Density Profile Research Articles

Unexpectedly Localized and Grid-like Density Profiles for Bethe Solutions of the Open-boundary XXX Spin Chain with Two Down-spins

Unexpectedly Localized and Grid-like Density Profiles for Bethe Solutions of the Open-boundary XXX Spin Chain with Two Down-spins

Influence of charge on conformations, inter-molecular structure and thermodynamics of symmetric polystyrene-block-polymethacrylic acid (PS-b-PMA) polyelectrolyte micelle in aqueous solution

ABSTRACT The various aspects of molecular structure, kinetics, and thermodynamics of symmetric polystyrene-b-poly(methacrylic acid) (PS-b-PMA) block copolymer micelle in salt-free aqueous solution as a function of degree-of-ionisation (f) of PMA (corona) block was investigated by explicit molecular dynamics (MD) simulations. Micelle size increases linearly with f in a qualitative agreement with simulation results in the literature. With increase in charge density of the corona-forming PMA chain block, the micelle becomes more spherical, and there is a decrease in the surface area of micelle core and an increase in the favourable interactions among the PS chains. The structure of the micelle changes with f. The behaviour of the RDF’s of core and corona PMA atoms and the enthalpy of solvation show that the interactions among the segments of the core PS blocks are insensitive to variation in f. The atom density profiles, solvation enthalpy, and coordination number of PMA-Na+ and Water-Na+ pairs reveal the existence of the micelle in the ‘osmotic regime’ in agreement with results from experiments and mean-field theory in literature. The significance of electrostatic interactions on the kinetics of formation, structural aspects, and thermodynamics of micellisation is shown. The characteristics of PMA-b-PS micelle are compared with those of PAA-b-PS.

Interfacial Characteristics of Ice-Supporting Substrates via Molecular Dynamics Simulations.

Ice accumulation on aircraft surfaces poses significant safety and performance risks, necessitating the development of coatings to prevent ice adhesion. The present work focuses on characterizing the interfacial properties of ice on various substrates through molecular descriptors. We follow the hypothesis that has been previously proposed in several experimental works according to which a disordered, quasi-liquid layer (QLL) of water at the substrate/ice interface is developed, which in turn acts as a self-lubricant reducing material's ice adhesion strength. To put this idea into the test, we conducted extensive molecular dynamics (MD) simulations on ice supported by different types of substrates, such as graphite, boron nitride, and a cross-linked epoxy polymer. Our findings reveal that the ice structure becomes disordered near the interface for all substrates, with a more pronounced effect in the polymer substrate. The formation of QLL at the interface was quantified using metrics such as local density, Q6 order parameter, and hydrogen bonding. The polymer substrate showed a thicker QLL compared to the two flat surfaces, as this was verified by both the significant differences in the local water density profiles and the distribution of the employed order parameter. The latter ones were directly correlated to the development of hydrogen bonds between the interfacial water molecules and the polymer substrate's polar atoms, which was found to induce a more intense disruption of ice's crystal structure. Moreover, our analysis revealed that the polymer's oxygen atoms contribute more to hydrogen bonding with the water molecules than the nitrogen atoms, with hydroxyl oxygens (-OH) contributing more compared to the epoxy ones (-O-). The analysis related to the dynamics of the interfacial water molecules revealed a substantial reduction in mobility on the epoxy, exceeding the slowdown observed on boron nitride, with graphite demonstrating the least reduction in dynamic behavior among the substrates studied.

