Structure of spherically symmetric objects: a study based on structure scalars

The aim of this paper is to explore the consequences of extra curvature terms mediated from f(R, T, Q) (where Q ≡ R μ ν T μ ν ) theory on the formation of scalar functions and their importance in the study of populations who are crowded with regular relativistic objects. For this purpose, we model our system comprising of non-rotating spherical geometry formed due to gravitation of locally anisotropic and radiating sources. After considering a particular f(R, T, Q) model, we form a peculiar relation among Misner-Sharp mass, tidal forces, and matter variables. Through structure scalars, we have modeled shear, Weyl, and expansion evolutions equations. The investigation for the causes of the irregular distribution of energy density is also performed with and without constant curvature conditions. It is deduced that our computed one of the f(R, T, Q) structure scalars (Y T ) has a vital role to play in understanding celestial mechanisms in which gravitational interactions cause singularities to emerge.

Two-dimensional turbulence on a sphere

Following Fjørtoft (Tellus, vol. 5, 1953, pp. 225–230) we undertake a spectral analysis of a non-divergent flow on a sphere. It is shown that the spherical harmonic energy spectrum is invariant under rotations of the polar axis of the spherical harmonic system and argued that a constraint of isotropy would not simplify the analysis but only exclude low-order modes. The spectral energy equation is derived and it is shown that the viscous term has a slightly different form than given in previous studies. The relations involving energy transfer within a triad of modes, which Fjørtoft (Tellus, vol. 5, 1953, pp. 225–230) derived under the condition that energy transfer is restricted to three modes, are derived under general conditions. These relations show that there are two types of interaction within a triad. The first type is where the middle mode acts as a source for the two other modes and the second type is where it acts as a sink. The inequality indicating cascade directions which was derived by Gkioulekas & Tung (J. Fluid Mech., vol. 576, 2007, pp. 173–189) in Fourier space under the assumptions of narrow band forcing and stationarity is derived in spherical harmonic space under the assumption of dominance of first type interactions. The double cascade theory of Kraichnan (Phys. Fluids, vol. 10, 1967, pp. 1417–1423) is discussed in the light of the derived equations and it is hypothesised that in flows with limited scale separation the two cascades may, to a large extent, be produced by the same triad interactions. Finally, we conclude that the spherical geometry is the optimal test ground for exploration of two-dimensional turbulence by means of simulations.

Highly Accurate Derivation of the Electron Magnetic Moment Anomaly From Spherical Geometry Using a Single Evaluation

The electron magnetic moment anomaly (ae), is normally derived from the fine structure constant using an intricate method requiring over 13,500 evaluations, which is accurate to 11dp. This paper advances the derivation using the fine structure constant and a spherical geometric model for the charge of the electron to reformulate the equation for ae. This highly accurate derivation is also based on the natural log eπ, and the zero-order spherical Bessel function. This determines a value for the electron magnetic moment anomaly accurate to 13 decimal places, which gives a result which is 2 orders of magnitude greater in accuracy than the conventional derivation. Thus, this derivation supersedes the accuracy of the conventional derivation using only a single evaluation.

Variable dynamic styles of primordial heterogeneity preservation in the Earth’s lower mantle

The evolution of the system Earth is critically influenced by the long-term dynamics, composition and structure of the mantle. While cosmochemical and geochemical constraints indicate that the lower mantle hosts an ancient primordial reservoir that may be enriched in SiO2 with respect to the upper mantle, geophysical observations and models point to efficient mass transfer and convective mixing across the entire mantle. Recent hypotheses of primordial-material preservation in a convecting mantle involve delayed mixing of intrinsically dense and/or intrinsically strong heterogeneity. Yet, the effects of composition-dependent rheology and density upon heterogeneity preservation and the dynamics of mantle mixing remain poorly understood. Here, we present two-dimensional numerical models in spherical geometry, investigating the preservation styles of primordial material as a function of its physical properties (i.e., viscosity and density contrasts). We establish multiple regimes of primordial-material preservation that can occur in terrestrial planets. These include (1) efficient mixing, (2) double-layered convection with or without topography, and (3) variable styles of partial heterogeneity preservation (e.g., as diffuse domains, piles or viscous blobs in the lower mantle). Some of these regimes are here characterised for the first time, and all regimes are put into context with each other as a function of model parameters. The viscous-blobs and diffuse-domains regimes can reconcile the preservation of primordial domains in a convecting mantle, potentially resolving the discrepancy between geochemical and geophysical constraints for planet Earth. Several, if not all, regimes characterised here may be relevant to understand the long-term evolution of terrestrial planets in general.

