Gravitational Influence Research Articles

Mechanisms of Gravitational Influence on Weld Pool Behavior and Weld Bead Performance in Variable Polarity Plasma Arc Welding across Different Welding Position.

This article comprehensively explores the cross-scale effects of gravity on macroscopic flow formation and weld bead formation in variable polarity plasma arc welding. Gravity-induced changes in welding direction were achieved through welding at different spatial positions. The properties of the weld bead were investigated at various spatial locations. Additionally, an elemental tracing technique was employed to study the internal flow behavior of molten metal. In the flat welding position, there is an observable trend of increasing grain size in the welded bead, accompanied by a significant expansion of the coarse grain zone. Consequently, the properties of the weld bead in the flat position are inferior to those achieved in the vertical welding position. This phenomenon can be attributed to the accumulation of molten metal at the exit side of the keyhole, resulting in temperature accumulation. Research indicates that the internal flow within the weld pool plays a critical role in causing this phenomenon. The study's findings reveal the presence of two distinct vortex flow patterns within the weld pool: one aligned with the welding direction and the other directed towards the interior of the weld pool. Particularly noteworthy is the substantial expansion of the flow channel area in the flat welding position, which significantly amplifies the impact of internal flow. This enhanced flow intensity inevitably leads to the increased buildup of molten metal at the keyhole exit side. These studies lay the groundwork for achieving high-quality and controllable spatial-position welding.

Simultaneous Motion Replanning and Gravity Model Refinement near Small Solar System Bodies

Strategic missions to orbit celestial bodies have primarily considered spacecraft trajectories as a two-step process: capture of the spacecraft within the gravitational influence of the body, followed by in-orbit maneuvers. Moreover, a priori maneuver planning approaches using Earth-based measurements tend to generate motion plans that have little scope of replanning, especially when the spacecraft is in the body’s vicinity. Fine-grained motion plans that respond to mission conditions require a detailed understanding of the gravitational forces around the body, which can provide essential information about the body. Our research focuses on a problem variant where the orbital maneuvers are designed to continually refine the onboard gravitational model of the body while simultaneously using the model to perform increasingly smoother orbital maneuvers. We develop a receding horizon approach. Starting with a (low-fidelity) gravity model created from Earth-based observations, the gravity model is continually updated as the spacecraft experiences varying gravitational forces. The updated model is simultaneously and continually used to replan the craft’s trajectory, ensuring that successive maneuvers respect the most up-to-date gravity model. The motion plan eventually attains a near-stable orbital motion. Such an approach has the potential to expand to autonomous missions to improve the mapping and exploration of smaller bodies.

Is There an Earth-like Planet in the Distant Kuiper Belt?

The orbits of trans-Neptunian objects (TNOs) can indicate the existence of an undiscovered planet in the outer solar system. Here we used N-body computer simulations to investigate the effects of a hypothetical Kuiper Belt planet (KBP) on the orbital structure of TNOs in the distant Kuiper Belt beyond ∼50 au. We used observations to constrain model results, including the well-characterized Outer Solar System Origins Survey (OSSOS). We determined that an Earth-like planet (m ∼ 1.5–3 M ⊕) located on a distant (semimajor axis a ∼ 250–500 au, perihelion q ∼ 200 au) and inclined (i ∼ 30°) orbit can explain three fundamental properties of the distant Kuiper Belt: a prominent population of TNOs with orbits beyond Neptune’s gravitational influence (i.e., detached objects with q > 40 au), a significant population of high-i objects (i > 45°), and the existence of some extreme objects with peculiar orbits (e.g., Sedna). Furthermore, the proposed KBP is compatible with the existence of identified gigayear-stable TNOs in the 2:1, 5:2, 3:1, 4:1, 5:1, and 6:1 Neptunian mean motion resonances. These stable populations are often neglected in other studies. We predict the existence of an Earth-like planet and several TNOs on peculiar orbits in the outer solar system, which can serve as observationally testable signatures of the putative planet’s perturbations.

