Isotropic Distribution Research Articles

Singularity-free dark energy star in Rastall gravity

The notion of dark energy presents a potential avenue to avoid the gravitational collapse of compact objects, leading to singularities. The present article is devoted primarily to study a novel singularity-free relativistic solution of the Einstein field equations for dark energy stars in the framework of the Rastall theory of gravity. To analyse our model, we consider the Low-Mass X-ray Binary (LMXB) 4U 1608-52 having a mass of 1.74M⊙ and a radius of 9.3 Km (Güver et al., 2010) as a possible dark energy star candidate. We begin with the dark energy equation of state, where the density of dark energy is proportional to the isotropic perfect fluid distribution through a coupling parameter α. We compute the induced metric and extrinsic curvature tensors at the stellar hyper-surface to evaluate the necessary unknown constants appearing in the model. We conduct a thorough and comprehensive analysis to demonstrate the dependence of the physical behaviour of the model on the Rastall parameter (ξ), and interestingly, we obtain a possible phase transition from the dark to baryonic profile, which is sensitive to both α and ξ. We also compute the percentage of dark energy present in the model by varying ξ. However, for a fixed value of ξ, the percentage variation of dark energy with the mass of a star shows that the percentage of dark energy depends on the mass and radius of a star. The causality and energy conditions are well met in the present model, which describes its physical acceptability. The stability of the stellar configuration is established through the study of stability analysis. The graphical nature of the physical parameters and the present theoretical study show that our proposed model is non-singular and a viable representation of a stable realistic stellar structure in the presence of dark and baryonic matter simultaneously.

Directional miscentering dependence in weak lensing mass bias

Abstract Galaxy cluster masses estimated from parametric modeling of weak lensing shear observations are known to be biased by inaccuracies in observationally determined centers. It has recently been shown that such systematic effects can be non-isotropic when centers are derived from X-ray or Compton-Y (Sunyaev-Zeldovich effect) observations, which is often the case in practice. This fact challenges current methods of accurately correcting for weak lensing mass biases using simulations paired with isotropic empirical miscentering distributions, in particular as the effect on determined masses is currently a dominant source of systematic uncertainty. We use hydrodanamical cosmological simulations taken from the Magneticum Pathfinder simulations to show that the non-isotropic component of the mass bias can be reduced to within one percent of the mass when considering the center of mass, rather than the bottom of the gravitational potential, as the reference center of a galaxy cluster.

Combined Fit of Spectrum and Composition for FR0 Radio-galaxy-emitted Ultra–high energy Cosmic Rays with Resulting Secondary Photons and Neutrinos

This study comprehensively investigates the gamma-ray dim population of Fanaroff–Riley Type 0 (FR0) radio galaxies as potentially significant sources of ultra–high energy cosmic rays (UHECRs, E > 1018 eV) detected on Earth. While individual FR0 luminosities are relatively low compared to the more powerful Fanaroff–Riley Type 1 and Type 2 galaxies, FR0s are substantially more prevalent in the local universe, outnumbering the more energetic galaxies by a factor of ∼5 within a redshift of z ≤ 0.05. Employing CRPropa3 simulations, we estimate the mass composition and energy spectra of UHECRs originating from FR0 galaxies for energies above 1018.6 eV. This estimation fits data from the Pierre Auger Observatory (Auger) using three extensive air shower models; both constant and energy-dependent observed elemental fractions are considered. The simulation integrates an approximately isotropic distribution of FR0 galaxies, extrapolated from observed characteristics, with UHECR propagation in the intergalactic medium, incorporating various plausible configurations of extragalactic magnetic fields, both random and structured. We then compare the resulting emission spectral indices, rigidity cutoffs, and elemental fractions with recent Auger results. In total, 25 combined energy-spectrum and mass-composition fits are considered. Beyond the cosmic-ray fluxes emitted by FR0 galaxies, this study predicts the secondary photon and neutrino fluxes from UHECR interactions with intergalactic cosmic photon backgrounds. The multimessenger approach, encompassing observational data and theoretical models, helps elucidate the contribution of low-luminosity FR0 radio galaxies to the total cosmic-ray energy density.

