Mass Profile Research Articles

Star cluster progenitors are dynamically decoupled from their parent molecular clouds

ABSTRACT The formation of stellar clusters dictates the pace at which galaxies evolve, and solving the question of their formation will undoubtedly lead to a better understanding of the Universe as a whole. While it is well known that star clusters form within parsec-scale overdensities of interstellar molecular gas called clumps, it is, however, unclear whether these clumps represent the high-density tip of a continuous gaseous flow that gradually leads towards the formation of stars, or a transition within the gas physical properties. Here, we present a unique analysis of a sample of 27 infrared dark clouds embedded within 24 individual molecular clouds that combine a large set of observations, allowing us to compute the mass and velocity dispersion profiles of each, from the scale of tens of parsecs down to the scale of tenths of a parsec. These profiles reveal that the vast majority of the clouds, if not all, are consistent with being self-gravitating on all scales, and that the clumps, on parsec-scale, are often dynamically decoupled from their surrounding molecular clouds, exhibiting steeper density profiles (ρ∝r−2) and flat velocity dispersion profiles (σ∝r0), clearly departing from Larson’s relations. These findings suggest that the formation of star clusters correspond to a transition regime within the properties of the self-gravitating molecular gas. We propose that this transition regime is one that corresponds to the gravitational collapse of parsec-scale clumps within otherwise stable molecular clouds.

Condensed tannins, novel compounds and sources of variation determine the antiparasitic activity of Nordic conifer bark against gastrointestinal nematodes

The antiparasitic potential of plants could offer a vital solution to alleviating the costs of gastrointestinal nematode (GIN) infections in ruminant production globally. Leveraging known bioactive molecules, however, is complex, where plant species, extraction processes and seasonality impact bioavailability and efficacy. This study assessed the impact of a comprehensive set of factors on the antiparasitic activity of Norwegian conifers to identify bark compounds specific against GIN. Antiparasitic activity was determined using in vitro assays targeting morphologically distinct life stages of ovine GIN: the egg hatch assay and larval motility assay. In depth characterisation of the chemical composition of the bark extracts was carried out using chromatographic separation, UV-absorbance, and molecular mass profiles to identify compounds implicated in the activity. Three key findings emerged: (1) the activity of bark extracts varied markedly from 0 to 100% antiparasitic efficacy, owing to tree species, extraction solvent and seasonality; (2) the GIN exhibited species-and stage-specific susceptibility to the bark extracts; (3) the presence of condensed tannins, amongst other compounds, was associated with anthelmintic activity. These findings add new insights into urgently needed alternative parasite control strategies in livestock.

Motile microorganisms hybrid nanoliquid flow with the influence of activation energy and heat source over a rotating disc

The present article examines the consequences of a magnetic field, Hall current, and thermal radiation on the spinning flow of hybrid nanofluid (HNF) across a revolving disc. The core objective of the study is to improve the energy transference rate through hybrid nano liquid for industrial and engineering operations. The HNFs have advanced thermophysical characteristics. Therefore, in the current study, a superior class of nanomaterials (carbon nanotubes (CNTs) and Al2O3) are added to the base fluid. The modeled equations are demoted to a dimensionless set of Ordinary differential equations (ODEs) through similarity conversion and are analytically solved by engaging the homotopy analysis method. The physical constraints’ effect on energy, velocity, motile microorganism, and mass profiles have been drawn and discussed. For accuracy, the results are compared to the published studies, which ensures the accuracy and reliability of the technique and results. It is observed that the energy communication rate lessens with the flourishing values of thermal radiation and for Hall current. Furthermore, it is noted that due to its carbon–carbon bonding in CNTs, it has a greater tendency for energy propagation than Al2O3 nanoparticles.