Breakdown of homoclinic orbits to L3 in the RPC3BP (II). An asymptotic formula

The Restricted 3-Body Problem models the motion of a body of negligible mass under the gravitational influence of two massive bodies called the primaries. If one assumes that the primaries perform circular motions and that all three bodies are coplanar, one has the Restricted Planar Circular 3-Body Problem (RPC3BP). In rotating coordinates, it can be modeled by a two degrees of freedom Hamiltonian, which has five critical points called the Lagrange points L1,…,L5.The Lagrange point L3 is a saddle-center critical point which is collinear with the primaries and beyond the largest of the two. In this paper, we obtain an asymptotic formula for the distance between the stable and unstable manifolds of L3 for small values of the mass ratio 0<μ≪1. In particular we show that L3 cannot have (one round) homoclinic orbits.If the ratio between the masses of the primaries μ is small, the hyperbolic eigenvalues of L3 are weaker, by a factor of order μ, than the elliptic ones. This rapidly rotating dynamics makes the distance between manifolds exponentially small with respect to μ. Thus, classical perturbative methods (i.e. the Melnikov-Poincaré method) can not be applied.The obtention of this asymptotic formula relies on the results obtained in the prequel paper [10] on the complex singularities of the homoclinic of a certain averaged equation and on the associated inner equation.In this second paper, we relate the solutions of the inner equation to the analytic continuation of the parameterizations of the invariant manifolds of L3 via complex matching techniques. We complete the proof of the asymptotic formula for their distance showing that its dominant term is the one given by the analysis of the inner equation.

A Gravitation-Based Hierarchical Community Detection Algorithm for Structuring Supply Chain Network

As industrial production outsourcing expands, the collaboration relationship of firms evolves to be more entangled, which means that the enterprise communities in the supply chain network become increasingly overlapping and their boundaries are ambiguous. Given the network complexity, deeper insight into the sequencing orders of suppliers and assemblers is required to orchestrate the supply chain partner collaboration. Considering the overlapping community and multi-layered connectivity characteristics of the supply chain network, in this paper, we design a gravitation-based hierarchical community detection algorithm for structuring the supply chain network. The solution applies a functional modules identification strategy based on node gravitation and a hierarchical clustering strategy based on module gravitation to structure the supply chain network architecture. The key technique is to investigate the global gravitational influence of focal firms, segment the functional modules by characterizing the overlapping conditions among communities, and construct the dendrogram by measuring the gravitational forces between modules in order to map the hierarchical architecture of the dendrogram to structure the supply chain network. The proposed algorithm does not necessitate a prior knowledge about the network. It is adaptable to construct the supply chain network that exhibits scale-free, highly overlapped modular community, and hierarchical characteristics. Experimental results on synthetic benchmark and real-world networks demonstrate the effectiveness and applicability of the proposed algorithm.

Dynamics of dust and meteoroids due to electromagnetic transport in the heliosphere

ABSTRACT Observations of dust in the Solar system have indicated the existence of structures at higher ecliptic latitudes, the origin of which is still an ongoing debate. In a previous study, we studied how the interplanetary magnetic field affects the orbital motion of charged dust particles that are moving in co-orbital motion with Jupiter. Our findings revealed that the Lorentz force causes oscillations in orbital inclinations that lead to electromagnetic transport of the dust particles to higher ecliptic latitudes. In this work, using numerical simulations, we investigate how this transportation depends on orbital lifetime, strength of the background magnetic field, planetary mass, and distance from the Sun. In addition, we study the dynamics also outside resonance. We present our findings using the saturation curve, which gives a relation between the maximum amplitude in inclination with respect to the particle size ranging from 1 to 501 $\mu$m. We further study the influence of the solar radiation pressure, the Poynting–Robertson, and the solar wind effects on the shape of the saturation curve and find that a stronger gravitational influence of the planet leads to a steeper curve, decreasing the strength of the electromagnetic transport. The radiative forces lead to a gradual dampening of the latitudinal oscillations of particles inside resonance, while they are unchanged for objects outside of resonance. We argue that the dynamics of dust and meteoroids in the Solar system can only be understood by including space weathering effects.