Testing the Isotropic Cauchy Hypothesis.

The isotropic Cauchy distribution is a member of the central α-stable family that plays a role in the set of heavy-tailed distributions similar to that of the Gaussian density among finite second-moment laws. Given a sequence of n observations, we are interested in characterizing the performance of Likelihood Ratio Tests, where two hypotheses are plausible for the observed quantities: either isotropic Cauchy or isotropic Gaussian. Under various setups, we show that the probability of error of such detectors is not always exponentially decaying with n, with the leading term in the exponent shown to be logarithmic instead, and we determine the constants in that leading term. Perhaps surprisingly, the optimal Bayesian probabilities of error are found to exhibit different asymptotic behaviors.

Observational Signatures of AGN Feedback in the Morphology and the Ionization States of Milky Way-like Galaxies

We make an in-depth analysis of different active galactic nuclei (AGN) jet models’ signatures, inducing quiescence in galaxies with a halo mass of 1012 M ⊙. Three jet models, including cosmic-ray-dominant, hot thermal, and precessing kinetic jets, are studied at two energy flux levels each, compared to a jet-free, stellar feedback-only simulation. Each of our simulations is idealized isolated galaxy simulations with AGN jet powers that are constant in time and generated using GIZMO and with FIRE stellar feedback. We examine the distribution of Mg ii, O vi, and O viii ions, alongside gas temperature and density profiles. Low-energy ions, like Mg ii, concentrate in the interstellar medium (ISM), while higher energy ions, e.g., O viii, prevail at the AGN jet cocoon’s edge. High-energy flux jets display an isotropic ion distribution with lower overall density. High-energy thermal or cosmic-ray jets pressurize at smaller radii, significantly suppressing core density. The cosmic-ray jet provides extra pressure support, extending cool and warm gas distribution. A break in the ion-to-mass ratio slope in O vi and O viii is demonstrated in the ISM-to-circumgalactic medium (CGM) transition (between 10 and 30 kpc), growing smoothly toward the CGM at greater distances.

Tuning load redistribution and damage near heterogeneous interfaces

We investigate interface failure of model materials representing architected thin films in contact with heterogeneous substrates. We find that, while systems with statistically isotropic distributions of impurities derive their fracture strength from the ability to develop rough detachment fronts, materials with hierarchical microstructures confine failure near a prescribed surface, where crack growth is arrested and crack surface correlations are suppressed. We develop a theory of network Green’s functions for the systems at hand, and we find that the ability of hierarchical microstructures to control failure mode and locations comes at no performance cost in terms of peak stress and specific work of failure and derives from the quenched local anistotropy of the elastic interaction kernel.

Topological transition in filamentous cyanobacteria: from motion to structure

Many active systems are capable of forming intriguing patterns at scales significantly larger than the size of their individual constituents. Cyanobacteria are one of the most ancient and important phyla of organisms that has allowed the evolution of more complex life forms. Despite its importance, the role of motility on the pattern formation of their colonies is not understood. Here, we investigate the large-scale collective effects and rich dynamics of gliding filamentous cyanobacteria colonies, while still retaining information about the individual constituents’ dynamics and their interactions. We investigate both the colony’s transient and steady-state dynamics and find good agreement with experiments. We furthermore show that the Péclet number and aligning interaction strength govern the system’s topological transition from an isotropic distribution to a state of large-scale reticulate patterns. Although the system is topologically non-trivial, the parallel and perpendicular pair correlation functions provide structural information about the colony, and thus can be used to extract information about the early stages of biofilm formation. Finally, we find that the effects of the filaments’ length cannot be reduced to a system of interacting points. Our model proves to reproduce both cyanobacteria colonies and systems of biofilaments where curvature is transported by motility.

Highly Active NiRu/C Cathode Catalyst Synthesized by Displacement Reaction for Anion Exchange Membrane Water Electrolysis.

