(R)$ gravity. With regards to the first approach, by using well known techniques, we find the $F(R)$ gravity which realizes a given constant-roll evolution in the scalar-tensor theory. We also perform a conformal transformation in the resulting $F(R)$ gravity and we find the Einstein frame counterpart theory. As we demonstrate, the resulting scalar potential is different in comparison to the original scalar constant-roll case, and the same applies for the corresponding observational indices. Moreover, we discuss how cosmological evolutions that can realize constant-roll to constant-roll eras transitions in the scalar-tensor description, can be realized by vacuum $F(R)$ gravity. With regards to the second approach, we examine directly the effects of the constant-roll condition on the inflationary dynamics of vacuum $F(R)$ gravity. We present in detail the formalism of constant-roll $F(R)$ gravity inflationary dynamics and we discuss how the inflationary indices become in this case. We use two well known $F(R)$ gravities in order to illustrate our findings, the $R^2$ model and a power-law $F(R)$ gravity in vacuum. As we demonstrate, in both cases the parameter space is enlarged in comparison to the slow-roll counterparts of the models, and in effect, the models can also be compatible with the observational data. Finally, we briefly address the graceful exit issue.

Mobile robots path planning: Electrostatic potential field approach

Abstract: This paper deals with the mobile robots path planning problem in the presence of scattered obstacles in a visually known environment. Utilizing the theory of charged particles’ potential fields and inspired by a key idea of the authors’ recent work, an optimization based approach is proposed to obtain an optimal and robust path planning solution. By assigning a potential function for each individual obstacle, the interaction of all scattered obstacles are integrated in a scalar potential surface (SPS) which strongly depends on the physical features of the mobile robot and obstacles. The optimum path is then obtained from a cost function optimization by attaining a trade-off between traversing the shortest path and avoiding collisions, simultaneously. Hence, irrespective of any physical constraints on the obstacles/mobile-robot and the adjacency of the target to the obstacles, the achieved results demonstrate a feasible, fast, oscillation-free and collision-free path planning of the proposed method. Utilizing a scalar decision variable makes it extremely simple in terms of mathematical computations and thus practically feasible that can be applied to both static and dynamic environments. Finally, simulation results verified the performance and fulfillment of the mentioned objectives of the approach.

When scalar field is kinetically coupled to the Einstein tensor

Abstract: We explore the cosmic evolution of a scalar field with the kinetic term coupled to the Einstein tensor. We find that, in the absence of other matter sources or in the presence of only pressureless matter, the scalar behaves as pressureless matter and the sound speed of the scalar is vanishing. These properties enable the scalar field to be a candidate of cold dark matter. By also considering the scalar potential, we find the scalar field may play the role of both dark matter and dark energy. In this case, the equation of state of the scalar can cross the phantom divide, but this can lead to the sound speed becoming superluminal as it crosses the divide, and so is physically forbidden. Finally, if the kinetic term is coupled to more than one Einstein tensor, we find the equation of state is always approximately equal to -1 whether the potential is flat or not, and so the scalar may also be a candidate for the inflaton.