Delivery of icy planetesimals to inner planets in the Proxima Centauri planetary system

AbstractThe estimates of the delivery of icy planetesimals from the feeding zone of Proxima Centauri c (with mass equal to 7mE, mE is the mass of the Earth) to inner planets b and d were made. They included the studies of the total mass of planetesimals in the feeding zone of planet c and the probabilities of collisions of such planetesimals with inner planets. This total mass could be about 10–15mE. It was estimated based on studies of the ratio of the mass of planetesimals ejected into hyperbolic orbits to the mass of planetesimals collided with forming planet c. At integration of the motion of planetesimals, the gravitational influence of planets c and b and the star was taken into account. In most series of calculations, planetesimals collided with planets were excluded from integrations. Based on estimates of the mass of planetesimals ejected into hyperbolic orbits, it was concluded that during the growth of the mass of planet c the semi‐major axis of its orbit could decrease by at least a factor of 1.5. Depending on possible gravitational scattering due to mutual encounters of planetesimals, the total mass of material delivered by planetesimals from the feeding zone of planet c to planet b was estimated to be between 0.002mE and 0.015mE. Probably, the amount of water delivered to Proxima Centauri b exceeded the mass of water in Earth's oceans. The amount of material delivered to planet d could be a little less than that delivered to planet b.

Gravitational influence of Saturn’s rings on its moons: a case for free granular flow

Exploratory missions have found that regolith on interplanetary bodies can be loosely packed and freely flowing—a state that strongly affects mission plans and that may also influence the large-scale shapes of these bodies. We investigate here whether notable circumferential ridges seen on Saturn’s moons may be a byproduct of free flow of loosely packed regolith. Such ridges and other features likely record the history of the moons, and we find that if surface grains are freely flowing, then the combined gravity of Saturn itself and its tenuous ring generate similar circumferential features. Moreover, analysis of these features reveals the possibility of previously unreported morphologies, for example, a stationary torus around a non-rotating satellite. Some of these features persist even for a very low density and distant disk, which raises the prospect that nonlinear analysis of interactions from disks to moons and back again may lead to new insights.

WISDOM project – XIV. SMBH mass in the early-type galaxies NGC 0612, NGC 1574, and NGC 4261 from CO dynamical modelling

ABSTRACT We present a CO dynamical estimate of the mass of the supermassive black hole (SMBH) in three nearby early-type galaxies: NGC 0612, NGC 1574, and NGC 4261. Our analysis is based on Atacama Large Millimeter/submillimeter Array (ALMA) Cycle 3–6 observations of the 12CO(2–1) emission line with spatial resolutions of 14–58 pc (0.01″–0.26″). We detect disc-like CO distributions on scales from ≲ 200 pc (NGC 1574 and NGC 4261) to ≈10 kpc (NGC 0612). In NGC 0612 and NGC 1574 the bulk of the gas is regularly rotating. The data also provide evidence for the presence of a massive dark object at the centre of NGC 1574, allowing us to obtain the first measure of its mass, MBH = (1.0 ± 0.2) × 108 M⊙ (1σ uncertainty). In NGC 4261, the CO kinematics is clearly dominated by the SMBH gravitational influence, allowing us to determine an accurate black hole mass of (1.62 ± 0.04) × 109 M⊙ (1σ uncertainty). This is fully consistent with a previous CO dynamical estimate obtained using a different modelling technique. Signs of non-circular gas motions (likely outflow) are also identified in the inner regions of NGC 4261. In NGC 0612, we are only able to obtain a (conservative) upper limit of MBH ≲ 3.2 × 109 M⊙. This has likely to be ascribed to the presence of a central CO hole (with a radius much larger than that of the SMBH sphere of influence), combined with the inability of obtaining a robust prediction for the CO velocity curve. The three SMBH mass estimates are overall in agreement with predictions from the MBH − σ* relation.

Gravity’s Impact on Flow Patterns in Liquid-Gas Systems with Mass Transfer Considerations

This paper investigates bilayer flows of liquid and cocurrent gas in an inclined channel with considerations for heat and mass transfer at the thermocapillary interface, which remains undeformable. The mathematical modeling is based on exact solutions of the special Ostroumov — Birikh type of Navier — Stokes equations in the Oberbek — Boussinesq approximation, accounting for the effect of thermodiffusion and diffusive thermal conductivity effect in the gas-vapor layer. Vapor in the gas is assumed to be a passive admixture that does not affect the properties of the gas. The paper considers the case with the vapor concentration function satisfying the condition of zero vapor flux on the upper wall of the channel. The working system chosen for this study is &lt;&lt;HFE-7l00-nitrogen&gt;&gt;, for which the paper provides examples of velocity profiles, temperature, and vapor concentration distribution in the upper layer. The study analyzes the effect of gravitational influence on the flow pattern and the value of the mass flow rate. The paper presents results for cases when the condition of closed liquid flow is fulfilled, at a negative value of the parameter determining the longitudinal temperature gradient, and at a given value of the gas flow rate.