Anion exchange membrane water electrolysis (AEMWE) is highly promising for cost-effective green hydrogen production due to its basic operating conditions facilitating the use of non-noble catalysts. While non-noble Ni/Fe-based catalysts are utilized at the anode, its cathode catalyst still requires precious Pt. Due to the high cost of Pt and the sluggish hydrogen evolution reaction (HER) at the cathode in basic conditions, developing alternative catalysts to replace Pt is highly important. Here, a synthesis procedure for a Ru-based catalyst is reported and its high activity toward the HER in alkaline media is demonstrated in both half-cell and single-cell tests. The catalyst is synthesized in a two-step approach. A highly dispersed Ni catalyst is prepared on carbon support in the first step. In the second step, Ru is deposited on its surface using a galvanic displacement reaction. The uniqueness of this method is that Ru is deposited over the entire electrically conductive surface, resulting in an isotropic and homogeneous Ru distribution within the catalyst powder. It is demonstrated that this material remarkably outperforms state-of-the-art Pt/C catalysts in half-cell and single-cell tests. The single cell only requires 1.73V at 1A cm-2 with an overall PGM content of 0.05mg cm-2.

The Navier-Stokes equation and a fully developed turbulence

In fairly general conditions we give explicit (smooth) solutions for the potential flow. We show that, rigorously speaking, the equations of the fluid mechanics have not rotational solutions. However, within the usual approximations of an incompressible fluid and an isentropic flow, the Navier-Stokes equation has approximate vorticial (rotational) solutions, generated by viscosity. However, in general, these vortices are unstable, and a discrete distribution of vorticial solutions is not in me chanical equilibrium; it forms an unstable vorticial liquid. On the other hand, these solutions may exhibit turbulent, fluctuating instabilities for large variations of the velocity over short distances. We represent a fully developed turbulence as a homogeneous, isotropic and highly-fluctuating distribution of singular centres of turbulence. A regular mean flow can be included. In these circumstances the Navier-Stokes equation exhibits three time scales. The equations of the mean flow can be disentangled from the equations of the fluctuating part, which is reduced to a vanishing inertial term. This latter equation is not satisfied after averaging out the temporal fluctuations. For a homogeneous and isotropic distribution of non-singular turbulence centres the equation for the inertial term is satisfied trivially, i.e. both the average fluctuating velocity and the average fluctuating inertial term are zero. If the velocity is singular at the turbulence centres, we are left with a quasi-ideal classical gas of singularities, or a solution of singularities (solute) in quasi thermal equilibrium in the background fluid (solvent). This is an example of an emergent dynamics. We give three examples of vorticial liquids.

Proton Cyclotron Waves and Pickup Ion Ring Distribution Instabilities Upstream of Mars

AbstractProton cyclotron waves (PCWs) upstream of Mars are thought to be associated with the instabilities of pickup ions. The instabilities of pickup ions of ring distributions have larger maximum growth rates compared with beam distributions. However, observations revealed a notably‐reduced occurrence rate of PCWs for pickup ions of ring distributions. Linear instability analysis and a corresponding two‐dimensional particle‐in‐cell (PIC) simulation are performed to investigate the instabilities of pickup ion ring distributions upstream of Mars. Linear instability analysis indicates that a pickup ion ring distribution is unstable to the ion cyclotron, ion Bernstein, and mirror instabilities. The corresponding PIC simulation confirms the linear analysis results and further demonstrates that the pickup ions are scattered toward an isotropic shell distribution by the waves excited. Interestingly, the saturation energy of the waves is much lower than that driven by a corresponding pickup ion beam distribution, and mirror waves eventually dominate the system.