Entropy minimization of GO–Ag/KO cross-hybrid nanofluid over a convectively heated surface

Abstract The aim of this study is to provide numerical solutions to magnetohydrodynamic (MHD) cross flow with heat and mass transfer over a stretching sheet in a hybrid nanofluid with suction/injection and convective boundary conditions. This will be accomplished by presenting numeric solutions. Nanoparticles of graphene oxide and silver were suspended in kerosene oil as the base fluid taken into consideration is a nanofluid hybrid. After that, the physical flow problem is modeled as a set of partial differential equations, which are then transformed into an equivalent system of nonlinear ordinary differential equations (ODEs) by making use of the relevant similarity transformations. To gain different graphical and numerical results for analyzing the influence of numerous physical restrictions on velocity, heat, and mass profiles, the system of ODEs is solved using the computing power of the Lobatto IIIA technique. The plot of the velocity profile, temperature, concentration, entropy generation and Bejan number with separating magnitude like that power index number ( 0.1 < n < 2.0 0.1\lt n\lt 2.0 ), Weissenberg number ( 0.1 < We < 1.0 0.1\lt {\rm{We}}\lt 1.0 ), Suction/injection ( 0.1 < S < 1.0 0.1\lt S\lt 1.0 ), Magnetic parameter (0.1 < M < 1.0), Biot number ( 0.1 < Bi < 0.3 0.1\lt {\rm{Bi}}\lt 0.3 ), Radiation parameter ( 0.1 < Rd < 2.0 0.1\lt {\rm{Rd}}\lt 2.0 ), Schmidt number ( 1.1 < Sc < 2.0 1.1\lt {\rm{Sc}}\lt 2.0 ), and Chemical reaction parameter ( 1.1 < Sc < 2.0 1.1\lt {\rm{Sc}}\lt 2.0 ). We noted that when the Weissenberg parameter ( We {\rm{We}} ) increases, the flow speed will increase as well. Also, the increasing values of M M slows the flow speed but the opposite effect is observed in the temperature profile. Moreover, the greater values of M M , We, and S reduced in the local skin friction. It is concluded that hybrid nanofluid is better than ordinary nanofluid by percentage values. The results are used in industry and technology in fluid-based systems with shrinkable or flexible materials, MHD flow meters, pumps, and the drawing of plastic strips. Because hybrid nanoparticles speed up the cooling process, they are important in cutting and production.

Dynamics of MHD Casson fluid in non-Darcy porous medium: The impact of thermal radiation, Dufour–Soret, and chemical reaction

In this research, the dynamics of MHD Casson fluid flow has been discussed in the presence of non-Darcy Forchheimer porous medium. The investigation is focused on how thermal radiation, Soret–Dufour, and chemical reactions affect the incompressible Casson flow in a non-Darcy Forchheimer porous medium, taking account of pressure force. The mathematical model of the system is solved using the finite difference scheme followed by the shooting technique with bvp4c tool in MATLAB. The effects of physical parameters on velocity and transport (heat and mass) profile are illustrated through graphs. From the results, it is observed that Soret effect reduces the thermal boundary layer thickness which leads to the asymptotic increase in heat dissipation. The findings of the study on MHD Casson fluid model considering the non-Darcy Forchheimer porous medium are useful in engineering and science areas such as chemical machinery systems, geophysics, etc.

Physical Evolution of Dark Matter Halo around the Depletion Boundary

We investigate the buildup of the halo profile out to large scale in a cosmological simulation, focusing on the roles played by the recently proposed depletion radii. We explicitly show that halo growth is accompanied by the depletion of the environment, with the inner depletion radius demarcating the two. This evolution process is also observed via the formation of a trough in the bias profile, with the two depletion radii identifying key scales in the evolution. The ratio between the inner depletion radius and the virial radius is approximately a constant factor of 2 across redshifts and halo masses. The ratio between their enclosed densities is also close to a constant of 0.18. These simple scaling relations reflect the largely universal scaled mass profile on these scales, which only evolves weakly with redshift. The overall picture of the boundary evolution can be broadly divided into three stages according to the maturity of the depletion process, with cluster halos lagging behind low-mass ones in the evolution. We also show that the traditional slow and fast accretion dichotomy of halo growth can be identified as accelerated and decelerated depletion phases, respectively.