Analysis of the construction of a port-storm mathematical model of a articulated two-link road train regarding the vertical storage

The article considers possible ways of development and improvement of a flat mathematical model of the movement of an articulated two-link road train considering the track and bringing this model to a spatial model that could consider the change in vertical loads and the subsequent change in the lateral deflection forces, which affect the indicators of turning and controllability of the articulated vehicle. This article proposes constructing a spatial mathematical model of a two-link road train considering the vertical component. The authors consider the problems associated with the movement of a two-track train over uneven terrain and height differences that may occur on the track. They consider the gravitational force's influence on the train's movement and develop a mathematical model that describes this process. The article presents mathematical equations describing the direction of a two-track train in three-dimensional space. They consider the mass of the train, traction forces, air resistance, gravitational force, and reactions from the ground. The authors use numerical methods to solve these equations and conduct computer simulations to study train motion under various conditions. The results of the study demonstrate that the vertical component significantly impacts the movement of a two-track train. It can affect the train's speed, energy efficiency, and stability. The authors conclude with the need to consider the vertical component when building mathematical models of double-track road trains. This paper is essential for researchers and engineers developing and designing road trains. Considering the vertical part will help improve the accuracy of mathematical models and increase the efficiency of two-track road trains in actual operating conditions. The obtained results are essential for developing and improving control systems for two-track road trains, particularly in transport, logistics, and mobile robots. The proposed model can be used to optimize the traffic trajectory and improve the efficiency and safety of the operation of road trains in natural conditions. The proposed model is designed for circular stationary and transient modes of movement of an articulated road train with the possibility of conducting a comparative analysis with a full-scale experiment. Keywords: spatial mathematical model, circular modes, vertical oscillations, articulated train.

Распределение плотности в газовой оболочке планеты

Purpose: Theoretical study of gas density distribution around the planet given self-gravity. Methods: Proposed in this paper equations for the planet gaseous envelope density with corresponding boundary conditions are solved analytically and numerically by Runge-Kutta method. Results: For the first time, the analysis of numerical solution of equations for all the space where the planet gravitational influence prevails - in the distance range from the planet surface till Hill radius - has been pursued using similarity method. Near the planet, the solution coincides with classical barometric formula, at intermediary distances, - with barometric formula which takes into consideration the dependence of free fall acceleration from the distance till the planet, at large distances, - with the dependence of density for singular isothermal gas sphere due to self-gravity. Practical significance: On the basis of the solution obtained, the unified picture of the planet gaseous envelope density distribution was analyzed. The results presented in the paper can be useful both for university physics professors and for the researchers involved in astrophysics.

A semi-analytic study of self-interacting dark-matter haloes with baryons

ABSTRACT We combine the isothermal Jeans model and the model of adiabatic halo contraction into a semi-analytic procedure for computing the density profile of self-interacting dark-matter (SIDM) haloes with the gravitational influence from the inhabitant galaxies. The model agrees well with cosmological SIDM simulations over the entire core-forming stage up to the onset of gravothermal core-collapse. Using this model, we show that the halo response to baryons is more diverse in SIDM than in CDM and depends sensitively on galaxy size, a desirable feature in the context of the structural diversity of bright dwarfs. The fast speed of the method facilitates analyses that would be challenging for numerical simulations – notably, we quantify the SIDM halo response as functions of the baryonic properties, on a fine mesh grid spanned by the baryon-to-total-mass ratio, Mb/Mvir, and galaxy compactness, r1/2/Rvir; we show with high statistical precision that for typical Milky-Way-like systems, the SIDM profiles are similar to their CDM counterparts; and we delineate the regime of core-collapse in the Mb/Mvir − r1/2/Rvir space, for a given cross section and concentration. Finally, we compare the isothermal Jeans model with the more sophisticated gravothermal fluid model, and show that the former yields faster core formation and agrees better with cosmological simulations. We attribute the difference to whether the target CDM halo is used as a boundary condition or as the initial condition for the gravothermal evolution, and thus comment on possible improvements of the fluid model. We have made our model publicly available at https://github.com/JiangFangzhou/SIDM.

