Static solutions in the Freund – Nambu scalar-tensor theory of gravitation

Herein, the system of Einstein equations and the equation of the Freund – Nambu massless scalar field for static spherically symmetric and axially symmetric fields are considered. It is shown that this system of field equations decouples into gravitational and scalar subsystems. In the second post-Newtonian approximation, the solutions for spherically symmetric and slowly rotating sources are obtained. The application of the obtained solutions to astrophysical problems is discussed.

Small batteryless wireless solar powered GPS receivers for subcentimeter land deformation monitoring

<p>We design, implement, and validate a unique permanently deployed land deformation monitoring system using small (brick sized), cheap (approximately $100 USD), batteryless, solar powered singleband GPS wireless sensor nodes. Both hardware and software were designed, implemented, and validated by us. Constraints by our hardware and application prompted us to design a unique distributed relative static positioning algorithm designed for intermittent poor quality phase observable measurements, for sites with high multipath and high node densities requiring good solution accuracies; the static solutions were calculated on a daily basis. Our algorithm used a quarter of the bandwidth that would typically be required for an RF link used for a comparable application. GPS on time was observed to vary greatly from as little as 0.5 hours a day in winter to over 8 hours a day and summer in one of our tests. Typical solution precision was 4 mm 2DRMS. Simulations predicted an undesirable slowly changing solution bias that would repeat every year.</p>

Small batteryless wireless solar powered GPS receivers for subcentimeter land deformation monitoring

<p>We design, implement, and validate a unique permanently deployed land deformation monitoring system using small (brick sized), cheap (approximately $100 USD), batteryless, solar powered singleband GPS wireless sensor nodes. Both hardware and software were designed, implemented, and validated by us. Constraints by our hardware and application prompted us to design a unique distributed relative static positioning algorithm designed for intermittent poor quality phase observable measurements, for sites with high multipath and high node densities requiring good solution accuracies; the static solutions were calculated on a daily basis. Our algorithm used a quarter of the bandwidth that would typically be required for an RF link used for a comparable application. GPS on time was observed to vary greatly from as little as 0.5 hours a day in winter to over 8 hours a day and summer in one of our tests. Typical solution precision was 4 mm 2DRMS. Simulations predicted an undesirable slowly changing solution bias that would repeat every year.</p>

Hyperbolically symmetric sources in Palatini f(R) gravity

A thorough examination of static hyperbolically symmetric matter configuration in the context of Palatini f(R) gravitational theory has been carried out in this manuscript. Following the work of Herrera et al. (Phys. Rev. D 103: 024037, 2021) we worked out the modified gravitational equations and matching conditions using the Palatini technique of variation in Einstein–Hilbert action. It is found from the evaluations that the energy density along with the contribution of dark source terms is inevitably negative which is quite useful in explaining several quantum field effects, because negative energies are closely linked with the quantum field theory. Such negative energies may also assist in time-travel to the past and formation of artificial wormholes. Furthermore, we evaluated the algebraic expressions for the mass of interior hyperbolical geometry and total energy budget, i.e., the Tolman mass of the considered source. Also, the structure scalars are evaluated to analyze the properties of matter configuration. Few analytical techniques are also presented by considering several cases to exhibit the exact analytical static solutions of the modified gravitational equations.

Spherically Symmetric Exact Vacuum Solutions in Einstein-Aether Theory

We study spherically symmetric spacetimes in Einstein-aether theory in three different coordinate systems, the isotropic, Painlevè-Gullstrand, and Schwarzschild coordinates, in which the aether is always comoving, and present both time-dependent and time-independent exact vacuum solutions. In particular, in the isotropic coordinates we find a class of exact static solutions characterized by a single parameter c14 in closed forms, which satisfies all the current observational constraints of the theory, and reduces to the Schwarzschild vacuum black hole solution in the decoupling limit (c14=0). However, as long as c14≠0, a marginally trapped throat with a finite non-zero radius always exists, and on one side of it the spacetime is asymptotically flat, while on the other side the spacetime becomes singular within a finite proper distance from the throat, although the geometric area is infinitely large at the singularity. Moreover, the singularity is a strong and spacetime curvature singularity, at which both of the Ricci and Kretschmann scalars become infinitely large.

Positive energy static solutions for the Chern–Simons–Schrödinger system under a large-distance fall-off requirement on the gauge potentials

In this paper we prove the existence of a positive energy static solution for the Chern–Simons–Schrödinger system under a large-distance fall-off requirement on the gauge potentials. We are also interested in existence of ground state solutions.

Kinematic and Static Solutions for Beam Column with Nonlinear Springs Using the Extended Linear Matching Method

In this paper, the kinematic and static solutions for solving the static response of the beam column with nonlinear springs are presented by adopting the extended linear matching method (LMM). The extended LMM can be used to predict the displacement response of the beam-column system consisting of perfectly plastic and strain-softening materials. It is found that the kinematic solution generated by the extended LMM demonstrates a monotonic decrease for perfect plastic materials with certain restrictions on the yield surface. The potential energy of the system is proved to decrease with iterations for both perfect plastic and strain-softening materials if the loading multiplier remains constant. The extended LMM method is then applied to analyse the response of the pile system in a 3-leg offshore platform. An incremental procedure is recommended to determine the peak load for the soil exhibiting strain-softening. A displacement-control approach is used with the loading multiplier obtained from the variation of the potential energy. Good convergence of the method is obtained.