93 research outputs found

    A Unified Approach to Variational Derivatives of Modified Gravitational Actions

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    Our main aim in this paper is to promote the coframe variational method as a unified approach to derive field equations for any given gravitational action containing the algebraic functions of the scalars constructed from the Riemann curvature tensor and its contractions. We are able to derive a master equation which expresses the variational derivatives of the generalized gravitational actions in terms of the variational derivatives of its constituent curvature scalars. Using the Lagrange multiplier method relative to an orthonormal coframe, we investigate the variational procedures for modified gravitational Lagrangian densities in spacetime dimensions n3n\geqslant 3. We study well-known gravitational actions such as those involving the Gauss-Bonnet and Ricci-squared, Kretchmann scalar, Weyl-squared terms and their algebraic generalizations similar to generic f(R)f(R) theories and the algebraic generalization of sixth order gravitational Lagrangians. We put forth a new model involving the gravitational Chern-Simons term and also give three dimensional New massive gravity equations in a new form in terms of the Cotton 2-form

    Higher Dimensional Cylindrical or Kasner Type Electrovacuum Solutions

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    We consider a D dimensional Kasner type diagonal spacetime where metric functions depend only on a single coordinate and electromagnetic field shares the symmetries of spacetime. These solutions can describe static cylindrical or cosmological Einstein-Maxwell vacuum spacetimes. We mainly focus on electrovacuum solutions and four different types of solutions are obtained in which one of them has no four dimensional counterpart. We also consider the properties of the general solution corresponding to the exterior field of a charged line mass and discuss its several properties. Although it resembles the same form with four dimensional one, there is a difference on the range of the solutions for fixed signs of the parameters. General magnetic field vacuum solution are also briefly discussed, which reduces to Bonnor-Melvin magnetic universe for a special choice of the parameters. The Kasner forms of the general solution are also presented for the cylindrical or cosmological cases.Comment: 16 pages, Revtex. Text and references are extended, Published versio

    Goal-Directed Reasoning and Cooperation in Robots in Shared Workspaces: an Internal Simulation Based Neural Framework

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    From social dining in households to product assembly in manufacturing lines, goal-directed reasoning and cooperation with other agents in shared workspaces is a ubiquitous aspect of our day-to-day activities. Critical for such behaviours is the ability to spontaneously anticipate what is doable by oneself as well as the interacting partner based on the evolving environmental context and thereby exploit such information to engage in goal-oriented action sequences. In the setting of an industrial task where two robots are jointly assembling objects in a shared workspace, we describe a bioinspired neural architecture for goal-directed action planning based on coupled interactions between multiple internal models, primarily of the robot’s body and its peripersonal space. The internal models (of each robot’s body and peripersonal space) are learnt jointly through a process of sensorimotor exploration and then employed in a range of anticipations related to the feasibility and consequence of potential actions of two industrial robots in the context of a joint goal. The ensuing behaviours are demonstrated in a real-world industrial scenario where two robots are assembling industrial fuse-boxes from multiple constituent objects (fuses, fuse-stands) scattered randomly in their workspace. In a spatially unstructured and temporally evolving assembly scenario, the robots employ reward-based dynamics to plan and anticipate which objects to act on at what time instances so as to successfully complete as many assemblies as possible. The existing spatial setting fundamentally necessitates planning collision-free trajectories and avoiding potential collisions between the robots. Furthermore, an interesting scenario where the assembly goal is not realizable by either of the robots individually but only realizable if they meaningfully cooperate is used to demonstrate the interplay between perception, simulation of multiple internal models and the resulting complementary goal-directed actions of both robots. Finally, the proposed neural framework is benchmarked against a typically engineered solution to evaluate its performance in the assembly task. The framework provides a computational outlook to the emerging results from neurosciences related to the learning and use of body schema and peripersonal space for embodied simulation of action and prediction. While experiments reported here engage the architecture in a complex planning task specifically, the internal model based framework is domain-agnostic facilitating portability to several other tasks and platforms

    Multi-criteria decision analysis with goal programming in engineering, management and social sciences: a state-of-the art review

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