Uranus ring occultation observations: 1977–2006

The Uranian rings were discovered serendipitously on 10 March 1977 during a stellar occultation (Elliot et al., 1977a; Millis et al., 1977), and a rich set of subsequent Earth-based occultations revealed that these narrow and sharp-edged rings were eccentric and inclined, precessing under the gravitational influence of the oblate central planet. Considerable progress has been made in understanding the observed characteristics of narrow rings and sharp edges (Nicholson et al., 2018) and their associated dynamics (Longaretti, 2018), but ever since their discovery, the Uranian rings have posed dynamical puzzles that resist simple explanations. The observational basis to address these questions for the Uranus system rests largely on occultation measurements of the narrow rings spanning nearly 30 years, beginning in 1977 and concluding most recently in 2006. Nearly all of these occultation data sets are available in digital form on NASA’s Planetary Data System (PDS) Ring-Moon Systems node, but many of them have not been previously published or described in detail. This paper serves as a guide to the PDS archive and provides essential information about the observations and the methods used to determine the ring widths, mean optical depths, and occultation event times from individual occultation profiles. Additional detail is provided in the Supplementary Online Material accompanying this publication. In a companion paper (French et al., 2023b), we make use of these observations to determine the Uranus ring orbits, pole direction, and gravity field, and the orbital characteristics and masses of three small Uranian moons – Cressida, Ophelia, and Cordelia – from their forced normal modes on the rings.

Forming equal-mass planetary binaries via pebble accretion

Context. Binary Solar System objects are common, ranging from satellite systems with very large mass ratios, M1/M2, to those with mass ratios approaching unity. One well-known example of a binary is the Pluto-Charon system. With Charon being 'only' eight times less massive than Pluto, the question arises (as in the case of many other systems) as to why the mass ratio is still close to unity. There is much evidence that (binary) planet(esimal) formation happened early, when the protoplanetary gas disk was still present. It is likely that (at least some of) these binaries evolved together, as a result of pebble accretion. Pebble accretion is a new key paradigm in planetary formation and it is believed to play a major role in many aspects of the formation of planetary systems, from the radial transport of material to the rapid growth of planetary embryos throughout the system. Aims. Here, we focus on the question of how the mass arriving in the gravitational influence zone of the binary during pebble accretion is distributed over the binary components for a given initial mass ratio. We also consider whether accretion over time leads to equal-mass binaries (converging mass ratio) or to a dominant primary mass with a small moon (diverging mass ratio). Methods. We numerically integrated two-dimensional (2D) pebble trajectories in the same typical fashion as for a single mass that is subject to pebble accretion. We tracked the efficiency of accretion for the two separate binary components, compared to a single body with the same mass. These numerical simulations were done for a range of binary mass ratios, mutual separations, Stokes numbers, and two orbital distances, 2.5 and 39 au. Results. We find that in the limit where pebbles start to spiral around the primary (this holds for relatively large pebbles), the pebble preferentially collides with the secondary, causing the mass ratio to converge towards unity. In our tested case, where the total binary mass is equal to that of the Pluto-Charon system, this takes place on ~Myr timescales. In this regime the total sweep-up efficiency can lower to half that of a pebble-accreting single body because pebbles that are thrown out of the system, after close encounters with the system. These timescales and sweep-up efficiency are calculated under the assumption our 2D simulations compare with the 3D reality. The results show that systems such as Pluto-Charon and other larger equal mass binaries may well have co-accreted by means of pebble accretion in the disk phase without producing binaries, with highly diverging mass ratios.

The cosmic energy gravitational genesis of the strongest earthquakes of the earth occurred near the date 2021.1

We have presented (on January 27, 2023) to the Advances in Environment and Energies the convincing evidence of the cosmic energy gravitational genesis of the strongest earthquakes of the Earth (especially, the Japanese earthquakes) occurred (on February 10, 2021 AD; February 13, 2021 AD and March 4, 2021 AD) near the previously published (in 2019 AD) date 2021.1 AD (corresponding to February 7, 2021 AD) of the local maximal combined planetary and solar integral energy gravitational influence on the internal rigid core of the Earth (and on the Earth as a whole). The date 2021.1 AD is calculated according to the global prediction thermohydrogravidynamic principles (in the frame of the established thermohydrogravidynamic technology) under the first approximation of the circular orbits of the planets around the Sun. The revealed convincing cosmic energy gravitational genesis of the strongest earthquakes of the Earth (occurred near the date 2021.1 AD) is based on the detailed analysis (in the frame of the thermohydrogravidynamic technology) of the strongest earthquakes (according to the U.S. Geological Survey) of the Earth occurred near the local maximal values of the calculated combined planetary and solar integral energy gravitational influences on the internal rigid core of the Earth.

