Critical Density Research Articles

Does the HCN/CO ratio trace the fraction of gravitationally bound gas? II. Variations in CO and HCN emissivity

We modeled emissivities of the HCN and CO $J=1-0$ transitions across a grid of molecular cloud models encapsulating observed properties that span from normal star-forming galaxies to more extreme merging systems. These models are compared with archival observations of the HCN and CO $J=1-0$ transitions, in addition to the radio continuum at 93 GHz, for ten nearby galaxies. We combined these model emissivities with the predictions of gravoturbulent models of star formation presented in the first paper in this series. In particular, we explored the impact of excitation and optical depth on CO and HCN emission and assess if the HCN/CO ratio tracks the fraction of gravitationally bound dense gas, $f_ grav $, in molecular clouds. We find that our modeled HCN/CO ratios are consistent with the measurements within our sample, and our modeled HCN and CO emissivities are consistent with the results of observational studies of nearby galaxies and clouds in the Milky Way. CO emission shows a wide range of optical depths across different environments, ranging from optically thick in normal galaxies to moderately optically thin in more extreme systems. HCN appears only moderately optically thick and shows significant subthermal excitation in both normal and extreme galaxies. We find an anticorrelation between HCN/CO and $f_ grav $, which implies that the HCN/CO ratio is not a reliable tracer of $f_ grav $. Instead, this ratio appears to best track gas at moderate densities ($n>10^ cm $), which is below the typically assumed dense gas threshold of $n>10^ cm $. We also find that variations in CO emissivity depend strongly on optical depth, which is a product of variations in the dynamics of the cloud gas. HCN emissivity is more strongly dependent on excitation, as opposed to optical depth, and thus does not necessarily track variations in CO emissivity. We further conclude that a single line ratio, such as HCN/CO, will not consistently track the fraction of gravitationally bound, star-forming gas if the critical density for star formation varies in molecular clouds. This work highlights important uncertainties that need to be considered when observationally applying an HCN conversion factor in order to estimate the dense (i.e.,\ cm $) gas content in nearby galaxies.

Flame spread characteristics of densified wood with various sample widths and densities

Densified wood (DW) is a novel functional material with great mechanical properties, its structural characteristics make it attractive as an ideal building material for mid-to-high-rise timber constructions. However, its flame spread characteristics is not yet fully understood, which threatens its further developments and applications. This study experimentally and analytically investigates the impact of density and width on the flame spread behaviors and heat transfer characteristics of DW. Flame spread rate, mass loss rate (MLR), and flame height decrease with increasing wood density. Both MLR and flame height increase with the increasing width, while flame spread rate increases first and then decreases. Dimensionless power-law relationships among them were established, which well predict the measurements. The dominant gaseous heat transfer transits from radiation to convection with the increase of density. The critical density for this transition is increased with width. Both width and density impact the preheating length and total heat flux, which are combined to influence the flame spread rate. A dimensionless correlation among them was established with an R2 of 0.915 to the experiments of current and previous publications. This work helps to understand flame spread of DW and benefits the fire safety in timber construction.

Firn seismic anisotropy in the Northeast Greenland Ice Stream from ambient-noise surface waves

Abstract. We analyse ambient-noise seismic data from 23 three-component seismic nodes to study firn velocity structure and seismic anisotropy near the EastGRIP camp along the Northeast Greenland Ice Stream (NEGIS). Using nine-component correlation tensors, we derive dispersion curves of Rayleigh and Love wave group velocities from 3 to 40 Hz. These velocity distributions exhibit anisotropy along and across the flow. To assess these variations, we invert dispersion curves for shear wave velocities (Vsh and Vsv) in the top 150 m of the NEGIS using a Markov chain Monte Carlo approach. The reconstructed 1-D shear velocity model reveals radial anisotropy in the firn, with Vsh 12 %–15 % greater than Vsv, peaking at the critical density (550 kg m−3). We combine density data from firn cores drilled in 2016 and 2018 to create a new density parameterisation for the NEGIS, serving as a reference for our results. We link seismic anisotropy in the NEGIS to effective and intrinsic causes. Seasonal densification, wind crusts, and melt layers induce effective anisotropy, leading to faster Vsh waves. Changes in firn recrystallisation cause intrinsic anisotropy, altering the Vsv / Vsh ratio. We observe a shallower firn–ice transition across the flow (≈ 50 m) compared with along the flow (≈ 60 m), suggesting increased firn compaction due to the predominant wind direction and increased deformation towards the shear margin. We demonstrate that short-duration (9 d minimum), passive, seismic deployments and noise-based analysis can determine seismic anisotropy in firn, and we reveal 2-D firn structure and variability.

