The Relativistic Generalization of the Gravitational Force for Arbitrary Spacetimes

It has been suggested that re-expressing relativity in terms of forces could provide fresh insights. The formalism developed for this purpose only applied to static, or conformally static, space-times. Here we extend it to arbitrary space-times. It is hoped that this formalism may lead to a workable definition of mass and energy in relativity.Comment: 16 page

Weyl collineations that are not curvature collineations

Though the Weyl tensor is a linear combination of the curvature tensor, Ricci tensor and Ricci scalar, it does not have all and only the Lie symmetries of these tensors since it is possible, in principle, that "asymmetries cancel". Here we investigate if, when and how the symmetries can be different. It is found that we can obtain a metric with a finite dimensional Lie algebra of Weyl symmetries that properly contains the Lie algebra of curvature symmetries. There is no example found for the converse requirement. It is speculated that there may be a fundamental reason for this lack of "duality".Comment: 9 page

Similarities Between Classical Timelike Geodesics in a Naked Reissner-Nordstrom Singularity Background and the Behaviour of Electrons in Quantum Theory

It is generally assumed that naked singularities must be physically excluded, as they could otherwise introduce unpredictable influences in their future null cones. Considering geodesics for a naked Reissner-Nordstrom singularity, it is found that the singularity is effectively clothed by its repulsive nature. Regarding electron as naked singularity, the size of the clothed singularity (electron) turns out to be classical electro-magnetic radius of the electron, to an observer falling freely from infinity, initially at rest. The size shrinks for an observer falling freely from infinity, with a positive initial velocity. For geodetic parameters corresponding to negative energy there are trapped geodesics. The similarity of this picture with that arising in the Quantum Theory is discussed.Comment: 8 pages, 6 figure

Uniqueness of Flat Spherically Symmetric Spacelike Hypersurfaces Admitted by Spherically Symmetric Static Spactimes

It is known that spherically symmetric static spacetimes admit a foliation by {\deg}at hypersurfaces. Such foliations have explicitly been constructed for some spacetimes, using different approaches, but none of them have proved or even discussed the uniqueness of these foliations. The issue of uniqueness becomes more important due to suitability of {\deg}at foliations for studying black hole physics. Here {\deg}at spherically symmetric spacelike hy- persurfaces are obtained by a direct method. It is found that spherically symmetric static spacetimes admit {\deg}at spherically symmetric hypersurfaces, and that these hypersurfaces are unique up to translation under the time- like Killing vector. This result guarantees the uniqueness of {\deg}at spherically symmetric foliations for such spacetimes.Comment: 10 page

Spherically Symmetric Gravitational Collapse

In this paper, we discuss gravitational collapse of spherically symmetric spacetimes. We derive a general formalism by taking two arbitrary spherically symmetric spacetimes with $g_{00}=1$. Israel's junction conditions are used to develop this formalism. The formulae for extrinsic curvature tensor are obtained. The general form of the surface energy-momentum tensor depending on extrinsic curvature tensor components is derived. This leads us to the surface energy density and the tangential pressure. The formalism is applied to two known spherically symmetric spacetimes. The results obtained show the regions for the collapse and expansion of the shell.Comment: 12 pages, 4 figures, accepted for publication in Mod. Phys. Lett.

Design optimisation for cold rolled steel beam sections with web and flange stiffeners

This paper presents the analysis and design optimisation of the cold rolled steel sections for flexural strength considering the effect of cold working exerted on the section during the roll forming process. The sections included channel and zed shapes with complex longitudinal web and flange stiffeners. Nonlinear Finite Element (FE) modelling was developed to model the flexural strength of the channel and zed beams and validated against the four-point bending experiments for these sections. The material properties of steel at the section’s flat parts, corners, and stiffener bends were obtained from tensile tests and were incorporated into the FE simulations to account for the true material properties at these regions due to the cold working during the roll forming process. The strength enhancement at the section corners and stiffener bends obtained from tensile tests were also compared with the predicted values from design standards. The section strength was then optimised using FE modelling results based on the Design Of Experiments (DOE) and response surface methodology. Optimal designs for the channel and zed sections with maximum strength in distortional buckling could be obtained while changing the stiffeners’ position, shape, sizes, and considering true material properties at section corners and stiffener bends. It revealed that, for the two sets of channel and zed sections with the depths of 145 mm and 170 mm, the optimal designs provided up to 43% and 39% increase in flexural strength for the channel and zed sections, respectively; however, when the true material properties at the section corner and the stiffener’s bend regions was included, the increase in flexural strength increased up to 50% and 41%, respectively. Including flange stiffeners to the sections with longitudinal web stiffeners generally increased further the section strength. However, the levels of increase were largely dependent on the section depths and material properties