The role of the hot porous layer in the gas flow in the inner coma

The objective of this work is to study the influence of a highly non-isothermal porous dust layer on the formation of a comet's inner coma. We studied the water gas activity of comet 67P/Churyumov-Gerasimenko to find a link between the gas properties around the comet and the properties of the dust surface crust. The effects on the radiative transfer spectral lines were studied and compared with MIRO remote sensing observations. For cases of spherical and complex nucleus shapes, we validated surface boundary conditions for gas flow obtained from the two-layer consistent thermophysical model. This model accurately estimates the properties of the sublimation products as the gas diffuses through the layer. The gas expansion was then modeled using a 3D parallel implementation of a direct simulation Monte Carlo algorithm. A multi-beam linear interpolation was used to extract the gas density, velocity, and temperature profiles along a given line of sight. Finally, the radiative transfer equation was used to calculate the brightness temperature of the water vapor. The presence of a porous layer results in an increase in gas temperature and a decrease in gas density at the surface. The gas has a greater acceleration due to the higher initial temperature and increased conversion of translational energy to kinetic energy. This reduces the difference in density between the different models, with the densest gas being the coolest, and increases the terminal expansion velocity of the hotter gas. While the gas density differences are small at large distances, the observable water absorption lines are significantly affected. The presence of a porous layer has a large effect on the properties of the gas in the coma, which can be seen by comparing the spectral lines. This demonstrates the potential interest of the approach in improving surface activity models and placing physical constraints on the dust layer.

The contact angle and structure of water on the graphite‐like substrate: A classical density functional approach

AbstractThe influences of temperature and water−graphite interaction energy on the contact angle (θ) and structure of water on the graphite‐like substrate have been investigated using the classical density functional theory. We find that the temperature‐dependent behavior of cosθ is contingent upon the water−graphite interaction energy, manifesting in three distinct patterns: increasing, decreasing, or remaining nearly invariant with temperature within the examined range (273.16–640K). Furthermore, a novel simple equation has been derived to describe the temperature‐dependent variation of cosθ at constant water−graphite interaction energy, that is, , where is the water−vapor interfacial tension, and the value of depends on the water−graphite interaction energy. According to different values of , this equation is able to successfully represent the three aforementioned patterns. At last, the density profile and hydrogen bonding structure of water near the substrate have been analyzed to offer microscopic insights.

Multi-physics ensemble modelling of Arctic tundra snowpack properties

Abstract. Sophisticated snowpack models such as Crocus and SNOWPACK struggle to properly simulate profiles of density and specific surface area (SSA) within Arctic snowpacks due to underestimation of wind-induced compaction, misrepresentation of basal vegetation influencing compaction and metamorphism, and omission of water vapour flux transport. To improve the simulation of profiles of density and SSA, parameterisations of snow physical processes that consider the effect of high wind speeds, the presence of basal vegetation, and alternate thermal conductivity formulations were implemented into an ensemble version of the Soil, Vegetation, and Snow version 2 (SVS2-Crocus) land surface model, creating Arctic SVS2-Crocus. The ensemble versions of the default and Arctic SVS2-Crocus were driven with in situ meteorological data and evaluated using measurements of snowpack properties (snow water equivalent, SWE; depth; density; and SSA) at Trail Valley Creek (TVC), Northwest Territories, Canada, over 32 years (1991–2023). Results show that both the default and Arctic SVS2-Crocus can simulate the correct magnitude of SWE (root-mean-square error, RMSE, for both ensembles – 55 kg m−2) and snow depth (default RMSE – 0.22 m; Arctic RMSE – 0.18 m) at TVC in comparison to measurements. Wind-induced compaction within Arctic SVS2-Crocus effectively compacts the surface layers of the snowpack, increasing the density, and reducing the RMSE by 41 % (176 kg m−3 to 103 kg m−3). Parameterisations of basal vegetation are less effective in reducing compaction of basal snow layers (default RMSE – 67 kg m−3; Arctic RMSE – 65 kg m−3), reaffirming the need to consider water vapour flux transport for simulation of low-density basal layers. The top 100 ensemble members of Arctic SVS2-Crocus produced lower continuous ranked probability scores (CRPS) than the default SVS2-Crocus when simulating snow density profiles. The top-performing members of the Arctic SVS2-Crocus ensemble featured modifications that raise wind speeds to increase compaction in snow surface layers and to prevent snowdrift and increase viscosity in basal layers. Selecting these process representations in Arctic SVS2-Crocus will improve simulation of snow density profiles, which is crucial for many applications.