Влияние космических факторов на грязевулканическую деятельность Земли

In this work, the influence of various cosmic factors (gravitational influence of the Moon and the Sun, solar activity, the Earth’s rotation) on mud volcanic activity was analyzed for the first time. The analysis was carried out mainly on the example of mud volcanoes in Azerbaijan, for which there is the largest and most complete catalog of eruptions (431 events over almost 210 years). It has been found that the activity of mud volcanoes can increase after syzygial tides, when the Earth is in line with the Moon and the Sun (their tidal forces are summed up in this case). The response of mud volcanoes to the tidal influence of the Moon is delayed by 5–10 days. It is also found that the number of mud volcanic eruptions is distributed unevenly throughout the year with maximums in March–June and September–October. The presence of these maximums may be due to a change in the distance between the Sun and the Earth and variations in solar tidal forces during the periods of perihelion and aphelion. At the same time, the response of mud volcanoes to the tidal influence of the Sun is delayed by several months and is quite strongly extended in time. It was revealed that there are fluctuations in mud volcanic activity with a period of 14–20 years, which do not coincide with the cycles of solar activity (with periods of 11 and 22 years), although some researchers talk about a connection between solar and mud volcanic activity. It is possible that the indicated fluctuations in mud volcanic activity are related to the main harmonic of the Earth’s nutation (18.6 years). It is shown that the maximum number of mud volcanoes on the Earth falls on the latitudinal belts of 30–45° N and 10–15° N (about 22 and 46 % of the total number of volcanoes, respectively). In the southern hemisphere, the largest number of volcanoes (about 3 % of their total number) is located within the boundaries of 5–10° S.

Collimation of the Relativistic Jet in the Quasar 3C 273

The collimation of relativistic jets launched from the vicinity of supermassive black holes (SMBHs) at the centers of active galactic nuclei (AGNs) is one of the key questions to understand the nature of AGN jets. However, little is known about the detailed jet structure for AGN like quasars since very high angular resolutions are required to resolve these objects. We present very long baseline interferometry (VLBI) observations of the archetypical quasar 3C 273 at 86 GHz, performed with the Global Millimeter VLBI Array, for the first time including the Atacama Large Millimeter/submillimeter Array. Our observations achieve a high angular resolution down to ∼60 μas, resolving the innermost part of the jet ever on scales of ∼105 Schwarzschild radii. Our observations, including close-in-time High Sensitivity Array observations of 3C 273 at 15, 22, and 43 GHz, suggest that the inner jet collimates parabolically, while the outer jet expands conically, similar to jets from other nearby low-luminosity AGNs. We discovered the jet collimation break around 107 Schwarzschild radii, providing the first compelling evidence for structural transition in a quasar jet. The location of the collimation break for 3C 273 is farther downstream from the sphere of gravitational influence (SGI) from the central SMBH. With the results for other AGN jets, our results show that the end of the collimation zone in AGN jets is governed not only by the SGI of the SMBH but also by the more diverse properties of the central nuclei.

A Possible Solution of the Cosmological Constant Problem Based on GW170817 and Planck Observations with Minimal Length Uncertainty

We propose generalized uncertainty principle (GUP) with an additional term of quadratic momentum motivated by string theory and black hole physics and providing a quantum mechanical framework for the minimal length uncertainty, at the Planck scale. We demonstrate that the GUP parameter, β 0 , could be best constrained by the gravitational wave observations, GW170817 event. To determine the difference between the group velocity of graviton and that of the light, we suggest another proposal based on the modified dispersion relations (MDRs). We conclude that the upper bound of β 0 reads ≃1060. Utilizing features of the UV/IR correspondence and the apparent similarities between GUP (including nongravitating and gravitating impacts on Heisenberg uncertainty principle) and the discrepancy between the theoretical and the observed cosmological constant Λ (obviously manifesting gravitational influences on the vacuum energy density), known as catastrophe of nongravitating vacuum, we suggest a possible solution for this long-standing physical problem, Λ ≃ 1 0 − 47 GeV4/ℏ3c3.

Erratum to: Elastodynamic Responses of Magneto Micropolar Isotropic Media under the Gravitational Influence

Erratum to: Elastodynamic Responses of Magneto Micropolar Isotropic Media under the Gravitational Influence