Rapid predator-prey balance shift follows critical-population-density transmission between cod (Gadus morhua) and capelin (Mallotus villosus)

Sensing limitations have impeded knowledge about how individual predator-prey interactions build to organized multi-species group behaviour across an ecosystem. Population densities of overlapping interacting oceanic fish predator and prey species, however, can be instantaneously distinguished and quantified from roughly the elemental individual to spatial scales spanning thousands of square kilometres by wide-area multispectral underwater-acoustic sensing, as shown here. This enables fundamental mechanisms behind large-scale ordered predator-prey interactions to be investigated. Critical population densities that transition random individual behaviour to ordered group behaviour are found to rapidly propagate to form vast adversarial prey and predator shoals of capelin and surrounding cod in the Barents Sea Arctic ecosystem for these keystone species. This leads to a sudden major shift in predator-prey balance. Only a small change in local behaviour triggers the shift due to an unstable equilibrium. Such unstable equilibria and associated balance shifts at predation hotspots are often overlooked as blind spots in present ocean ecosystem monitoring and assessment due to use of highly undersampled spatio-temporal sampling methods.

A ZO-2 scaffolding mechanism regulates the Hippo signalling pathway.

Contact inhibition of proliferation is a critical cell density control mechanism governed by the Hippo signalling pathway. The biochemical signalling underlying cell density-dependent cues regulating Hippo signalling and its downstream effectors, YAP, remains poorly understood. Here, we reveal that the tight junction protein ZO-2 is required for the contact-mediated inhibition of proliferation. We additionally determined that the well-established molecular players of this process, namely Hippo kinase LATS1 and YAP, are regulated by ZO-2 and that the scaffolding function of ZO-2 promotes the interaction with and phosphorylation of YAP by LATS1. Mechanistically, YAP is phosphorylated when ZO-2 brings LATS1 and YAP together via its SH3 and PDZ domains, respectively, subsequently leading to the cytoplasmic retention and inactivation of YAP. In conclusion, we demonstrate that ZO-2 maintains Hippo signalling pathway activation by promoting the stability of LATS1 to inactivate YAP.

Quasi-continuous exhaust operational space

Abstract The IPED predictive pedestal code has been used to determine the critical gradients for the onset of 1) separatrix ballooning modes and 2) global peeling-ballooning modes as a function of plasma shaping. This results in a scaling of the onset threshold of separatrix ballooning modes as a function of elongation and triangularity αedge,crit = 0.64κ2.2(1+δ)0.9, while the critical gradient for global peeling-balloonig modes increases as αedge,crit 1.5. This implies that operational space for a ballooning unstable separatrix and stable peeling-ballooning modes exists at sufficiently high shaping. Applying a collisional broadnening based scaling of the separatrix gradients allows the critical separatrix density, required to drive the separatrix ballooning mode, to be derived from global plasma parameters for any operational scenario on any device. Evaluations for ASDEX Upgrade, JET, and the ITER 15 MA baseline plasma predict critical separatrix densities of 0.3-0.4 nGW for QCE access, making the QCE an attractive operational scenario for fusion devices.

Dynamics of Polymer Films on Polymer-Grafted Substrates: A Molecular Dynamics Simulation.

For substrate-supported polymer films, the tails of adsorbed chains are generally assumed to play important roles in the propagation of the substrate's effect inside polymer films. The effects of the grafting density and the rigidity of substrate-grafted polymers, the simplest model for the adsorbed tails, on the diffusivity of film polymers are investigated by performing molecular dynamics simulations. An optimal grafting density σo, around the critical grafting density for the transition from "mushroom" to "brush", is found with the most pronounced suppression of diffusivity on the film polymers; i.e., the penetration of the film polymers into the grafting layer reaches the maximum. However, at high grafting density, the crowded and vertically stretched brush excludes the coil-like film polymers, and the suppression is thus reduced. At σo, with an increase in the rigidity of the grafted polymers, the suppression is increased quickly at low rigidity but slowly at high rigidity. The dynamic suppression is attributed to the combination of the conformation change from stretching at low rigidity to tilted orientation at high rigidity and decelerated mobility induced by the rigidity. The stretching conformation enhances, whereas the tilted conformation weakens the interpenetration between the grafted polymers and the film polymers. Our results reflect the importance of both conformational variation and interchain interaction in the interface region.

