Related papers: Simple geometric approximations for global atmosph…
Near-surface atmospheric conditions can differ sharply over tens to hundreds of meters due to land cover and topography, yet this variability is absent from current weather analyses and forecasts. It is unclear whether such meter-scale…
A higher order theory of gravitation is considered which is obtained by modifying Einstein field equations. The Lagrange used to modify this in the form a polynomial in (scalar curvature) R. In this equation we have studied spherical…
We investigate the gravitational field of an extended spherically symmetric body within the framework of Extended Relativity (ER), a Lorentz-covariant formulation of relativistic gravity on a Minkowski background. Using a relativistic…
We studied spherically symmetric solutions in scalar-torsion gravity theories in which a scalar field is coupled to torsion with a derivative coupling. We obtained the general field equations from which we extracted a decoupled master…
Only a severely restricted class of tensor fields can provide classical spacetime geometries, namely those that can carry matter field equations that are predictive, interpretable and quantizable. These three conditions on matter translate…
The Universe is a physical object. Physical objects have shapes and sizes. General relativity is insufficient to describe the global shape and size of the Universe: the Hilbert-Einstein equations only treat limiting quantities towards an…
In this paper, we introduce the concepts of gamma and beta approximations via general ordered topological approximation spaces. Also, increasing (decreasing) gamma and beta boundary, positive and negative regions are given in general…
We construct globally regular gravitating Skyrmions, which possess only discrete symmetries. In particular, we present tetrahedral and cubic Skyrmions. The SU(2) Skyrme field is parametrized by an improved harmonic map ansatz. Consistency…
One of the strategies to detect the pose and shape of unknown objects is their geometric modeling, consisting on fitting known geometric entities. Classical geometric modeling fits simple shapes such as spheres or cylinders, but often those…
We derive regularized contour dynamics equations for the motion of infinite sharp fronts in the two-dimensional incompressible Euler, surface quasi-geostrophic (SQG), and generalized surface quasi-geostrophic (gSQG) equations. We derive a…
With the explosive deployment of non-terrestrial networks (NTNs), the computational complexity of network performance analysis is rapidly escalating. As one of the most suitable mathematical tools for analyzing large-scale network…
The self-consistent Gaussian approximation (SCGA) for classical spin systems described by a completely anisotropic D-component vector model is proposed, which takes into account fluctuations of the molecular field and thus is a next step…
One-dimensional (vertical) models of planetary atmospheres typically balance the net solar and internal energy fluxes against the net thermal radiative and convective heat fluxes to determine an equilibrium thermal structure. Thus,simple…
We provide an updated 5 $^\prime $ $\times $ 5 $^\prime $ global geoid model GGM2022, which is determined based on the shallow layer method (Shen method). First, we choose an inner surface $\Gamma$ below the EGM2008 global geoid by 15 m,…
Toroidal orbifolds and their resolutions are described within the framework of (2,2) Gauged Linear Sigma Models (GLSMs). Our procedure describes two-tori as hypersurfaces in (weighted) projective spaces. The description is chosen such that…
Spherical Whittle--Mat\'ern Gaussian random fields are considered as solutions to fractional elliptic stochastic partial differential equations on the sphere. Approximation is done with surface finite elements. While the non-fractional part…
Astrometric missions like Gaia provide exceptionally precise measurements of stellar positions and proper motions. Gravitational waves traveling between the observer and distant stars can induce small, correlated shifts in these apparent…
The concept of turnaround surface in an accelerating universe is generalized to arbitrarily large deviations from spherical symmetry, to close the gap between the idealized theoretical literature and the real world observed by astronomers.…
Let x be a point in R^2 with irrational slope and let \Gamma denote the lattice SL(2,Z) acting linearly on R^2. Then, the orbit \Gamma x is dense in R^2. We give efective results on the approximation of a point y in R^2 by points of the…
A general form of a metric preserving all symmetries of a spherically symmetric gravitational field and angular momentum in spherical coordinates is obtained. Such metric may have $g_{01}(r)\neq 0$. The Newtonian limit uniquely defines…