Reanalysis of the MACHO Constraints on PBH in the Light of Gaia DR3 Data

The recent astrometric data of hundreds of millions of stars from Gaia DR3 has allowed for a precise determination of the Milky Way rotation curve up to 28 kpc. The data suggest a rapid decline in the density of dark matter beyond 19 kpc. We fit the whole rotation curve with four components (gas, disk, bulge, and halo), and compute the microlensing optical depth to the Large Magellanic Cloud. With this model of the galaxy we reanalyse the microlensing events of the MACHO and EROS-2 Collaborations. Using the published MACHO efficiency function for the duration of their survey, together with the rate of expected events according to the new density profile, we find that the Dark Matter halo could be composed of up to 20% of massive compact halo objects for any mass between 0.001 to 1M⊙. For the EROS-2 survey, using a modified efficiency curve for consistency with the MACHO analysis, we also find compatibility with a MACHO halo, but with a tighter constraint around 0.005M⊙ where the halo fraction cannot be larger than ∼10%. This result assumes that all the lenses have the same mass. If these were distributed in an extended mass function like that of the Thermal History Model, the constraints are weakened, allowing 100% of all DM in the form of Primordial Black Holes.

New constraints on the central mass contents of Omega Centauri from combined stellar kinematics and pulsar timing

We performed a combined analysis of stellar kinematics with line-of-sight accelerations of millisecond pulsars (MSPs) to probe the mass content of Omega Centauri (OC ). Our mass model includes the stellar mass distribution, a more concentrated mass component linked to the observed MSP population, a generic cluster of stellar remnants (assumed to be more concentrated than the stars and MSPs), and an intermediate-mass black hole (IMBH), allowing us to determine which of these is statistically preferred to account for these observations. We mass-modeled OC using the package GravSphere to solve the Jeans equations, including constraints in the form of proper motions, line-of-sight velocities, the surface density profile of the stars, the spatial distribution of MSPs, and the recently measured line-of-sight accelerations of a subset of these MSPs, self-consistently modeling their intrinsic spin-down. We explore the impact of different assumed centers of OC on our results and we infer the posterior distributions of the model parameters from the combined likelihood using the nested sampling package dynesty Our analysis favors an extended central mass of $ over an IMBH, setting a 3sigma upper limit on the IMBH mass of $6 We find that pulsar timing observations are an important additional constraint, favoring a central mass distribution that is $ 20<!PCT!>$ more massive and extended than implied by models that are constrained by the stellar kinematics alone. Finally, we find a 3sigma confidence level (CL) upper bound of $6 on the total mass traced by the MSPs, with the density profile following $ p (r) star (r)^ with $ 0.3,$ where $ star (r)$ is the stellar mass density and $ is the stellar velocity dispersion profile. This favors models in which MSPs form via stellar encounters, as in the leading paradigm whereby MSPs are the progeny of low-mass X-ray binaries. Our analysis demonstrates how combining stellar kinematics with MSP accelerations produces new constraints on mass models, shedding light on the presence or absence of IMBHs at the centers of globular clusters. Further, we provide the first validation of its kind where MSP positions are linked to their place of formation in globular clusters, which is in excellent agreement with the expectations of stellar encounter models of MSP formation. This sets a promising precedent amid the rapid growth in the number of observations and discoveries currently taking place in this field.

Radial variation of fiber morphology and wood density of the commercial species Drypetes sp. and Myroxylon balsamum

Studying the radial variation of wood density, an essential biophysical property that reflects the quality of commercial species in tropical forests, is crucial. Understanding how these variations relate to wood anatomy provides valuable insights. In this study, we evaluated fiber morphology and radial density variation using X-ray densitometry in two commercial species from southeastern Peru. Ten trees from each species, Drypetes sp. and Myroxylon balsamum (Peru balsam), were analyzed. Fiber characteristics were assessed using macerated tissue, and density profiles were obtained via X-ray densitometry. The results indicate that in Drypetes sp., density decreases from the pith to the bark, whereas Myroxylon balsamum shows no significant radial variation. These findings are important for the efficient use and processing of these species.