DESI-253.2534+26.8843: A New Einstein Cross Spectroscopically Confirmed with Very Large Telescope/MUSE and Modeled with GIGA-Lens

Gravitational lensing provides unique insights into astrophysics and cosmology, including the determination of galaxy mass profiles and constraining cosmological parameters. We present spectroscopic confirmation and lens modeling of the strong lensing system DESI-253.2534+26.8843, discovered in the Dark Energy Spectroscopic Instrument (DESI) Legacy Imaging Surveys data. This system consists of a massive elliptical galaxy surrounded by four blue images forming an Einstein Cross pattern. We obtained spectroscopic observations of this system using the Multi Unit Spectroscopic Explorer on ESO’s Very Large Telescope and confirmed its lensing nature. The main lens, which is the elliptical galaxy, has a redshift of z L1 = 0.636 ± 0.001, while the spectra of the background source images are typical of a starburst galaxy and have a redshift of z s = 2.597 ± 0.001. Additionally, we identified a faint galaxy foreground of one of the lensed images, with a redshift of z L2 = 0.386. We employed the GIGA-Lens modeling code to characterize this system and determined the Einstein radius of the main lens to be , which corresponds to a velocity dispersion of σ = 379 ± 2 km s−1. Our study contributes to a growing catalog of this rare kind of strong lensing system and demonstrates the effectiveness of spectroscopic integral field unit observations and advanced modeling techniques in understanding the properties of these systems.

Second law analysis on Ree-Eyring nanoliquid and Darcy Forchheimer flow through a significant stratification in the gyrotactic microorganism

PurposeThe modern day has seen an increase in the prevalence of the improvement of high-performance thermal systems for the enhancement of heat transmission. Numerous studies and research projects have been carried out to acquire an understanding of heat transport performance for their functional application to heat conveyance augmentation. The idea of this study is to inspect the entropy production in Darcy-Forchheimer Ree-Eyring nanofluid containing bioconvection flow toward a stretching surface is the topic of discussion in this paper. It is also important to take into account the influence of gravitational forces, double stratification, heat source–sink and thermal radiation. In light of the second rule of thermodynamics, a model of the generation of total entropy is presented.Design/methodology/approachIncorporating boundary layer assumptions allows one to derive the governing system of partial differential equations. The dimensional flow model is transformed into a non-dimensional representation by applying the appropriate transformations. To deal with dimensionless flow expressions, the built-in shooting method and the BVP4c code in the Matlab software are used. Graphical analysis is performed on the data to investigate the variation in velocity, temperature, concentration, motile microorganisms, Bejan number and entropy production concerning the involved parameters.FindingsThe authors have analytically assessed the impact of Darcy Forchheimer's flow of nanofluid due to a spinning disc with slip conditions and microorganisms. The modeled equations are reset into the non-dimensional form of ordinary differential equations. Which are further solved through the BVP4c approach. The results are presented in the form of tables and figures for velocity, mass, energy and motile microbe profiles. The key conclusions are: The rate of skin friction incessantly reduces with the variation of the Weissenberg number, porosity parameter and Forchheimer number. The rising values of the Prandtl number reduce the energy transmission rate while accelerating the mass transfer rate. Similarly, the effect of Nb (Brownian motion) enhances the energy and mass transfer rates. The rate of augments with the flourishing values of bioconvection Lewis and Peclet number. The factor of concentration of microorganisms is reported to have a diminishing effect on the profile. The velocity, energy and entropy generation enhance with the rising values of the Weissenberg number.Originality/valueAccording to the findings of the study, a slip flow of Ree-Eyring nanofluid was observed in the presence of entropy production and heat sources/sinks. There are features when the implementations of Darcy–Forchheimer come into play. In addition to that, double stratification with chemical reaction characteristics is presented as a new feature. The flow was caused by the stretching sheet. It has been brought to people's attention that although there are some investigations accessible on the flow of Ree-Eyring nanofluid with double stratification, they are not presented. This research draws attention to a previously unexplored topic and demonstrates a successful attempt to construct a model with distinctive characteristics.

