Generalized compact star models with conformal symmetry

We generate a new generalized regular charged anisotropic exact model that admits conformal symmetry in static spherically symmetric spacetime. Our model was examined for physical acceptability as realistic stellar models. The regularity is not violated, the energy conditions are satisfied, the physical forces balanced at equilibrium, the stability is satisfied via adiabatic index, and the surface red shift and mass–radius ratio are within the required bounds. Our conformal charged anisotropic exact solution contains models generated by Finch–Skea, Vaidya–Tikekar and Schwarzschild. Also, some recent charged or neutral and anisotropic or isotropic conformally symmetric models are found as special cases of our exact model. Our approach using a conformal symmetry provides a generalized geometric framework for studying compact objects.

Experimentally validated geometrically exact model for extreme nonlinear motions of cantilevers

A unique feature of flexible cantilevered beams, which is used in a range of applications from energy harvesting to bio-inspired actuation, is their capability to undergo motions of extremely large amplitudes. The well-known third-order nonlinear cantilever model is not capable of capturing such a behaviour, hence requiring the application of geometrically exact models. This study, for the first time, presents a thorough experimental investigation on nonlinear dynamics of a cantilever under base excitation in order to capture extremely large oscillations to validate a geometrically exact model based on the centreline rotation. To this end, a state-of-the-art in vacuo base excitation experimental set-up is utilised to excite the cantilever in the primary resonance region and drive it to extremely large amplitudes, and a high-speed camera is used to capture the motion. A robust image processing code is developed to extract the deformed state of the cantilever at each frame as well as the tip displacements and rotation. For the theoretical part, a geometrically exact model is developed based on the Euler–Bernoulli beam theory and inextensibility condition, while using Kelvin–Voigt material damping. To ensure accurate predictions, the equation of motion is derived for the centreline rotation and all terms are kept geometrically exact throughout the derivation and discretisation procedures. Thorough comparisons are conducted between experimental and theoretical results in the form of frequency response diagrams, time histories, motion snapshots, and motion videos. It is shown that the predictions of the geometrically exact model are in excellent agreement with the experimental results at both relatively large and extremely large oscillation amplitudes.

Harmonic/interharmonic estimation using standard deviation assisted ESPRIT method

Purpose This paper aims to accurately estimate harmonics/interharmonics in modern power system. There are several high spectral resolution techniques that have been in use for several years like Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT), Prony methods, etc. but these techniques require prior knowledge of number of modes present in the signal. Model Order (MO) estimation techniques have to make a trade-off between accuracy and their speed i.e., computational burden. Therefore, there is always a requirement of a technique that is fast as well as accurate. Design/methodology/approach The proposed standard deviation (SD) method eliminates the requirement of energy validation test and analyses the distribution pattern, i.e. standard deviation of eigenvalues to identify the number of modes present in the signal. Signal is reconstructed using estimated modes and reconstruction error is obtained to show accuracy of the proposed estimation. Findings Six test synthetic signals as well as one practical signal have been taken for validating the proposed method. The paper shows that proposed methodology has a better accuracy compared to modified exact model order (MEMO) method in high noise environment and takes very less computation time compared to the exact model order (EMO) method. Practical implications The proposed method has been practically implemented for harmonic/interharmonic analysis at a sewage treatment plant at GIFT City, Gujarat, India. Apart from this the proposed method is modeled in python-based tool and is run into low-cost Raspberry Pi like hardware to create an onsite as well as remote monitoring device. Originality/value SD-based approach for model order estimation is novel to this area. Further, the proposed method is compared with EMO and MEMO under varying noise conditions to check for accuracy and estimation time.

Isotropic uncharged model with compactness and stable configurations

In this study we have obtained a new exact model for relativistic stellar object by solving Einstein’s field equation with help of Buchdahl metric. The model is capable to represent some known compact stars like Her X-1,4U 1538-52 and SAX J1808.4-3658. The model satisfies the regularity, casuality, stability and energy conditions. Using the Tolman–Oppenheimer–Volkoff equations, we explore the hydrostatic equilibrium for an uncharged case. We have also compared these conditions with graphical representations that provide strong evidences for more realistic and viable models.

Checking for model failure and for prior-data conflict with the constrained multinomial model

Multinomial models can be difficult to use when constraints are placed on the probabilities. An exact model checking procedure for such models is developed based on a uniform prior on the full multinomial model. For inference, a nonuniform prior can be used and a consistency theorem is proved concerning a check for prior-data conflict with the chosen prior. Applications are presented and a new elicitation methodology is developed for multinomial models with ordered probabilities.