Isotropic Density Research Articles

Kerr black hole energy extraction, irreducible mass feedback, and the effect of captured particles charge

We analyze the extraction of the rotational energy of a Kerr black hole (BH) endowed with a test charge and surrounded by an external test magnetic field and ionized low-density matter. For a magnetic field parallel to the BH spin, electrons move outward(inward) and protons inward(outward) in a region around the BH poles(equator). For zero charge, the polar region comprises spherical polar angles -60∘≲θ≲60∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-60^\\circ \\lesssim \ heta \\lesssim 60^\\circ $$\\end{document} and the equatorial region 60∘≲θ≲120∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$60^\\circ \\lesssim \ heta \\lesssim 120^\\circ $$\\end{document}. The polar region shrinks for positive charge, and the equatorial region enlarges. For an isotropic particle density, we argue the BH could experience a cyclic behavior: starting from a zero charge, it accretes more polar protons than equatorial electrons, gaining net positive charge, energy and angular momentum. Then, the shrinking(enlarging) of the polar(equatorial) region makes it accrete more equatorial electrons than polar protons, gaining net negative charge, energy, and angular momentum. In this phase, the BH rotational energy is extracted. The extraction process continues until the new enlargement of the polar region reverses the situation, and the cycle repeats. We show that this electrodynamical process produces a relatively limited increase of the BH irreducible mass compared to gravitational mechanisms like the Penrose process, hence being a more efficient and promising mechanism for extracting the BH rotational energy.

On pseudo-𝒦-symmetric semi-Riemannian manifolds and relativistic applications

In this paper, we present a novel curvature tensor called the [Formula: see text]-curvature tensor, which is formed by combining the Weyl tensor and the [Formula: see text]-curvature tensor. It is proved that a semi-Riemannian manifold with traceless [Formula: see text]-curvature tensor is Einstein, while a [Formula: see text]-curvature flat semi-Riemannian manifold exhibits constant sectional curvature. We show that a space-time with traceless [Formula: see text]-curvature tensor or [Formula: see text]-curvature flat represents dark energy era. A semi-Riemannian manifold with divergence-free [Formula: see text]-curvature tensor is Weyl harmonic. In a space-time where the [Formula: see text]-curvature tensor is of divergence-free, both the isotropic pressure and energy density are constants. Under certain conditions, it is shown that a pseudo-[Formula: see text]-symmetric semi-Riemannian manifold reduces to a pseudo-Riemannian manifold. It is demonstrated that pseudo-[Formula: see text]-symmetric space-times can be regarded as generalized Robertson–Walker (GRW) space-times. Finally, a concrete example of pseudo-[Formula: see text]-symmetric semi-Riemannian manifolds is presented.

Mechanobiochemical bone remodelling around an uncemented acetabular component: influence of bone orthotropy.

Mechanical loosening of an implant is often caused by bone resorption, owing to stress/strain shielding. Adaptive bone remodelling elucidates the response of bone tissue to alterations in mechanical and biochemical environments. This study aims to propose a novel framework of bone remodelling based on the combined effects of bone orthotropy and mechanobiochemical stimulus. The proposed remodelling framework was employed in the finite element model of an implanted hemipelvis to predict evolutionary changes in bone density and associated orthotropic bone material properties. In order to account for variations in load transfer during common daily activities, several musculoskeletal loading conditions of hip joint corresponding to sitting down/up, stairs ascend/descend and normal walking were considered. The bone remodelling predictions were compared with those of isotropic strain energy density (SED)-based, isotropic mechanobiochemical and orthotropic strain-based bone remodelling formulations. Although similar trends of bone resorption were predicted by orthotropic mechanobiochemical (MBC) and orthotropic strain-based models across implanted acetabulum, more volume (10-20%) of bone elements was subjected to bone resorption for the orthotropic MBC model. Higher bone resorption (75-85%) was predicted by the orthotropic strain-based and orthotropic MBC models compared to the isotropic MBC and SED-based models. Higher bone apposition (35-160%) across the implanted acetabulum was predicted by the isotropic MBC model, compared to the SED-based model. The remodelling predictions indicated that a reduction in estrogen level might lead to an increase in bone resorption. The study highlighted the importance of including mechanobiochemical stimulus and bone anisotropy to predict bone remodelling adequately.