Gravitational effects on coffee-ring formation during the evaporation of sessile droplets

We consider the role of gravity in solute transport when a thin droplet evaporates. Under the physically relevant assumptions that the contact line is pinned and the solutal Péclet number, ${Pe}$ , is large, we identify two asymptotic regimes that depend on the size of the Bond number, ${Bo}$ . When ${Bo} = O(1)$ as ${Pe}\rightarrow \infty$ , the asymptotic structure of solute transport follows directly from the surface-tension-dominated regime, whereby advection drives solute towards the contact line, only to be countered by local diffusive effects, leading to the formation of the famous ‘coffee ring.’ In the distinguished limit in which ${Bo} = O({Pe}^{4/3})$ as ${Pe}\rightarrow \infty$ , this interplay between advection and diffusion takes place alongside that between surface tension and gravity. In each regime, we perform a systematic asymptotic analysis of the solute transport and compare our predictions to numerical simulations. We identify the effect of gravity on the nascent coffee ring, providing quantitative predictions of the size, location and shape of the solute mass profile. In particular, for a fixed Péclet number, as the effect of gravity increases, the coffee ring is diminished in height and situated further from the contact line. Furthermore, for certain values of ${Bo}$ , ${Pe}$ and the evaporation time, a secondary peak may exist inside the classical coffee ring. The onset of this secondary peak is linked to the change in type of the critical point in the solute mass profile at the droplet centre. Both the onset and the peak characteristics are shown to be independent of ${Pe}$ .

Numerical Calculation of Thermal Radiative Boundary Layer Nanofluid Flow across an Extending Inclined Cylinder

This research presents the numerical analysis of the fluid flow containing the micro gyrotactic organism with heat and mass transfer. The flow is allowed to pass through an inclined stretching cylinder with the effects of heat generation/a heat source and activation energy subject to the symmetric boundary conditions at the cylinder walls. Similarity transformation is employed in the system of PDEs (partial differential equations) to transform them into non-dimensional ODEs (ordinary differential equations). The solution to the proposed problem is obtained by using the bvp4c (numerical scheme). The graphical results are plotted for various flow parameters in order to show their impact on the flow, mass, energy, and motile microorganism profiles. Moreover, the angle of inclination disturbs the flow within an inclined cylinder and slows down the fluid motion, while it elevates the energy of the fluid inside an inclined cylinder. Similarly, the curvature effect is also highlighted in the dynamics of fluid velocity, temperature, and the motile microorganism profile. From the obtained results, it is elucidated that growing values of the curvature factor accelerate the temperature, velocity, and motile microbes’ profiles. Finally, some engineering quantities are calculated in terms of skin friction, the Nusselt and Sherwood number, and the density of motile microbes. The acquired results are also displayed in tabular form.

Fractional modeling of drug diffusion from cylindrical tablets based on Fickian and relaxed approaches with in vivo validation.

Mathematical simulation of drug diffusion is a significant tool for predicting the bio-transport process. Moreover, the reported models in the literature are based on Fick's approach, which leads to an infinite propagation speed. Consequently, it is essential to construct a mathematical model to represent the diffusion processes for estimating drug concentrations at different sites and throughout the circulation. Thus, in this article, the diffusion process is employed to propose three models for estimating the drug release from multi-layer cylindrical tablets. A fractional model is presented based on Fick's approach, while classical and fractional Cattaneo models are presented using the relaxed principle. Various numerical methods are used to solve the specified problem. The numerical scheme's stability and convergence are demonstrated. Drug concentration and mass profiles are presented for the tablet and the external medium and compared with the in vivo plasma profiles. The results show the efficiency and precision of the proposed fractional models based on the fourth-order weighted-shifted Grünwald-Letnikov difference operator approximation. These models are compatible with the in vivo data compared with the classical Fick's one.

Numerical solution for the electrically conducting hybrid nanofluid flow between two parallel rotating surfaces subject to thermal radiation

In the current analysis, the steady and incompressible magnetohydrodynamics hybrid nanofluid (hnf) flow across two spinning permeable surfaces is studied. The hybrid nanoliquid has been examined under the additional effects of heat source, magnetic field, and Arrhenius activation energy. The hnf is synthesized by the dispersion of silicon dioxide and molybdenum disulfide nanoparticles in ethylene glycol. The flow scenario has been communicated in the form of a system of nonlinear Partial Differential Equations (PDEs), which are degraded and dimensionless to a set of nonlinear ordinary differential equations through appropriate similarity replacement. For the solution of reduced first-order differential equations, a numerical technique is employed. The consequences of physical flow parameters on energy, mass, and velocity profiles are shown through figures. It has been observed that the radial velocity profile increases with the influence of the suction factor and decreases with the effect of surface stretching and the rotation factor. The heat transmission rate increases with the impact of the Reynolds number.