The e-MANTIS emulator: Fast and accurate predictions of the halo mass function in f(R)CDM and wCDM cosmologies

In this work, we present a novel emulator of the halo mass function (HMF), which we implemented in the framework of the e-MANTIS emulator of $f(R)$ gravity models. We also extended e-MANTIS to cover a larger cosmological parameter space and to include models of dark energy with a constant equation of state $w$CDM. We used a Latin hypercube sampling of the $w$CDM and $f(R)$CDM cosmological parameter spaces, over a wide range, and carried out a large suite of more than $10000$ $N$-body simulations with a different volume, mass resolution, and random phase for the initial conditions. For each simulation in the suite, we generated halo catalogues using the friends-of-friends (FoF) halo finder, as well as the spherical overdensity (SO) algorithm for different overdensity thresholds (200, 500, and 1000 times the critical density). We decomposed the corresponding HMFs on a B-spline basis, while adopting a minimal set of assumptions on their shape. We used this decomposition to train an emulator based on Gaussian processes. The resulting emulator is able to predict the HMF for redshifts $ 1.5$ and for halo masses $M_h M_ The typical HMF errors for SO haloes with $ c $ at $z=0$ in $w$CDM (respectively $f(R)$CDM) are of the order of $ up to a transition mass $M_t M_ ($M_t M_ For larger masses, the errors are dominated by the shot noise and scale as $ with $ up to $M_h M_ Independently of this general trend, the emulator is able to provide an estimation of its own error as a function of the cosmological parameters, halo mass, and redshift. We have performed an extensive comparison against analytical parametrizations and shown that e-MANTIS is able to better capture the cosmological dependence of the HMF, while being complementary to other existing emulators. The e-MANTIS emulator, which is publicly available, can be used to obtain fast and accurate predictions of the HMF in the $f(R)$CDM and $w$CDM non-standard cosmological models. As such, it represents a useful theoretical tool to constrain the nature of dark energy using data from galaxy cluster surveys.

A peridynamic compensated critical energy density criterion for mixed-mode fracturing in quasi-brittle materials

This study integrates a compensated critical energy density criterion (CCED) into the ordinary state-based peridynamics framework to enable detailed analysis of mode I, mode II, and mixed-mode fracturing. The proposed bond failure criterion builds upon the advantages of the traditional critical energy density (CED) to enable precise calculation of strain energy density. Additionally, the critical bond rotation criterion (CR) is employed to account for shear bonds that the CED might overlook. Using the peridynamic differential operator (PDDO) format in formulating the entire computational framework enhances both accuracy and numerical stability. The model’s validation is conducted through benchmark examples, including the mode I double cantilever beam test, the mode II compact shear test, and a mixed-mode mechanical fracturing test in pre-notched specimens with central borehole loading. Convergence studies, comparative analyses with finite element method simulations and theoretical solutions thoroughly examine the proposed model’s performance and accuracy.

On estimation of betatron radiation spectrum characteristics of DLA electrons in NCD plasma

Action of a relativistically intense subpicosecond laser pulse on the near critical density (NCD) plasma can give rise to the formation of ion channel inside the plasma and effective acceleration of background electrons. Thus, one can produce high current (electron charges from tens nCl to several mkCl), high energy (from several MeV to several hundreds of MeV) electron bunches, demanded in different practical applications. Synchrotron (betatron) radiation of these electrons can serve as an important tool both for practical applications and also for diagnostic of the process in laser plasma, which is important for better understanding of these processes and for optimization of experimental conditions. For the last goals, an approximate model is proposed for calculating the spatial and energy characteristics of a bunch of DLA (direct laser accelerated) electrons in the ion channel formed in the NCD plasma and the characteristics describing the spectrum of their synchrotron radiation. For the considered example of a powerful laser pulse action on NCD plasma, the predictions of the proposed model are in good agreement with the results of particles in cell simulations and with the experimental measurements of the synchrotron radiation specter. It is shown that with the assumption of the rotation of the initial plane of motion of DLA electrons, the experimental data on the measurements of synchrotron radiation specters can be explained on the basis of the concept of betatron radiation of electrons accelerated in NCD plasma by DLA mechanism.