A petrophysical study of the composition of Taiwan's middle and lower crust

A first-order approximation of the lithological make-up of an orogen's middle and lower crust can provide insights into its structure, as well as the tectono-metamorphic and geodynamic processes taking place there. In this study, we investigate the possible lithological and chemical composition of Taiwan's middle and lower crust by matching in situ physical properties measured by the TAIGER tomography data with isotropic wavespeeds, density, and major element composition for a variety of upper amphibolite and granulite facies rocks modelled at ambient pressure and temperature using the AbersHacker Macro. The modelling suggests that Taiwan's middle crust is possibly comprised of some combination of biotite-poor metapelite, garnet-poor felsic granulite, mafic granulite, amphibolite, and marble. The lower crust is likely comprised of mafic granulite, garnet-rich felsic granulite, biotite-free metapelite, and eclogite. Furthermore, the modelling shows that the modal abundance of garnet and/or sillimanite has a significant effect on physical properties, elevating seismic wavespeeds and density of felsic rocks to those of mafic rocks. The modelled wt% major oxide composition suggests that Taiwan's middle and lower crust have a more mafic chemical composition than that of global compilations of the continental crust. Nevertheless, this reflects the choices made when assigning rock types for the lithological mix used to calculate the wt% oxides, since increasing the percentage of garnet-rich metapelite and felsic granulite would result in a more felsic bulk composition.

Controllable Deformations of Unconstrained Ideal Nematic Elastomers

We establish that, for ideal unconstrained uniaxial nematic elastomers described by a homogeneous isotropic strain-energy density function, the only smooth deformations that can be controlled by the application of surface tractions only and are universal in the sense that they are independent of the strain-energy density are those for which the deformation gradient is constant and the liquid crystal director is either aligned uniformly or oriented randomly in Cartesian coordinates. This result generalizes the classical Ericksen’s theorem for nonlinear homogeneous isotropic hyperelastic materials. While Ericksen’s theorem is directly applicable to liquid crystal elastomers in an isotropic phase where the director is oriented randomly, in a nematic phase, the constitutive strain-energy density must account also for the liquid crystal orientation which leads to significant differences in the analysis compared to the purely elastic counterpart.

Investigation of space-times through W2-curvature tensor in [formula omitted] gravity

The W2-curvature tensor is an important geometric invariant with relativistic significance, introduced in the early 1970s by Pokhariyal and Mishra, which can be identified in class 4 in the classification of skew-symmetric operators. In this work, we investigate 4-dimensional space-times admitting W2-curvature tensor in f(R,G) modified theory of gravity. It is proved that the W2-curvature flat perfect fluid space-times obeying f(R,G) gravity represent inflation. Also, it is shown that the isotropic pressure and the energy density of such space-times are constant. It is to be noted that in such space-times the considered energy conditions are consistently satisfied if the scalar curvature is positive. Next, we study perfect fluid space-times admitting divergence free W2-curvature tensor in f(R,G) gravity. Amongst other results, we prove that if the energy-momentum tensor of such space-times is bi-recurrent, then either the space-times represent inflation or their isotropic pressure and energy density are constants.

A note on spacetimes in f(R)-gravity

In this work, the investigation of spacetimes admitting semiconformal curvature tensor in f(R)-gravity theory is the major goal. First, semiconformally flat spacetimes in the presence of f(R)-gravity are investigated, and the relationship between isotropic pressure and energy density is discovered. Some energy conditions are then taken into account. Finally, spacetimes with divergence-free semiconformal curvature tensors in f(R)-gravity are explored.

Surface Smoothing by Gas Cluster Ion Beam Using Decreasing Three-Step Energy Treatment

A three-step treatment of Si wafers by gas cluster ion beam with decreasing energy was used to improve the performance of surface smoothing. First, a high energy treatment at 15 keV and an ion fluence of 2 × 1016 cm−2 was used to remove initial surface features (scratches). Next, treatments at 8 and 5 keV with the same fluences reduced the roughness that arose due to the formation of morphological features induced by the surface sputtering at the first high energy step. The surface morphology was characterized by the atomic force microscopy. The root mean square roughness Rq and 2D isotropic power spectral density functions were analyzed. For comparison, the smoothing performances of single-step treatments at 15, 8, and 5 keV were also studied. The lowest roughness values achieved for the single and three-step treatments were 1.06 and 0.65 nm, respectively.