Surface wave imaging with stationary-phase noise sources based on ultrashort traffic-induced data: An application in karst cave detection

Abstract In urban environments, abundant traffic-induced noise data are analyzed through crosscorrelation to retrieve high-frequency (> 1 Hz) surface waves, providing a cost-effective technique for detecting near-surface structures. The isotropic noise source distribution is an essential prerequisite for the correct reconstruction of the Green’s function. The azimuth of traffic noise sources, however, can change with human activities in highly populated urban areas, resulting in non-random distributions in time and space. Due to the uneven distribution of traffic noise sources, spurious signals are generated in the noise crosscorrelation functions and phase velocities calculated from the retrieved surface waves are overestimated, leading to incorrect S-wave velocity profiles. By analyzing the noise source distribution of each segment, we selected the stationary-phase segments to improve the retrieval of surface waves. We processed approximately one-day ultrashort continuous recordings to obtain virtual shot gathers with larger multichannel-coherency coefficients and dispersion images with more surface-wave dispersion data. S-wave velocity profiles for different arrays, including a 3D S-wave velocity model, were produced by inverting the surface-wave dispersion data to reveal the distribution of karst caves beneath the surface. The results demonstrate the effectiveness of the strategy of the stationary-phase segment selection and the great potential of traffic-induced surface waves in monitoring subsurface changes in urban areas.

A 3D view of multiple populations’ kinematics in Galactic globular clusters

We present the first 3D kinematic analysis of multiple stellar populations (MPs) in a representative sample of 16 Galactic globular clusters (GCs). For each GC in the sample, we studied the MP line-of-sight, plane-of-the-sky and 3D rotation, and velocity distribution anisotropy. The differences between first-population (FP) and second-population (SP) kinematic patterns were constrained by means of parameters specifically defined to provide a global measure of the relevant physical quantities and to enable a meaningful comparison among different clusters. Our analysis provides the first observational description of the MP kinematic properties and of the path they follow during their long-term dynamical evolution. In particular, we find evidence of differences between the rotation of MPs along all velocity components with the SP preferentially rotating faster than the FP. The difference between the rotation strength of MPs is anticorrelated with the cluster dynamical age. We also observe that FPs are characterized by isotropic velocity distributions at any dynamical age probed by our sample. On the contrary, the velocity distribution of SP stars is found to be radially anisotropic in dynamically young clusters and isotropic at later evolutionary stages. The comparison with a set of numerical simulations shows that these observational results are consistent with the long-term evolution of clusters forming with an initially more centrally concentrated and more rapidly rotating SP subsystem. We discuss the possible implications these findings have on our understanding of MP formation and early evolution.

Plausibility of Capture into High-obliquity States for Exoplanets in the M Dwarf Habitable Zone

For temperate exoplanets orbiting M-dwarf hosts, the proximity of the habitable zone to the star necessitates careful consideration of tidal effects. Spin synchronization of the planetary orbital period and rotation period, tidal locking, and the subsequent impact on surface conditions frames common assumptions about M-dwarf planets. We investigate the plausibility of capture into Cassini State 2 (CS2) for a known sample of 280 multiplanet systems orbiting M-dwarf hosts. This resonance of the spin precession and orbital precession frequencies can excite planets into stable nonzero rotational obliquities, breaking tidal locking and inducing a version of “day” and “night.” Considering each planetary pair and estimating the spin and orbital precession frequencies, we find that 75% of detected planets orbiting M dwarfs may be plausibly excited to a high obliquity and maintain it through subsequent tidal dissipation over long timescales. We also investigate two possible mechanisms for capture into CS2: quantifying the orbital migration or primordial obliquity necessary for CS2. We find orbital migrations by a factor of ≲2 and an isotropic initial spin distribution can produce high-obliquity planets, aligning with similar findings for planets orbiting close-in to FGK dwarfs. Many of the planets in our sample reside in both CS2 and within their stellar habitable zone. Over half of the planets with T eq < 400 K around host stars with T eff < 3000 K could possess nonzero obliquity due to residence in CS2. This overlap renders the potential capture into Cassini States extremely relevant to understanding the galaxy’s most common temperate planets.