Numerical study on positive streamer in parallel-rod dielectric barrier discharge in atmospheric air

In this work, a parallel-rod dielectric barrier discharge (DBD) operating in atmospheric air is investigated through the two-dimensional plasma fluid model. The effects of applied voltage (Vp), secondary electron emission coefficient (γ), and photoionization are examined. Photoionization can significantly influence streamer dynamics by accelerating and broadening both volumetric and surface streamers and enhance the impact of the applied voltage. Without photoionization, the propagation distance of the surface streamer along the curved dielectric surface is limited to 0.1–0.2 mm under applied voltages of 8–8.5 kV. In contrast, with photoionization, this distance can extend to 0.3–0.6 mm. Achieving the same distance requires much higher voltages (10–11 kV) if without photoionization. The “double-layer” structure of the surface streamer is investigated, revealing that γ predominantly affects the surface branch with little impact on the volumetric branch. The critical charge density for streamer onset is found to be about 1018 m−3, and the volume-to-surface streamer transition is attributed to the lateral electric field provided by the space charges. This work provides insights into the regulation strategies and underlying mechanisms of streamer dynamics in parallel-rod DBDs in atmospheric air.

Critical current density of high-temperature superconducting ceramics BSCCO Bi-2223

In the paper the results of the study on the synthesis of high-temperature superconducting ceramics of nomi- nal composition Bi1.6Pb0.4Sr2Ca2Cu3Oy by various methods were presented based on amorphous phases using glass-ceramic technology and solid-phase method. For comparison, amorphous phases were obtained in two ways. In the first case, a heating furnace of a special design was developed to obtain an amorphous phase, which provides melting without using a crucible. The heating of the initial samples for melting is carried out due to the combined effect of the convection heat flux and the radiation of heating elements, which consists of the IR region of the spectrum at a melting temperature in the spectral range of 1300–1350 nm. In the se- cond case, melting is carried out under the influence of broadband optical radiation, including UV, visible and IR spectral regions. The production of glassy precursors is carried out by draining the melt onto a quenching device in the form of a propeller made of stainless steel. Studies of the formation rate of the superconducting high-temperature phase Bi-2223 were carried out in the same temperature conditions at 848–850 °C with in- termediate grinding every 24 hours and the study of the phase composition by X-ray diffraction method. Studies showed that the glass phase-based method ensures the completeness of the formation of the high- temperature phase Bi-2223 and the rate of its formation is significantly higher than by the solid-phase method (2.5–3 times). Studies of the critical density of the transport current have shown that the current value is 7.05×103 mA/cm2, (measured by the criterion of 1 µV/cm), which is significantly higher compared to other methods.

Two state model for the ML-BOP potential

The coarse-grained machine-learning derived ML-BOP model [Chan et al., Nature Commun. 10, 379 (2019)] provides a monoatomic representation of the water-water interaction potential in which orientational interactions are included as three-body contributions. Despite its simplicity, the model reproduces the phase diagram of water and its anomalies. Here, we show that a two-state Gibbs free energy expression – fitted simultaneously on the temperature and pressure dependence of the density and internal energy – predicts the existence of a liquid–liquid critical point, with critical parameters consistent with previous estimates. We also show that in this model: (i) while the low density liquid is pre-empted by crystal nucleation, the high-density liquid and its spinodal are accessible in numerical studies down to 100 K; (ii) crystallisation requires the presence of a local low density region. Thus, for densities larger than the critical density, spinodal decomposition (or nucleation of the low-density liquid) is a pre-requisite for ice nucleation.

Analysis of congestion key parameters, dynamic discharge process, and capacity estimation at urban freeway bottlenecks: a case study in Beijing, China

ABSTRACT Recurring bottlenecks significantly contribute to urban freeway congestion, making their analysis essential. This study examines six bottlenecks on Beijing’s Ring Road using multi-day data, identifying them via Dynamic Time Warping and Fuzzy C-Means Clustering (DTW+FCM). Key parameters—free-flow speed, critical speed, critical density, and jam density—are calibrated using fundamental diagram models. The Weibull distribution analyzes flow and speed patterns during congestion phases. The DTW+FCM method effectively identified bottlenecks and congestion levels. Severe congestion lasting over 10 hours on the West Second and Third Ring Roads averaged speeds of 15 km/h. The S3 model best fits data for the West Ring Roads, while the Van Aerde model suits the North Ring Roads. Different methods yield varying traffic capacity estimates, highlighting the need for nuanced approaches in urban expressway planning to maintain traffic quality and comfort. These findings offer valuable guidance for research and practical traffic management solutions.