Foliation of the Kottler-Schwarzschild-De Sitter Spacetime by Flat Spacelike Hypersurfaces

There exist Kruskal like coordinates for the Reissner-Nordstrom (RN) black hole spacetime which are regular at coordinate singularities. Non existence of such coordinates for the extreme RN black hole spacetime has already been shown. Also the Carter coordinates available for the extreme case are not manifestly regular at the coordinate singularity, therefore, a numerical procedure was developed to obtain free fall geodesics and flat foliation for the extreme RN black hole spacetime. The Kottler-Schwarzschild-de Sitter (KSSdS) spacetime geometry is similar to the RN geometry in the sense that, like the RN case, there exist non-singular coordinates when there are two distinct coordinate singularities. There are no manifestly regular coordinates for the extreme KSSdS case. In this paper foliation of all the cases of the KSSdS spacetime by flat spacelike hypersurfaces is obtained by introducing a non-singular time coordinate.Comment: 12 pages, 4 figure

Gravitational wave scintillation by a stellar cluster

The diffraction effects on gravitational waves propagating through a stellar cluster are analyzed in the relevant approximation of Fresnel diffraction limit. We find that a gravitational wave scintillation effect - similar to the radio source scintillation effect - comes out naturally, implying that the gravitational wave intensity changes in a characteristic way as the observer moves.Comment: 9 pages, in press in IJMP

Optimal charging and state-of-charge estimation of a Lithium-ion cell using a simplified full homogenised macro-scale model

Advanced battery management systems (BMS) need accurate and computationally efficient Li-ion cell model for optimum operation as the performance of charging and estimation algorithms of BMS are dependent upon the accuracy of the mathematical model of a cell. This research work presents a novel, accurate and computationally efficient electrochemical model and develops charging and estimation algorithm based on the model. The simplified model is based on the novel full homogenised macroscale model (FHM). The simplified FHM model is compared with a simplified model based on the pseudo-two-dimensional (P2D) model. The FHM model is based on the homogenisation theory, while the volume averaging technique is the basis of the P2D model. Diffusion partial differential equations (PDEs) are approximated by ordinary differential equations with time-varying coefficients. The intercalation current and conduction equation are also approximated to develop variants of the simplified model. The diffusion and reaction rate parameters of the FHM model are more accurate at high temperatures than the parameters based on the empirical Bruggeman method, as the FHM model parameters are based on the numerical model of the electrode structure. The simulations results verify that, compared with a similar simplified model based on the P2D model, the proposed simplified FHM model is more accurate at 318K and higher temperature. The output voltage predicted by the proposed simplified model and the simplified P2D model has a root mean square (RMS) tracking error of 0.6% and 2%, respectively, at 1C input current and 318K temperature. The computational time of the proposed simplified model is reduced by 35% compared with that of the FHM model. Subsequently we present optimal charging of Li-ion cell based on the simplified full homogenised macro-scale (FHM) model. A solid electrolyte interface (SEI) layer model is included in the simplified FHM model to quantify health degradation. With these models, a multi-objective optimal control problem subject to constraints from safety concerns is formulated to achieve the health-conscious optimal charging. This constrained optimal control problem is converted to a nonlinear programming problem (NLP). A nonlinear model predictive control (NMPC) strategy is adopted by solving the NLP at each sampling time using the pseudo-spectral optimisation method. The effect of the input current upper bound on the cell film resistance Rfilm and state of health (SoH) reveals that Rfilm and SoH are more sensitive to input current upper bound at lower values of input current upper bound. Simulation results show that the simplified model and pseudo-spectral method are crucial for reducing the computational load to achieve feasible real-time implementation. The proposed algorithm is more efficient in reducing the health degradation than the conventional constant current constant voltage (CCCV ) charging algorithm since it can explicitly handle the film resistance and capacity as health parameters. Multiple cycle charging simulation reveals that the health-conscious algorithm decrease health degradation and increase battery life. Three observers are used and compared for output feedback charging of a Li-ion cell, i.e. extended Kalman filter (EKF), sliding mode observer (SMO) and moving horizon estimator (MHE). The observers are used in a closed-loop with an NMPC for optimal, health-conscious charging of a Li-ion cell. Simulation results show that EKF and SMO have a low computational burden, whereas MHE exhibits superior performance