Spacetime admitting semiconformal curvature tensor in f(ℛ) modify gravity

The primary goal of this paper is to examine spacetimes admitting semiconformal curvature tensor in [Formula: see text] modify gravity. The semiconformal flatness of general spacetime and spacetime in [Formula: see text] gravity with perfect fluid, has been analyzed. For this consideration, we generate the forms of isotropic pressure [Formula: see text] and energy density [Formula: see text]. After that, a few energy conditions are taken into account. Finally, we study the divergence-free semiconformal curvature tensor in [Formula: see text] gravity in presence of perfect fluid. We emphasize that for recurrent or bi-recurrent energy–momentum tensor, Ricci tensor of this spacetime is semi-symmetric and consequently, the resulting spacetimes either accomplish inflation or possess fixed isotropic pressure and energy density.

A STUDY ON MANIFOLD KAEHLERIAIN SPACE

This work delves into the space-time theory of the 4-dimensional Kaehler manifold. Since the isotropic pressure, energy density, and energy momentum tensor all vanish in a perfect fluid Kaehler space-time manifold, we have established that this space-time manifold is an Einstein manifold and studied the Einstein equation with a cosmological constant in it. Finally, we demonstrated that, on a conformally flat, perfectly fluid Kaehler space-time manifold, the velocity vector field is infinitesimally spatially isotropic. Ideal fluid dilution to the point where only Ricci and minimal symmetry hold. We have proven that Kaehler space-time manifolds have either 0 scalar curvature or a connection between the respective rho and alpha vector fields via g(rho,alpha) = 4. To conclude, we have proved that a Kaehler space-time manifold cannot have both perfect fluidity and non-zero scalar curvature (weak Ricci symmetry).

Boosting Energy Storage of Poly(vinylidene difluoride) Nanocomposite Based Flexible Self-Standing Film with Low Amount of Hydroxylated V2O5

Polymer-ceramic based nanocomposite dielectric materials have become an attraction for researchers due to their lightweight and high dielectric breakdown strength as well as good dielectric properties. We have synthesized poly(vinylidene difluoride) (PVDF)/hydroxylated-V2O5 (Hy-V2O5) ferroelectric polymer nanocomposite self-standing film, with an average thickness of 0.07 ± 0.005 mm. The phase identification, surface analysis, and structural analysis were performed using differential scanning calorimetry, X-ray photoelectron spectroscopy analysis, and X-ray diffraction, respectively. The analysis of atomic force micrographs reveals lower surface roughness of the nanocomposite films and confirms that the film is suitable for energy storage rather than charge transport with the help of the isotropic power spectral density (PSD) profile. The loading of a low amount of Hy-V2O5 filler in PVDF significantly enhances the ferroelectric polarization, making it highly suitable for high energy storage applications. Enhancement of the dielectric constant (from ∼9 to 29.86) and polarization (Pmax for PVDF = 0.86 μC/cm2 to Pmax for PVDF/Hy-V2O5 = 2.7 μC/cm2 at the 1000 kV/cm field) is obtained. The energy density for the nanocomposite increased to 220% of that of the pure PVDF. Due to the low amount of filler, there is no substantial reduction in the dielectric breakdown strength of the nanocomposite, which is maintained at 1766.93 kV/cm.

A deep look into the dagum family of isotropic covariance functions

AbstractThe Dagum family of isotropic covariance functions has two parameters that allow for decoupling of the fractal dimension and the Hurst effect for Gaussian random fields that are stationary and isotropic over Euclidean spaces. Sufficient conditions that allow for positive definiteness in $\mathbb{R}^d$ of the Dagum family have been proposed on the basis of the fact that the Dagum family allows for complete monotonicity under some parameter restrictions. The spectral properties of the Dagum family have been inspected to a very limited extent only, and this paper gives insight into this direction. Specifically, we study finite and asymptotic properties of the isotropic spectral density (intended as the Hankel transform) of the Dagum model. Also, we establish some closed-form expressions for the Dagum spectral density in terms of the Fox–Wright functions. Finally, we provide asymptotic properties for such a class of spectral densities.