Compaction‐Driven Convection in the Growing Inner Core

AbstractThe Earth's inner core (IC) is known to exhibit heterogeneous structures with their origins still unknown. From the onset of nucleation, the IC can grow via sedimentation and compaction of iron crystals freezing out from the fluid outer core. Previous studies of IC growth have shown entrapment of fluid within the solid matrix, and unstable density profiles in 1D can appear depending on the efficiency of fluid percolation. In this study, we perform simulations of IC growth in spherical geometries (assuming axisymmetry). We find that it is possible for the IC to develop large‐scale convective flows under certain conditions and, in some instances, produce small‐scale heterogeneites close to the IC boundary. Assuming representative values for the physical properties of the Earth's IC, we show that it is possible for the IC to exhibit compaction‐driven convection today.

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.

Advances in laser-based bremsstrahlung x-ray sources. II. Laser pulse propagation and guiding in nonuniform plasma media in the presence of self-focusing

An analytic Wentzel–Kramers–Brillouin model is presented of Gaussian laser pulse propagation through plasma with a quadratic transverse density profile and an arbitrarily varying, longitudinal density gradient under conditions of nonlinear self-focusing. From these solutions, it is shown that in the absence of nonlinear self-focusing and transverse nonuniformity, for exponential pre-plasma density profiles, the use of a low density coating of the laser target with electron density n0∼11 ncr (e.g., a CH foam of density 35 mg/cm3 for 1-micron laser light) maximizes laser intensity at best focus. Also, under laser and plasma conditions relevant to recent experiments on high-power laser systems, conditions are obtained for a Gaussian laser pulse to propagate stably through the pre-plasma medium. Such conditions would be expected to enhance the production of relativistic electrons from laser-target coupling, providing a possible explanation for the observed increase in MeV photon dose and enabling applications such as laser-based MeV X-ray radiography.

A new method for producing uniform, loose, initially unsaturated specimens

Moist tamping (MT) forms the most common method for the reconstitution of predominately sand tailings, largely owing to its ability to produce loose specimens without segregation. However, MT has been subject to considerable criticism for not producing a fabric like hydraulically placed sands or tailings and owing to non-uniform initial internal density profile. Alternatively, given the increased implementation of filtered tailings stacks, MT is commonly applied to characterise such materials owing to the initial unsaturated and sometimes loose state achievable, while still suffering from potential issues from non-uniformity. To enable the advantages of MT to be realised while also achieving high initial sample uniformity, and therefore tests that can be treated as an element, a new method referred to as moist vibration (MV) is proposed. This method involves preparation of a sample in a tube with vibration used to densify and increase uniformity, prior to extrusion and trimming for testing. Assessments carried out on two soils demonstrated that high uniformity is achieved with the new method. Finally, comparison of MT and MV samples by means of undrained shearing shows no discernible difference in the results for a sand and only subtle differences in a clay–sand mixture.

Density corrugation due to beating of two modes of a quasi-electrostatic wave near the upper hybrid resonance

The effect of beating of two modes of a quasi-electrostatic wave near the linear-mode conversion point in magnetized plasmas is analyzed in the kinetic approximation. It is shown that the effect is accompanied by spatial modulation and corrugation of the plasma density profile.

Process-Based Evaluation of Intraseasonal Oceanic Kelvin Waves in the Pacific Ocean in CMIP6 Models

Abstract Oceanic intraseasonal Kelvin waves (KWs) help modulate upper-ocean thermal characteristics, providing feedbacks to important coupled air–sea phenomena in the tropics. The recent availability of daily thermocline depth fields from several phase 6 of the Coupled Model Intercomparison Project (CMIP6) models makes it possible to evaluate the performance of KWs and identify potential sources of bias. Most models fail to simulate a realistic spatial distribution of KW variability. Models simulate a large variability of KWs in the western or eastern Pacific rather than in the central Pacific as observed. The modeled KWs propagate slowly (about 1.5 m s−1) compared to observations (about 2.5 m s−1). This slow propagation is also identified in wavenumber–frequency spectra for KWs and meridional KW structures, which is more consistent with a second baroclinic mode structure in models compared to the first baroclinic mode structure in observations. An analysis of the relative contributions of the vertical wavenumber and background ocean stability to KW phase speeds indicates that the high vertical wavenumber bias in models contributes most to the slow propagation, in which the higher-than-observed vertical wavenumbers imply the biased incorporation of higher baroclinic modes in the model KW structure. This finding is further supported by the results of vertical mode decomposition that incorporates background density profiles. These results indicate that a realistic representation of the KW vertical structure is essential to produce realistic KW propagations in models. Significance Statement Oceanic intraseasonal Kelvin waves (KWs) play a significant role in regulating the heat content and temperature of the ocean, which provides feedbacks to coupled ocean–atmosphere phenomena in the tropics such as El Niño–Southern Oscillation (ENSO). Consequently, identifying the biases in KWs and the potential sources of those biases in state-of-the-art models is essential to improve simulations of ENSO and its diversity and advance forecasts of weather extremes around the globe induced by ENSO. We find that KWs in the models propagate slower than observations, mainly due to biases in their vertical structure, with secondary effects due to biases in model ocean stability. These issues may be potential sources for current imperfect ENSO model simulations and predictions.