Negative-Free Self-Supervised Gaussian Embedding of Graphs

Graph Contrastive Learning (GCL) has recently emerged as a promising graph self-supervised learning framework for learning discriminative node representations without labels. The widely adopted objective function of GCL benefits from two key properties: alignment and uniformity, which align representations of positive node pairs while uniformly distributing all representations on the hypersphere. The uniformity property plays a critical role in preventing representation collapse and is achieved by pushing apart augmented views of different nodes (negative pairs). As such, existing GCL methods inherently rely on increasing the quantity and quality of negative samples, resulting in heavy computational demands, memory overhead, and potential class collision issues. In this study, we propose a negative-free objective to achieve uniformity, inspired by the fact that points distributed according to a normalized isotropic Gaussian are uniformly spread across the unit hypersphere. Therefore, we can minimize the distance between the distribution of learned representations and the isotropic Gaussian distribution to promote the uniformity of node representations. Our method also distinguishes itself from other approaches by eliminating the need for a parameterized mutual information estimator, an additional projector, asymmetric structures, and, crucially, negative samples. Extensive experiments over seven graph benchmarks demonstrate that our proposal achieves competitive performance with fewer parameters, shorter training times, and lower memory consumption compared to existing GCL methods.

Remote Sensing Image Segmentation Based on Probabilistic Fuzzy Local Information Clustering

Abstract. In this paper, a remote sensing image segmentation based on probabilistic fuzzy local information clustering algorithm is proposed. First, assuming that the spectral measure within the same ground object follows the same probability distribution. The dissimilarity between pixel and object is modeled by the negative logarithm of the Gaussian probability density function. It can improve the noise sensitive problem caused by the Euclidean distance which can only describe the data with isotropic distribution. Then, in order to consider the effect of local spatial constraint, on the one hand, the probability measure is used to modify the local fuzzy factor to establish the dissimilarity measure with spatial constraints. On the other hand, the hidden Markov random field is used to model the prior probability model of pixel membership. Next, the entropy regularization term of the objective function is built by combining the Kullback-Leibler(KL) maximum entropy model to further improve the robustness and noise resistance. The qualitative and quantitative analysis of simulated image and different types of real remote sensing images show that the proposed algorithm can effectively overcome the above problems and further improve the accuracy of image segmentation to over 95%.

Osteoblast Response to Widely Ranged Texturing Conditions Obtained through High Power Laser Beams on Ti Surfaces.

Titanium and titanium alloys are the prevailing dental implant materials owing to their favorable mechanical properties and biocompatibility, but how roughness dictates the biological response is still a matter of debate. In this study, laser texturing was used to generate eight paradigmatic roughened surfaces, with the aim of studying the early biological response elicited on MC3T3-E1 pre-osteoblasts. Prior to cell tests, the samples underwent SEM analysis, optical profilometry, protein adsorption assay, and optical contact angle measurement with water and diiodomethane to determine surface free energy. While all the specimens proved to be biocompatible, supporting similar cell viability at 1, 2, and 3 days, surface roughness could impact significantly on cell adhesion. Factorial analysis and linear regression showed, in a robust and unprecedented way, that an isotropic distribution of deep and closely spaced valleys provides the best condition for cell adhesion, to which both protein adsorption and surface free energy were highly correlated. Overall, here the authors provide, for the first time, a thorough investigation of the relationship between roughness parameters and osteoblast adhesion that may be applied to design and produce new tailored interfaces for implant materials.

Five-dimensional compact stars in Einstein-Gauss-Bonnet gravity

Within the framework of Einstein-Gauss-Bonnet theory in five-dimensional spacetime (5D EGB), we derive the hydrostatic equilibrium equations and solve them numerically to obtain neutron stars for both isotropic and anisotropic distribution of matter. The mass-radius relations are obtained for SLy equation of state, which describes both the solid crust and the liquid core of neutron stars, and for a wide range of the Gauss-Bonnet coupling parameter α. More specifically, we find that the contribution of the Gauss-Bonnet term leads to substantial deviations from Einstein gravity. We also discuss that after a certain value of α, the theory admits higher maximum masses compared with general relativity, however, the causality condition is violated in the high-mass region. Finally, our results are compared with the recent observations data on mass-radius diagram.

