Morse potential in relativistic contexts from generalized momentum operator: Schottky anomalies, Pekeris approximation and mapping

In this work, we explore a generalization of the Dirac and Klein–Gordon (KG) oscillators, provided with a deformed linear momentum inspired in nonextensive statistics, that gives place to the Morse potential in relativistic contexts by first principles. In the (1 + 1)-dimensional case, the relativistic oscillators are mapped into the quantum Morse potential. Using the Pekeris approximation, in the (3 + 1)-dimensional case, we study the thermodynamics of the S-waves states (l = 0) of the H2, LiH, HCl and CO molecules (in the non-relativistic limit) and of a relativistic electron, where Schottky anomalies (due to the finiteness of the Morse spectrum) and spin contributions to the heat capacity are reported. By revisiting a generalized Pekeris approximation, we provide a mapping from (3 + 1)-dimensional Dirac and KG equations with a spherical potential to an associated one-dimensional Schrödinger-like equation, and we obtain the family of potentials for which this mapping corresponds to a Schrödinger equation with non-minimal coupling.

Generalization of Thermal and Mass Fluxes for the Flow of Differential Type Fluid with Caputo–Fabrizio Approach of Fractional Derivative

In this research work, generalized thermal and mass transports for the unsteady flow model of an incompressible differential type fluid are considered. The Caputo–Fabrizio fractional derivative is used for the respective generalization of Fourier’s and Fick’s laws. A MHD fluid flow is considered near a flat vertical surface subject to unsteady mechanical, thermal, and mass conditions at boundary. The governing equations of flow model are solved by integral transform, and closed form results for generalized momentum, thermal, and concentration fields are obtained. Generalized thermal and mass fluxes at boundary are quantified in terms of Nusselt and Sherwood numbers, respectively, and presented in tabular form. The significance of the physical parameters over the momentum, thermal, and concentration profiles is characterized by sketching the graphs.

Algebraic Structure and Poisson Integral Method of Snake-Like Robot Systems

The algebraic structure and Poisson's integral of snake-like robot systems are studied. The generalized momentum, Hamiltonian function, generalized Hamilton canonical equations, and their contravariant algebraic forms are obtained for snake-like robot systems. The Lie-admissible algebra structures of the snake-like robot systems are proved and partial Poisson integral methods are applied to the snake-like robot systems. The first integral methods of the snake-like robot systems are given. An example is given to illustrate the results.

Sensorless Whole-Body Compliance Control of Collaborative Manipulator Based on Haptic Filter and Position Controller

This study presents a cost-effective sensorless whole-body compliance control strategy for collaborative manipulator. The control strategy realizes decoupled adjustable compliant effects, namely, stiffness, damping, and inertia controls, under a single control framework. The inherent position controller is retained, which ensures a smooth transition between normal position operation and compliance control. The two features can greatly simplify the customization of collaborative manipulator control algorithms. A modified sensorless disturbance observer based on generalized momentum is used to estimate the external torque, and this way eliminates the dependence on the force/torque sensors. Only basic motor position sensors are required. The compliant trajectory generated by the external torque is sufficiently smooth owing to the haptic filter. Various experiments prove that the modified sensorless disturbance observer is effective. The necessity of using the position servo loop for sensorless compliance control is discussed through a comparative experiment. The proposed compliance control strategy is further verified using sensorless and sensor-based disturbance observers.

Are environment, informal sector and poverty interrelated?

In developing countries, the informal sector plays a diverse role, from eradicating poverty to polluting the environment. Perhaps, due to inadequate awareness and scanty literature, the aspect remained ignored. This study was an attempt to determine the simultaneous relationship between environment, informal sector, and poverty. This study was based on panel data study of three countries, Pakistan, Bangladesh, and India. ARDL approach was used to measure the size of the informal sector economy of Pakistan, India, and Bangladesh. The generalized momentum (GMM) method was applied to determine the environment's simultaneous effects, on poverty, and the informal sector economy. The outcomes unveiled that informal sector employment and poverty expedited the carbon dioxide emission in three countries such as India, Pakistan and Sri Lanka. Secondly, poverty and CO2 emissions had a positive association with the informal sector whereas thirdly, there was a negative impact of the informal sector economy and CO2 emissions on the poverty. This study urges to channelize the informal sector because it can contribute towards poverty reduction in a better way once its channelized and provision of adequate awareness among the people regarding judicious use of natural resources. For instance, climate smart agriculture, sustainable farming and Good Agricultural Practices have been implemented to curtail the CO2 emissions from agriculture sector. The needs are to provoke other sectors as well followed by the initiation of legal restrictions on CO2 emissions

A generalized Momentum/Complexity correspondence

Holographic complexity, in the guise of the Complexity = Volume prescription, comes equipped with a natural correspondence between its rate of growth and the average infall momentum of matter in the bulk. This Momentum/Complexity correspondence can be related to an integrated version of the momentum constraint of general relativity. In this paper we propose a generalization, using the full Codazzi equations as a starting point, which successfully accounts for purely gravitational contributions to infall momentum. The proposed formula is explicitly checked in an exact pp-wave solution of the vacuum Einstein equations.