The Iron Spin Transitions in Hydrous Fe3+‐Bearing Bridgmanite and Its Geophysical Properties in the Lower Mantle

AbstractHydrous Fe3+‐bearing bridgmanite (Bdg) is potentially a critical water host in the lowermost mantle. The spin transition behaviors of such materials are pivotal for understanding geophysical heterogeneity in the deep Earth but are poorly understood. Here, we investigated the spin transition and related geophysical properties of Fe3+ with associated H defects [Fe3+‐H] at high P‐T conditions using first‐principles simulations. Our calculations predict that the presence of hydrogen reduces the onset pressure of the spin transition of Fe3+ in Bdg, leading to higher fractions of low spin Fe3+. Along standard geotherms, spin transition is predicted to remain incomplete even at the core‐mantle boundary (CMB), and lateral temperature variations would significantly affect the proportions of high and low spin Fe and related properties like elasticity. The thermoelastic property of hydrous Fe3+‐bearing bridgmanite exhibit stronger softening anomalies at the lower mantle conditions compared to dry system, which potentially enhancing the seismic detectability of the hydrous Bdg in the deep earth. Density profile of hydrous Fe3+‐bearing bridgmanite indicates that the [Fe3+‐H] defect modestly increases the system's density, but much less than that caused by incorporating an equivalent amount of iron alone. This is crucial for understanding regions like Large Low Shear Velocity Provinces (LLSVPs), which exhibits large velocity drops but only minor density changes. The co‐adsorption of Fe and H allows for the introduction of Fe to induce velocity drops without the concomitant sharp increase in density, as pure iron would, thus enabling Fe‐H enrichment as a potential source of LLSVPs.

Two-Dimensional Bi2Se3 Nanosheets Synthesis for Efficient Electrocatalytic Production of Ammonia from Nitrate

Ammonia (NH3), a critical component for various industries, is produced through the Haber-Bosch process, which, despite its importance, is a significant source of carbon emissions and operates on a centralized model, emphasizing the need for innovative solutions to decarbonize and decentralize its production. Electrochemical nitrate (NO3–) reduction to NH3 presents a promising alternative to the Haber-Bosch process for NH3 synthesis, with the added advantage of transforming waste into a valuable resource while mitigating water pollution concerns. However, achieving a well-defined active center and catalytic selectivity in the electrochemically driven reaction remains a significant challenge. In this study, we successfully fabricated a highly selective and active 2D Bi2Se3 catalyst, which demonstrated better performance in reducing NO3– to NH3 with a Faradaic efficiency (FE) of approximately 80% (−0.3V (RHE)) and a significant yield rate of 45mgh−1mgcat−1 (0.46 mmolh−1cm−2). Furthermore, the fabricated material exhibited exceptional stability and durability, maintaining a high NO3– reduction of 80% FE even after 10 consecutive cycles of extended use and continuous operation, demonstrating its remarkable resilience and reliability. Our findings show that the prepared catalyst selectively promotes the electrochemical reduction of NO3– to NH3 while suppressing the competing hydrogen evolution reaction (HER). The charge density profile indicates a pronounced charge localization around the Se atoms, implying that the Se active sites in the 2D Bi2Se3 catalyst act as the active center for the NO3– reduction mechanism, playing a crucial role in facilitating the reaction kinetics.

