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In this paper we analyze the local localization of gravity in $AdS_4$ thick brane embedded in $AdS_5$ space. The 3-brane is modelled by domain wall solution of a theory with a bulk scalar field coupled to five-dimensional gravity. In…
We examine brane induced gravity on codimension-1 branes, a.k.a DGP gravity, as a theory of five-dimensional gravity containing a certain class four-dimensional branes. From this perspective, the model suffers from a number of pathologies…
Autonomous navigation of mobile robots is a well studied problem in robotics. However, the navigation task becomes challenging when multi-robot systems have to cooperatively navigate dynamic environments with deadlock-prone layouts. We…
In this work, we study the geodesics of the space of certain geometrically and physically motivated subspaces of the space of immersed curves endowed with a first order Sobolev metric. This includes elastic curves and also an extension of…
Nature harbors crystals of dimensionality ($d$) only up to three. Here we introduce the notion of \emph{projected topological branes} (PTBs): Lower-dimensional branes embedded in higher-dimensional parent topological crystals, constructed…
We examine generalizations of the five-dimensional canonical metric by including a dependence of the extra coordinate in the four-dimensional metric. We discuss a more appropriate way to interpret the four-dimensional energy-momentum tensor…
The deep connection between black hole thermodynamics and spacetime geometry remains a central focus of general relativity. While recent studies have revealed a precise correspondence for null orbits, given by $K = -\lambda^2$ between the…
In autonomous navigation, trajectory replanning, refinement, and control command generation are essential for effective motion planning. This paper presents a resilient approach to trajectory replanning addressing scenarios where the…
Space-time--time is a natural hybrid of Kaluza's five-dimensional geometry and Weyl's conformal space-time geometry. Translations along the secondary time dimension produce the electromagnetic gauge transformations of Kaluza--Klein theory…
We consider the sEGB $4d$ gravitational model with a scalar field $\varphi\left(u\right)$, Einstein and Gauss-Bonnet terms. The model action contains a potential term $U\left(\varphi\right)$, a Gauss-Bonnet coupling function…
Energy-based predictive world models provide a powerful approach for multi-step visual planning by reasoning over latent energy landscapes rather than generating pixels. However, existing approaches face two major challenges: (i) their…
In induced gravity theory the solution of the dynamics equations for the test particle on null path leads to additional force in four-dimensional space-time. We find such force from five-dimensional geodesic line equations and try to apply…
Ergodic exploration has spawned a lot of interest in mobile robotics due to its ability to design time trajectories that match desired spatial coverage statistics. However, current ergodic approaches are for continuous spaces, which require…
We examine the time evolution of the five-dimensional Einstein field equations subjected to a flat, anisotropic Robertson-Walker metric, where the 3D and higher-dimensional scale factors are allowed to dynamically evolve at different rates.…
We study the classical geodesic motions of nonzero rest mass test particles and photons in five-dimensional warped product spaces. We show that it is possible to obtain a general picture of these motions, using the natural decoupling that…
In the present paper we develop an algorithm to solve the time dependent Ginzburg-Landau (TDGL) equations, by using the link variables technique, for circular geometries. In addition, we evaluate the Helmholtz and Gibbs free energy, the…
We investigate a scenario with two four-branes embedded in six dimensions. When the metric is periodic and compact in one of the dimensions parallel to the branes, the value of the effective cosmological constant for the remaining five…
The `braneworld' (described by the usual worldvolume action) is a D dimensional timelike surface embedded in a N dimensional ($N>D$) warped, nonfactorisable spacetime. We first address the conditions on the warp factor required to have an…
The particle-scale dynamics of granular materials have commonly been characterized by the self-diffusion coefficient $D$. However, this measure discards the collective and topological information known to be an important characteristic of…
The existence of Traversable Wormhole (TW) in the 4D Einstein-Gauss-Bonnet (4D-EGB) gravity is explored with phenomenological Bose-Einstein Condensates (BEC) dark matter density profile. In the framework of 4D EGB gravity, which one obtains…