Dyadic Green’s Function for Multilayered Planar, Cylindrical, and Spherical Structures with Impedance Boundary Condition

The integral equation (IE) method is one of the efficient approaches for solving electromagnetic problems, where dyadic Green’s function (DGF) plays an important role as the Kernel of the integrals. In general, a layered medium with planar, cylindrical, or spherical geometry can be used to model different biomedical media such as human skin, body, or head. Therefore, in this chapter, different approaches for the derivation of Green’s function for these structures will be introduced. Due to the recent great interest in two-dimensional (2D) materials, the chapter will also discuss the generalization of the technique to the same structures with interfaces made of isotropic and anisotropic surface impedances. To this end, general formulas for the dyadic Green’s function of the aforementioned structures are extracted based on the scattering superposition method by considering field and source points in the arbitrary locations. Apparently, by setting the surface conductivity of the interfaces equal to zero, the formulations will turn into the associated problem with dielectric boundaries. This section will also aid in the design of various biomedical devices such as sensors, cloaks, and spectrometers, with improved functionality. Finally, the Purcell factor of a dipole emitter in the presence of the layered structures will be discussed as another biomedical application of the formulation.

Holomorphicity, vortex attachment, gauge invariance and the fractional quantum hall effect

A gauge invariant reformulation of nonrelativistic fermions in background magnetic fields is used to obtain the Laughlin and Jain wave functions as exact results in Mean Field Theory (MFT). The gauge invariant framework trades the U(1) gauge symmetry for an emergent holomorphic symmetry and fluxes for vortices. The novel holomorphic invariance is used to develop an analytical method for attaching vortices to particles. Vortex attachment methods introduced in this paper are subsequently employed to construct the Read operator within a second quantized framework and obtain the Laughlin and Jain wave functions as exact results entirely within a mean-field approximation. The gauge invariant framework and vortex attachment techniques are generalized to the case of spherical geometry and spherical counterparts of Laughlin and Jain wave functions are also obtained exactly within MFT.

Self-correcting Sun Compass, Spherical Geometry and Cue-transfers Predict Naïve Migratory Performance

Migratory orientation of many animals is inheritable, enabling naïve migrants to reach remote destinations independently following stepwise (often, nightly) geomagnetic or celestial cues. Which if any such “compass courses” can explain narrow-front trans-continental routes remains unresolved, and evident error-corrections by naïve migrants remain unexplained. We assessed robustness to errors among airborne compass courses and quantified inaugural migration performance globally, accounting for cue transfers (e.g., sun to star compass), in-flight cue maintenance, and previously-overlooked spherical-geometry (longitude) effects. We found (i) sun-compass courses partially self-correct, making them most robust between flight-steps, (ii) within nocturnal flight-steps, geomagnetic or star-compass headings outperform cue-transferred sun-compass steps, (iii) across diverse airborne migration routes, the relative favourability of sun-compass over other courses increases with increasing goal-area, required flight steps and a spherical-geometry factor. Our results can explain enhanced naïve migrant performance, observed diversity in compass-cue hierarchies, and sun-compass orientation being key to many long-distance inaugural migrations.

Direct Numerical Simulations of Cosmic-ray Acceleration at Dense Circumstellar Medium: Magnetic-field Amplification and Maximum Energy

Galactic cosmic rays are believed to be accelerated at supernova remnants. However, whether supernova remnants can be PeV is still very unclear. In this work we argue that PeV cosmic rays can be accelerated during the early phase of a supernova blast-wave expansion in dense red supergiant winds. We solve in spherical geometry a system combining a diffusive–convection equation that treats cosmic-ray dynamics coupled to magnetohydrodynamics to follow gas dynamics. A fast shock expanding in a dense ionized wind is able to trigger fast, non-resonant streaming instability over day timescales and energizes cosmic rays even under the effect of p–p losses. We find that such environments produce PeV blast waves, although the maximum energy depends on various parameters such as the injection rate and mass-loss rate of the winds. Multi-PeV energies can be reached if the progenitor mass-loss rates are of the order of 10−3 M ⊙ yr−1. It has been recently proposed that, prior to the explosion, hydrogen-rich massive stars can produce enhanced mass-loss rates. These enhanced rates would then favor the production of a PeV phase in early times after shock breakout.