Perfect fluid spacetimes, Gray's decomposition and $f(\mathcal{R}, {T})$-gravity

In this paper, first we give the complete classifications of perfect fluid spacetimes under the Gray's decomposition. Then we investigate the condition under which the Ricci tensor is a conformal Killing tensor in a perfect fluid spacetime. Later, we study perfect fluid spacetimes in $f(\mathcal{R},T)$-gravity theory. We find some relations between isotropic pressure and energy density of the Ricci semisymmetric perfect fluid spacetimes satisfying $f(\mathcal{R},T)$-gravity equation to represent dark matter era.

Spacetimes Admitting Concircular Curvature Tensor in f(R) Gravity

The main object of this paper is to investigate spacetimes admitting concircular curvature tensor in f(R) gravity theory. At first, concircularly flat and concircularly flat perfect fluid spacetimes in fR gravity are studied. In this case, the forms of the isotropic pressure p and the energy density σ are obtained. Next, some energy conditions are considered. Finally, perfect fluid spacetimes with divergence free concircular curvature tensor in f(R) gravity are studied; amongst many results, it is proved that if the energy-momentum tensor of such spacetimes is recurrent or bi-recurrent, then the Ricci tensor is semi-symmetric and hence these spacetimes either represent inflation or their isotropic pressure and energy density are constants.

Domains of Magnetic Pressure Balance in Parker Solar Probe Observations of the Solar Wind

Abstract The Parker Solar Probe (PSP) spacecraft is performing the first in situ exploration of the solar wind within 0.2 au of the Sun. Initial observations confirmed the Alfvénic nature of aligned fluctuations of the magnetic field B and velocity V in solar wind plasma close to the Sun, in domains of nearly constant magnetic field magnitude ∣ B ∣, i.e., approximate magnetic pressure balance. Such domains are interrupted by particularly strong fluctuations, including but not limited to radial field (polarity) reversals, known as switchbacks. It has been proposed that nonlinear Kelvin–Helmholtz instabilities form near magnetic boundaries in the nascent solar wind leading to extensive shear-driven dynamics, strong turbulent fluctuations including switchbacks, and mixing layers that involve domains of approximate magnetic pressure balance. In this work we identify and analyze various aspects of such domains using data from the first five PSP solar encounters. The filling fraction of domains, a measure of Alfvénicity, varies from median values of 90% within 0.2 au to 38% outside 0.9 au, with strong fluctuations. We find an inverse association between the mean domain duration and plasma β. We examine whether the mean domain duration is also related to the crossing time of spatial structures frozen into the solar wind flow for extreme cases of the aspect ratio. Our results are inconsistent with long, thin domains aligned along the radial or Parker spiral direction, and compatible with isotropic domains, which is consistent with prior observations of isotropic density fluctuations or flocculae in the solar wind.

Uncertainty Estimation of Dense Optical Flow for Robust Visual Navigation.

This paper presents a novel dense optical-flow algorithm to solve the monocular simultaneous localisation and mapping (SLAM) problem for ground or aerial robots. Dense optical flow can effectively provide the ego-motion of the vehicle while enabling collision avoidance with the potential obstacles. Existing research has not fully utilised the uncertainty of the optical flow—at most, an isotropic Gaussian density model has been used. We estimate the full uncertainty of the optical flow and propose a new eight-point algorithm based on the statistical Mahalanobis distance. Combined with the pose-graph optimisation, the proposed method demonstrates enhanced robustness and accuracy for the public autonomous car dataset (KITTI) and aerial monocular dataset.

Intensity and anisotropies of the stochastic gravitational wave background from merging compact binaries in galaxies