Minimizing Superstructure Twist in Irregular Bridges through Optimization of Structural Parameters

Uneven distribution of mass, stiffness, and strength over the length of a bridge can produce rigid body rotation of the superstructure, or “twisting,” during an earthquake. Twisting response modes lead to the concentration or amplification of damage in the bridge substructure and, as such, are undesirable. AASHTO recommends a balanced stiffness approach to limiting bridge irregularities and provides possible modification techniques for bridges that do not satisfy the recommendations. However, there is a lack of research documenting the implementation details and benefits of these modification techniques on the performance of irregular bridges. This study investigated the effectiveness of three techniques to reduce the twisting response modes for geometrically irregular bridges during earthquakes: adjusting the effective heights of the bridge columns, modifying column end fixity conditions, and redistributing the superstructure mass profile. First, analytical equations were derived to estimate the values of parameters needed to achieve a balanced stiffness using each technique for any arbitrary bridge. Next, a finite-element model of an irregular, reinforced concrete, quarter-scale bridge previously tested on a shake table was validated against available experimental data. This model was used in conjunction with a metaheuristic optimization algorithm to determine the optimal values of the parameters such that the superstructure rotation was minimized for the experimental ground motions. Then, a parametric study was performed using a suite of hazard-consistent and spectrally matched ground motions to investigate the sensitivity of the optimization results to the number and spectral characteristics of the ground motions. The parametric study showed that reducing the effective heights of the columns by stiffening the lower portion of the columns was the most effective method to reduce the twisting response of the bridge and that three ground motions with different spectral shapes were the most computationally efficient subset when performing the optimization methodology.

A Generalized and Efficient Control-Oriented Modeling Approach for Vibration-Prone Delta 3D Printers Using Receptance Coupling

Delta 3D printers can significantly increase throughput in additive manufacturing by enabling faster and more precise motion compared to conventional serial-axis 3D printers. Further improvements in motion speed and part quality can be realized through model-based feedforward vibration control, as demonstrated on serial-axis 3D printers. However, delta machines have not benefited from model-based controllers because of the difficulty in accurately modeling their position-dependent, coupled nonlinear dynamics. In this paper, we propose an efficient framework to obtain accurate linear parameter-varying models of delta 3D printers at any position within their workspace from a few frequency response measurements. We decompose the dynamics into two sub-models&#x2013;(1) an experimentally-identified sub-model containing decoupled vibration dynamics; and (2) an analytically-derived sub-model containing coupled dynamics&#x2013;which are combined into one using receptance coupling. We generalize the framework by extending the analytical model of (2) to account for differing mass profiles and dynamic models of the printer&#x2019;s end-effector. Experiments demonstrate reasonably accurate predictions of the position-dependent dynamics of a commercial delta printer, augmented with a direct drive extruder, at various positions in its workspace. <i>Note to Practitioners</i>&#x2014;This work aims to equip high-speed 3D printers, like delta machines, with model-based controllers to complement their speed with high-accuracy. Due to the coupled kinematic chains of the delta, complex control methodologies, some of which require real-time state measurements, are often used to achieve satisfactory control performance. Our modeling approach provides an efficient methodology for obtaining accurate linear models without the need for real-time measurements, thus enabling practitioners to design linear model-based feedforward controllers to achieve the high throughput and accuracy desired in additive manufacturing (AM). The models we develop in this paper are intended for use with feedforward vibration compensation methods, which can be beneficial for both industrial-scale AM machines that have high-powered servo motors and feedback controllers, as well as consumer-grade AM machines which use stepper motors in feedforward control.