Two-dimensional ASEP model to study density profiles in CVD growth

The growth of two-dimensional (2D) transition metal dichalcogenides using chemical vapor deposition has been an area of intense study, primarily due to the scalability requirements for potential device applications. One of the major challenges of such growths is the large-scale thickness variation of the grown film. To investigate the role of different growth parameters computationally, we use a 2D asymmetric simple-exclusion process (ASEP) model with open boundaries as an approximation to the dynamics of deposition on the coarse-grained lattice. The variations in concentration of particles (growth profiles) at the lattice sites in the grown film are studied as functions of parameters like injection and ejection rate of particles from the lattice, time of observation, and the right bias difference between the hopping probabilities towards right and towards left) imposed by the carrier gas. In addition, the deposition rates at a given coarse-grained site is assumed to depend on the occupancy of that site. The effect of the maximum deposition rate, i.e., the deposition rate at a completely unoccupied site on the substrate, has been explored. The growth profiles stretch horizontally when either the evolution time or the right bias is increased. An increased deposition rate leads to a step-like profile, with the higher density region close to the left edge. In 3D, the growth profiles become more uniform with the increase in the height of the precursor with respect to the substrate surface. These results qualitatively agree with the experimental observations.

Automated Parametrization Approach for Coarse-Graining Soil Organic Matter Molecules.

Investigating the molecular structure of soil organic matter (SOM), along with its intramolecular interactions and interactions with other soil components and xenobiotics, is essential due to its ecological importance. However, the complexity and heterogeneity of SOM present significant challenges for systematic studies. While experimental methods are commonly employed, atomistic simulations provide a complementary approach to exploring molecular-level processes. The Vienna Soil Organic Matter Modeler 2 (VSOMM2) facilitates the construction of molecular models of SOM systems with various compositions at the atomistic scale, which can then be examined through molecular dynamics (MD) simulations. This study introduces a parametrization strategy that enables the conversion of VSOMM2-generated structures into a coarse-grained representation, thus allowing larger time and length scales to be explored. By employing a conformer search technique, direct construction and analysis of coarse-grained SOM models with diverse compositions were made possible, eliminating the need for atomistic MD simulations. To demonstrate this approach, coarse-grained SOM models were created based on selected samples from the International Humic Substances Society, considering different water content levels for each model. Comprehensive analyses, including density and potential energy profile calculations, revealed a partial correlation with the SOM compositions and demonstrated that electrostatic interactions govern the structural packing. Moreover, a local phase separation process, particularly the formation of SOM voids, was observed over several microseconds, underscoring the advantages of the coarse-graining technique.

Investigation on the density shoulder near the separatrix through monostatic reflectometry in EAST tokamak

Abstract The density shoulder represents a universal physical phenomenon that is closely related to the particle and energy transports occurring within the scrape-off layer (SOL) region of tokamak devices. A novel method has been developed to identify the density shoulder through the analysis of the bump structure in the time delay spectra from monostatic microwave reflectometry in EAST tokamak, obviating the need for density profile reconstruction. The density shoulder in EAST is characterized by a number of distinctive features. The density shoulder is mostly situated at a distance of 0–3 cm from the last closed flux surface, with a width of a few centimeters. No significant correlation is observed between its occurrence and the auxiliary heating or the confinement state. In the case of H-mode with quasi-coherent mode (QCM), a significant and positive correlation is observed between the density shoulder amplitude and QCM intensity. In the case of grassy-edge localized mode (ELM)-like H-mode, a density shoulder is also observed during the inter-ELM stage. Furthermore, as supersonic molecular beam injection (SMBI) deposits occur within the range of ρ = 0.9 ∼ 1, the density shoulder is also enhanced during the SMBI fueling process. Moreover, it appears that the neutral pressure has a more pronounced impact on the overall offset of the density profile than the strength of the density shoulder. These results collectively indicate that the outward particle transport from the pedestal to the SOL region plays a crucial role in the evolution of the density shoulder.