We investigate the isotropic and anisotropic components of the Stochastic Gravitational Wave Background (SGWB) originated from unresolved merging compact binaries in galaxies. We base our analysis on an empirical approach to galactic astrophysics that allows to follow the evolution of individual systems. We then characterize the energy density of the SGWB as a tracer of the total matter density, in order to compute the angular power spectrum of anisotropies with the Cosmic Linear Anisotropy Solving System (CLASS) public code in full generality. We obtain predictions for the isotropic energy density and for the angular power spectrum of the SGWB anisotropies, and study the prospect for their observations with advanced Laser Interferometer Gravitational-Wave and Virgo Observatories and with the Einstein Telescope. We identify the contributions coming from different type of sources (binary black holes, binary neutron stars and black hole-neutron star) and from different redshifts. We examine in detail the spectral shape of the energy density for all types of sources, comparing the results for the two detectors. We find that the power spectrum of the SGWB anisotropies behaves like a power law on large angular scales and drops at small scales: we explain this behavior in terms of the redshift distribution of sources that contribute most to the signal, and of the sensitivities of the two detectors. Finally, we simulate a high resolution full sky map of the SGWB starting from the power spectra obtained with CLASS and including Poisson statistics and clustering properties.

Bone remodelling in implanted proximal femur using topology optimization and parameterized cellular model

The clinical relevance of bone remodelling predictions calls for accurate finite element (FE) modelling of implant-bone structure and musculoskeletal loading conditions. However, simplifications in muscle loading, material properties, has often been used in FE simulations. Bone adaptation induces changes in bone apparent density and its microstructure. Multiscale simulations, involving optimization methods and biomimetic microstructural models, have proven to be promising for predicting changes in bone morphology. The objective of the study is to develop a novel computational framework to predict bone remodelling around an uncemented femoral implant, using multiscale topology optimization and a parameterized cellular model. The efficacy of the scheme was evaluated by comparing the remodelling predictions with those of isotropic strain energy density (SED) and orthotropy based formulations. The characteristic functional groups and low-density regions of Ward's triangle, predicted by the optimization scheme, were comparable to micro-CT images of the proximal femur. Although the optimization scheme predicted well comparable material distribution in the 2D femur models, the obscured material orientations in some planes of the 3D model indicate the need for a more robust modelling of the boundary conditions. Regression analysis revealed a higher correlation (0.6472) between the topology optimization and SED models than the orthotropic predictions (0.4219). Despite higher bone apposition of 10–20% around the distal tip of the implant, the bone density distributions were well comparable to clinical observations towards the proximal femur. The proposed computational scheme appears to be a viable method for including bone anisotropy in the remodelling formulation.

Evolution of cluster of stars in f(R) gravity

This paper explores the dynamics of evolving cluster of stars in the presences of exotic matter. The $f(R)$ theory is used to presume exotic terms for evolution scenario. We use structure scalars as evolution parameters to explore dynamics of spherically symmetric distribution of evolving cluster of stars. We consider Starobinsky model, $f(R)=R+\epsilon R^2$ and study different evolution modes having features like isotropic pressure, density homogeneity, homologous and geodesic behavior. It is concluded that dynamics of these modes of evolution depends upon the behavior of dark matter. The presences of dark matter directly affects the features of cluster like anisotropic pressure, dissipation, expansion, shear as well as density homogeneity. The evolution having homogeneous density and isotropic pressure depends upon conformally flat and non-dissipative behavior of baryonic as well as non baryonic matter. The dissipation factor induces density inhomogeneity in the expanding clusters having shear effects. The non dissipative homologous evolution also be discussed in the presence and absence of shear effects. It is found that high curvature geometry in the presence of shear supports homologous evolution. Expanding clusters are also explored in the presences of dissipation of dark matter and shear effects. By using quasi-homologous conditions the geodesic evolution is studied. It is theoretically showed that geodesic and homologous conditions depends upon each other. Finally we investigate behavior of Starobinsky model for a stellar structure $4U 1820-30$ toward center. It is found that for increasing values of $\epsilon$ the DM behavior is dominant as compare to baryonic matter.

Construction of unsymmetrical bis‐ureamacrocyclic host for neutral molecule and chloride‐ion binding

AbstractConstruction of synthetic macrocyclic host that can bind with neutral molecules and anions has potential applications in supramolecular chemistry. Herein, we have designed and synthesized blue light emitting an unsymmetrical neutral bis‐urea macrocyclic host. This macrocycle can bind with neutral DMF molecule (1:1) as well as Cl−ion (1:1) through noncovalent interactions. X‐Ray crystal structure,1H NMR titrations with Job's Plot, HRMS with isotropic distribution pattern, FT‐IR, and density functional theory analysis revealed the binding of bis‐urea macrocyclic host with the guest molecule.