An IllustrisTNG view of the caustic technique for galaxy cluster mass estimation

The TNG300-1 run of the IllustrisTNG simulations includes 1697 clusters of galaxies with M200c &gt; 1014 M⊙ covering the redshift range 0.01 − 1.04. We built mock spectroscopic redshift catalogs of simulated galaxies within these clusters and applied the caustic technique to estimate the cumulative cluster mass profiles. We computed the total true cumulative mass profile from the 3D simulation data, calculated the ratio of caustic mass to total 3D mass as a function of cluster-centric distance, and identified the radial range where this mass ratio is roughly constant. The ratio of 3D to caustic mass on this plateau defines ℱβ. The filling factor, ℱβ = 0.41 ± 0.08, is constant on a plateau that covers a wide cluster-centric distance range, (0.6 − 4.2) R200c. This calibration is insensitive to redshift. The calibrated caustic mass profiles are unbiased, with an average uncertainty of 23%. At R200c, the average MC/M3D = 1.03 ± 0.22; at 2 R200c, the average MC/M3D = 1.02 ± 0.23. Simulated galaxies are unbiased tracers of the mass distribution. IllustrisTNG is a broad statistical platform for application of the caustic technique to large samples of clusters with spectroscopic redshifts for ≳200 members in each system. These observations will allow extensive comparisons with weak-lensing masses and will complement other techniques for measuring the growth rate of structure in the Universe.

TDCOSMO

Time-delay distance measurements of strongly lensed quasars have provided a powerful and independent probe of the current expansion rate of the Universe (H0). However, in light of the discrepancies between early- and late-time cosmological studies, current efforts revolve around the characterisation of systematic uncertainties in the methods. In this work we focus on the mass-sheet degeneracy (MSD), which is commonly considered a significant source of systematics in time-delay strong lensing studies, and aim to assess the constraining power provided by integral field unit (IFU) stellar kinematics. To this end, we approximated the MSD with a cored, two-parameter extension to the adopted lensing mass profiles (with core radius rc and mass-sheet parameter λint), which introduces a full degeneracy between λint and H0 from lensing data alone. In addition, we utilised spatially resolved mock IFU stellar kinematics of time-delay strong lenses, given the prospects of obtaining such high-quality data with the James Webb Space Telescope (JWST) in the near future. We constructed joint strong lensing and generalised two-integral axisymmetric Jeans models, where the time delays, mock imaging, and IFU observations are used as input to constrain the mass profile of lens galaxies at the individual galaxy level and consequently yield joint constraints on the time-delay distance (DΔt) and the angular diameter distance (Dd) to the lens. We find that mock JWST-like stellar kinematics constrain the amount of internal mass sheet that is physically associated with the lens galaxy and limit its contribution to the uncertainties of DΔt and Dd, each at the ≤4% level, without assumptions on the background cosmological model. Incorporating additional uncertainties due to external mass sheets associated with mass structures along the lens line of sight, these distance constraints would translate to a ≲4% precision measurement on H0 in flat Λ cold dark matter cosmology for a single lens. Our study shows that future IFU stellar kinematics of time-delay lenses will be key in lifting the MSD on a per lens basis, assuming reasonable and physically motivated core sizes. However, even in the limit of infinite rc, where DΔt is fully degenerate with λint and is thus not constrained, stellar kinematics of the deflector, time delays, and imaging data will provide powerful constraints on Dd, which becomes the dominant source of information in the cosmological inference.

What causes the formation of discs and end of bursty star formation?

ABSTRACT As they grow, galaxies can transition from irregular/spheroidal with ‘bursty’ star formation histories (SFHs), to discy with smooth SFHs. But even in simulations, the direct physical cause of such transitions remains unclear. We therefore explore this in a large suite of numerical experiments re-running portions of cosmological simulations with widely varied physics, further validated with existing FIRE simulations. We show that gas supply, cooling/thermodynamics, star formation model, Toomre scale, galaxy dynamical times, and feedback properties do not have a direct causal effect on these transitions. Rather, both the formation of discs and cessation of bursty star formation are driven by the gravitational potential, but in different ways. Disc formation is promoted when the mass profile becomes sufficiently centrally concentrated in shape (relative to circularization radii): we show that this provides a well-defined dynamical centre, ceases to support the global ‘breathing modes’ that can persist indefinitely in less-concentrated profiles and efficiently destroy discs, promotes orbit mixing to form a coherent angular momentum, and stabilizes the disc. Smooth SF is promoted by the potential or escape velocity Vesc (not circular velocity Vc) becoming sufficiently large at the radii of star formation that cool, mass-loaded (momentum-conserving) outflows are trapped/confined near the galaxy, as opposed to escaping after bursts. We discuss the detailed physics, how these conditions arise in cosmological contexts, their relation to other correlated phenomena (e.g. inner halo virialization, vertical disc ‘settling’), and observations.