Deformation-induced gas adsorption and self-desorption dynamics of a carbon nano-network: Molecular dynamics modeling focusing on CO2 capture

Gas adsorption and separation/desorption are two pivotal stages in gas capture, demanding additional energy for liberating gas molecules from the adsorbent. Hence, it’s essential to engineer an adsorbent with minimal energy consumption yet effective gas adsorption–desorption characteristics. Accordingly, this research introduces a carbon nano-network (CNN) material capable of inhaling and exhaling gases via self-deformation. Molecular dynamics simulations demonstrate that the gas adsorption–desorption capabilities of CNN can be efficiently regulated by its deformation. While the size of CNN minimally affects the gas sorption rate, a larger CNN necessitates a prolonged duration to achieve saturation under identical gas conditions. Incorporating elongated appendages in CNN enhances both its stability during contraction and its efficiencies in gas adsorption and desorption. We discerned that attaining a critical gas density within a confined space is imperative to initiate self-desorption of CNN. Specifically, if the gas density dips below this critical threshold–set at 5.2 times that of CO2 at room temperature (300 K) and atmospheric pressure (1 Bar)–CNN exhibits no self-desorption capability. Nevertheless, even a marginal elevation in gas density triggers and maintains self-desorption with a consistently surpassing desorption ratio of 98 %. This discovery offers valuable insights for designing automatic self-desorption materials or apparatuses.

Ignition of Coal Microparticles by Laser Pulses of The Second Harmonic of a Ndodymium Laser in the Q-Switched Regime

The ignition of pelletized samples of hard coals of the long-flame gas (DG), gas (G), fat (L), coke (K) grades with particle sizes ≤63 μm by laser pulses (λ = 532 nm, τi = 10 ns) was studied. When the critical radiation energy density Hcr(1), specific for each grade of coal, is exceeded, an optical breakdown occurs and a dense plasma with a continuous emission spectrum is formed. As the plasma expands and rarefies, the spectra show the emission of carbon ions CII, excited nitrogen atoms N, excited carbon molecules C2, and carbon monoxide CO. The plasma glow intensity peaks at the end of the laser pulse, and the glow relaxation time is ~1 μs. The plasma glow amplitude increases nonlinearly with increasing laser pulse energy density. At radiation energy density H ≥ Hcr(2), specific for each grade of coal, thermochemical reactions are initiated in the volume of microparticles and coal particles are ignited in a submillisecond time interval.

Thermodynamic properties of perfluorooctane on the liquid-gas coexistence curve: calculation method and tabulated data

A technique has been developed for constructing a phase equilibrium line in the range from the triple to the critical point for a technically important substance, perfluorooctane (C8F18), which is currently used in various fields of industry and medicine. The proposed phase equilibrium line model includes the following equations: vapour pressure; saturated liquid density; saturated vapour density; “apparent” heat of vaporization. In this case, the vapour pressure equation satisfies the requirements of the scale theory of critical phenomena near the critical point, and the Wegner model in the vicinity of the triple point. The coexistence curve model in the vicinity of the critical point satisfies the Yang-Yang model and renormalization group theory for asymmetric systems, and in the region of rarefied gas it satisfies the linear model of average diameter. In the temperature range 246.15–496.99 K, table for perfluorooctane have been developed, including pressure and density of saturated vapor, density of saturated liquid, heat of vaporization, first and second derivatives of saturated vapor pressure. Using latest experimental data, as well as experimental data on the critical pressures of perfluoroalkanes as a function of their molecular weight, the following values of critical parameters were selected: critical pressure – 1.548 MPa, critical density – 596.4 kg/m3, critical temperature – 496.99 K. A number of statistical characteristics were calculated, including absolute mean deviation and standard deviation, characterizing the accuracy of the proposed phase equilibrium line model when describing experimental data obtained in generally recognized international thermophysical laboratories. The results obtained are useful for high-tech companies engaged in the development of innovative technologies: in the field of radio-electronic and electrical industries, in which perfluorooctane is used as a liquid dielectric and coolant; in medicine, where perfluorooctane is used as a gas transport liquid and is used for ophthalmic purposes; magnetic fluid sealers for the purpose of isolating hazardous substances from the environment and seals for devices operated in vacuum conditions or in contact with aggressive substances; magnetic fluid separators for separating non-ferrous metals by density, etc. The results of this study can also be used in developing the fundamental equation of state for perfluorooctane. The results obtained are useful for high-tech companies engaged in the development of innovative technologies: in the field of radio-electronic and electrical industries, in which perfluorooctane is used as a liquid dielectric and coolant; in medicine, where perfluorooctane is used as a gas transport liquid and is used for ophthalmic purposes; magnetic fluid sealers for the purpose of isolating hazardous substances from the environment and seals for devices operated in vacuum conditions or in contact with aggressive substances; magnetic fluid separators for separating non-ferrous metals by density, etc. The results of this study may also be useful in developing the fundamental equation of state for perfluorooctane.