Use of the 5P3/2→6P3/2 electric dipole forbidden transition in Rb as a non-perturbing probe of atom dynamics in an operating magneto-optical trap

Abstract Results of spectroscopy experiments using the $5P_{3/2} \to 6P_{3/2}$ electric dipole forbidden transition in cold rubidium atoms are presented. Production of this forbidden transition is detected by observing the emission of the $420 $ nm fluorescence photons that result from the decay of the $6P_{3/2} $ state into the ground state. The experiments are performed under the steady state operation conditions of a magneto-optical trap (MOT), and thus provide non-perturbing information on the atom-light system. The hyperfine structure of the $6P_{3/2}$ level is completely resolved, and the fluorescence peaks show the expected Autler-Townes (AT) splitting of the emission lines. This hyperfine structure is used to calibrate the frequency scale of all spectra recorded. A combination of this absolute frequency scale and an expression for the AT profile allows an absolute determination of the effective Rabi frequency and detuning of the MOT. The behavior of these AT doublets is studied as a function of frequency detuning and also as a function of the trapping light intensity.&amp;#xD;The experiments also take full advantage of the strong polarization dependence of the relative intensities of the hyperfine fluorescence components.&amp;#xD;This study results in a sensitive probe of the relative populations of the magnetic sublevel projections relative to the trapping magnetic field gradient.&amp;#xD;An almost isotropic population distribution was found, but small deviations from isotropy could be determined with this electric dipole forbidden probe.

Role of decoupling process on the configurations of compact stars induced by Thomas-Fermi dark matter with null complexity in f(T) gravity

Our goal in this work is to find an anisotropic solution for a self-bound compact object composed of dark matter with a null complexity factor in f(T)-gravity theory. We use a well-known gravitational decoupling via complete geometric deformation (CGD) technique to examine the role of decoupling parameters on the configuration of compact objects. Initially, we derive the null complexity condition for f(T)-gravity decoupled system which leads to a relation between gravitational potentials. Next, we apply the CGD approach to split the decoupled system into two subsystems. The initial system refers to a pure f(T) gravity system consisting of an isotropic fluid distribution, where the isotropy criterion is equivalent to the condition in Einstein's gravity. The solution of the first system is solved through the Vlasenk-Pronin space-time metrics while the second system associated with the deformation function is solved by the density constraints method by mimicking a new source with Thomas-Fermi dark matter density profile that generates the anisotropy in the decoupled system. The physical validity of the anisotropic solution is checked by the graphical analysis of the pressure, density, energy, and stability conditions. We have also shown the effect of torsion and decoupling parameters on the configuration of anisotropic compact objects. The energy exchange (ΔE) of fluid distribution is also discussed. We found that ΔE is positive throughout the stellar configuration, which implies that energy is effectively transmitted to the surrounding environment.

On sequences of convex records in the plane

Abstract Convex records have an appealing purely geometric definition. In a sequence of d-dimensional data points, the nth point is a convex record if it lies outside the convex hull of all preceding points. We specifically focus on the bivariate (i.e. two-dimensional) setting. For iid (independent and identically distributed) points, we establish an identity relating the mean number ⟨ R n ⟩ of convex records up to time n to the mean number ⟨ N n ⟩ of vertices in the convex hull of the first n points. By combining this identity with extensive numerical simulations, we provide a comprehensive overview of the statistics of convex records for various examples of iid data points in the plane: uniform points in the square and in the disk, Gaussian points and points with an isotropic power-law distribution. In all these cases, the mean values and variances of Nn and Rn grow proportionally to each other, resulting in the finite limit Fano factors FN and FR . We also consider planar random walks, i.e. sequences of points with iid increments. For both the Pearson walk in the continuum and the Pólya walk on a lattice, we characterise the growth of the mean number ⟨ R n ⟩ of convex records and demonstrate that the ratio R n / ⟨ R n ⟩ keeps fluctuating with a universal limit distribution.