The kinetic Hamiltonian with position-dependent mass

In the present paper we examine in a systematic way the most relevant orderings of pure kinetic Hamiltonians for five different position-dependent mass (PDM) profiles: soliton-like, reciprocal quadratic and biquadratic, exponential and parabolic. As a result of the non-commutativity between momentum and position operators, a diversity of effective potentials is generated. We analyze the whole set and find unexpected coincidences as well as discrepancies among them. We obtain analytically the full-spectrum of energies and solutions in the twenty-five cases considered. It is shown how the simple ordinary constant-mass solutions are transformed into a variety of complex combinations of transcendental functions and arguments. We find that particles with a non-uniform mass density can present discrete energy spectra as well as continuous ones which can be bounded or not. These results are consistent with the fact that although the external potential is zero, PDM eigenfunctions are not actual free states but a sort of effective waves in a solid-state sample. This is precisely the origin of the position-dependent mass. In all the events we obtain exact complete spectral expressions. Our methodological procedure thus puts a wide diversity of Hamiltonian seeds on an equal footing in order to be compared. This allows choosing the better arrangement to model a specific solid or heterostructure once the spectrum of a given material is experimentally available. Finally, we perform a one-dimensional model calculation of a double heterostructure with a parabolic PDM particle in the interface region. Our study is also indicated for applications inside material structures with the addition of external potentials.

An elusive dark central mass in the globular cluster M4

ABSTRACT Recent studies of nearby globular clusters have discovered excess dark mass in their cores, apparently in an extended distribution, and simulations indicate that this mass is composed mostly of white dwarfs (respectively stellar-mass black holes) in clusters that are core collapsed (respectively with a flatter core). We perform mass-anisotropy modelling of the closest globular cluster, M4, with intermediate slope for the inner stellar density. We use proper motion data from Gaia Early Data Release 3 (EDR3) and from observations by the Hubble Space Telescope. We extract the mass profile employing Bayesian Jeans modelling, and check our fits with realistic mock data. Our analyses return isotropic motions in the cluster core and tangential motions (β ≈ −0.4 ± 0.1) in the outskirts. We also robustly measure a dark central mass of roughly $800\pm 300 \, \rm M_\odot$ , but it is not possible to distinguish between a point-like source, such as an intermediate-mass black hole (IMBH), and a dark population of stellar remnants of extent ${\approx} 0.016\, {\rm pc} \simeq 3300\, {\rm au}$ . However, when removing a high-velocity star from the cluster centre, the same mass excess is found, but more extended (${\sim} 0.034\, {\rm pc} \approx 7000\, {\rm au}$ ). We use Monte Carlo N-body models of M4 to interpret the second outcome, and find that our excess mass is not sufficiently extended to be confidently associated with a dark population of remnants. Finally, we discuss the feasibility of these two scenarios (i.e. IMBH versus remnants), and propose new observations that could help to better grasp the complex dynamics in M4’s core.

Poiseuille and thermal transpiration flows of a dense gas between two parallel plates

The Poiseuille and thermal transpiration flows of a dense gas between two parallel plates are investigated on the basis of the Enskog kinetic equation under the diffuse reflection boundary condition. In contrast to the case of an ideal gas, the density and the gradients of pressure and the normal stress component in the flow direction are not uniform in the direction normal to the plates for a dense gas. The non-uniform normal stress gradient contributes also to the acceleration or deceleration of the thermal transpiration flow for small Knudsen numbers. The profiles of mass and heat flows as well as the net mass flows are obtained for various Knudsen numbers and ratios of the molecular diameter to the distance of plates. In the analysis of the Poiseuille flow, most characteristics of a force-driven flow with a small force are recovered. However, for the case of a dense gas, differences between the force-driven and the present pressure-driven flows are observed even within the linearized regime for small force and pressure gradient, especially at the microscopic level. The behaviour of the velocity distribution functions, in particular, the way in which they approach the ones for the Boltzmann equation as the molecular diameter becomes smaller, is clarified.