Hydrodynamic behavior near dynamical criticality of a facilitated conservative lattice gas.

We investigate a 2d-conservative lattice gas exhibiting a dynamical active-absorbing phase transition with critical density ρ_{c}. We derive the hydrodynamic equationfor this model, showing that all critical exponents governing the large scale behavior near criticality can be obtained from two independent ones. We show that as the supercritical density approaches criticality, distinct length scales naturally appear. Remarkably, this behavior is different from the subcritical one. Numerical simulations support the critical relations and the scale separation.

Experimental study and correlation of critical parameters for three binary mixtures containing R290 and hydrofluoroolefins

The mixtures of R290 (propane) and R1234yf (2,3,3,3-tetrafluoroprop-1-ene), R1243zf (3,3,3-trifluoropropene), or R1234ze(E) (trans-1,3,3,3-tetrafluoropropene) could be potential alternatives for high global warming potential (GWP) refrigerants hydrofluorocarbons (HFCs) and hydrochlorofluorocarbons (HCFCs). Obtaining the critical parameters of mixtures is crucial for establishing thermodynamic models, evaluating the highest operating temperature of refrigerants, determining the phase envelope, and confirming the starting point of the Widom line. However, few studies have been made on their critical properties. In this work, the critical properties of three binary systems containing R290 + R1234yf / R1243zf / R1234ze(E) are obtained experimentally with a metal-bellows volume apparatus. The critical state is judged by direct visual observation of critical opalescence and the recurrence of the vapor-liquid phase interface. The extended total uncertainties for the mole fraction, critical pressure, critical temperature, and critical density were below 0.004, 21 kPa, 50 mK, and 0.6 % (k = 2, 0.95 confidence coefficient), respectively. Experimentally obtained critical data are correlated by the Modified Wilson method and the Redlich–Kister method. The critical parameters of the R290 + R1234yf, R290 + R1243zf, and R290 + R1234ze(E) mixtures are predicted using the Correlated Modified Wilson (CMW) method, He et al.’s method, and the Modified Extended Chueh–Prausnitz (MECP) method. The correlated curve and predicted outcomes are employed for comparison with this work's experimental results. Meanwhile, the critical parameters data obtained experimentally are contrasted with the value of REFPROP 10.0 and other open literature. The fitting and prediction curves somewhat agree with the experimental results.

Two-plasmon-decay instability in the non-eigenmode regime in laser–plasma interaction

It is shown theoretically that the two-plasmon-decay instability (TPD) in laser–plasma interaction can be excited in the non-eigenmode regime, where the plasma density is larger than the quarter critical density. This appears when the laser amplitude is larger than a certain threshold value, which is found to increase with the plasma density. In this regime, the excited electrostatic modes have a constant frequency around half of the incident light frequency. The theoretical model is validated by particle-in-cell simulations. The simulation results show that the non-eigenmode TPD has a higher threshold amplitude for the pump laser than the non-eigenmode stimulated Raman scattering (SRS) excited in the plasma above the quarter critical density. In inhomogeneous plasma, competition between non-eigenmode TPD and non-eigenmode SRS occurs since the excitation of the former is normally accompanied by the latter.