Low Water Vapor Pressure Research Articles

IR and UV Spectroscopy of Gas-Phase Monohydrated Protonated Guanine.

We use UV and infrared photodissociation spectroscopy to study monohydrated protonated guanine in a dual cryogenic ion trap spectrometer. The monohydrated complexes are formed through helium-mediated collisions between bare electrosprayed protonated guanine and low-pressure water vapor in a clustering trap maintained at 180 K, before being transferred to a quadrupole ion trap at 10 K. The spectrum of the monohydrated complex exhibits sharp vibronic transitions at the band origin and becomes broader and higher in intensity further in blue, which is very similar to protonated guanine but with a notable blue shift of ∼1850 cm-1 (∼0.23 eV). The UV hole-burning experiments showed that the vibronic bands recorded in the region of the band origin belong to a single conformer under our experimental conditions. The IR photodissociation spectrum in the 3000-3600 cm-1 range, with the aid of theoretical calculations (SCS-CC2/aug-cc-pVDZ), allowed us to assign the structure to the lowest energy N7-O conformer.

Carnallite double salt for thermochemical heat storage

The potential use of carnallite (KMgCl3·6H2O) for low temperature thermochemical heat storage has been evaluated. Carnallite is an incongruently soluble double salt and its possible decomposition and dehydration reactions have been carefully evaluated from available thermodynamic data and the phase diagram has been constructed. The dehydration and rehydration reactions have been experimentally studied and the reaction products have been characterized using thermogravimetric mass spectrometry, water vapor sorption, X-ray powder diffraction, scanning electron microscopy, Raman microscopy and calorimetry. The results of the experimental investigation of these reactions confirm the model predictions and clearly show that a thermochemical cycle including carnallite and its dihydrate (KMgCl3·2H2O) is very promising for low temperature domestic thermochemical storage. In comparison to both pure MgCl2·6H2O and also other salts mentioned in the literature, the double salt carnallite offers significant advantages. It has a higher deliquescence humidity and, thus, is much less sensitive to over-hydration and liquefaction. It can be easily dehydrated at only 100 °C and is much less prone to hydrolysis (HCl release). Carnallite has also a good reversibility between dehydration and hydration and the re-formation of carnallite by rehydration is easily achieved at low water vapor pressure and faster reaction rate than the hydration of MgCl2·2H2O to MgCl2·6H2O. The enthalpy of hydration is slightly higher for the hydration of KMgCl3·2H2O than for the hydration of MgCl2·2H2O. The only price to be paid is a slightly reduced storage density of the double salt due to its larger molar volume. However, the theoretical storage density of 1.52 kJcm−3 is still excellent. Also, carnallite is a low-cost material as it is available as industrial waste material or can be easily synthesized.

OPTIMIZATION OF THE CONDENSATE PUMPING SYSTEM AT THE GASOLINE SELECTIVE HYDROTREATING PLANT

The article discusses issues related to energy saving of the coolant – high, medium and low pressure water vapor in the condensate pumping system at the gasoline selective hydrotreating plant. The analysis of the current condensate pumping system is carried out and its main disadvantages are indicated. Retrofitting of the pumping system is proposed. A return line has been added and a pair of centrifugal pumps has been included in the technological scheme, a calculation has been made. The replacement of the equipment will optimize the steam consumption inside the gasoline selective hydrotreating plant and will reduce the cost of repair and maintenance of the unit, as well as electricity consumed for technological needs.

Modeling of multilayer water adsorption and condensation in slits of cement minerals by molecule simulation and adsorption isotherm

The interactions between water and multiscale pores affect significantly most of the physical and chemical properties of cementitious materials such as cement mortar, paste, and concrete. In this paper, molecular mechanism of multilayer water adsorption and condensation in micropores of typical cementitious minerals, the dicalcium silicate (C2S) and calcium silicate hydrate (C-S-H), were investigated by molecular simulations. Classical adsorption isotherm models were examined for their applicability to describe the adsorption law in molecular scales. Besides, the Kelvin equation was modified to satisfy the description of condensation at the microscale. Calculation results show that the most commonly used Brunauer-Emmett-Teller (BET) model can only describe the isotherms within a limited range of low water vapor pressures. In comparison, the modified Brunauer-Emmett-Teller-Pickett (BETP) model can describe the adsorption of water molecular on the surface of C2S and C-S-H more precisely, due to considering the adsorption layers as finite at saturation pressure and the reduced escape probability of the outermost layer of adsorbed water molecules. As for the condensation of water molecules in C2S and C-S-H slits, the traditional Kelvin equation is not applicable. Therefore, a refined Kelvin equation was proposed to describe the relationship between pore size and the pressure required for condensation accurately by considering the critical pore size, adsorption thickness, and decay rate of adsorption potential energy. Further analysis suggests that C2S releases more first-layer adsorption heat and thus shows stronger adsorption of water molecules compared to C-S-H.

Patterns in acute aortic dissection and a connection to meteorological conditions in Germany.

Acute type A aortic dissection (ATAAD) is a dramatic emergency exhibiting a mortality of 50% within the first 48 hours if not operated. This study found an absolute value of cosine-like seasonal variation pattern for Germany with significantly fewer ATAAD events (Wilcoxon test) for the warm months of June, July, and August from 2005 to 2015. Many studies suspect a connection between ATAAD events and weather conditions. Using ERA5 reanalysis data and an objective weather type classification in a contingency table approach showed that for Germany, significantly more ATAAD events occurred during lower temperatures (by about 4.8 K), lower water vapor pressure (by about 2.6 hPa), and prevailing wind patterns from the northeast. In addition, we used data from a classification scheme for human-biometeorological weather conditions which was not used before in ATAAD studies. For the German region of Berlin and Brandenburg, for 2006 to 2019, the proportion of days with ATAAD events during weather conditions favoring hypertension (cold air advection, in the center of a cyclone, conditions with cold stress or thermal comfort) was significantly increased by 13% (Chi-squared test for difference of proportions). In contrast, the proportion was decreased by 19% for conditions associated with a higher risk for patients with hypotension and therefore a lower risk for patients with hypertension (warm air advection ahead of warm fronts, conditions with no thermal stress or heat stress, in the center of a cyclone with thermal stress). As many studies have shown that hypertension is a risk factor for ATAAD, our findings support the hypothesized relation between ATAAD and hypertension-favoring weather conditions.

Wet to Dry Controls Lanthanide Scandate Synthesis

The choice of temperature and gas conditions used in a water pressure-controlled reactor is guided by density functional theory (DFT) to synthesize nearly phase-pure lanthanide scandate nanoparticles (LnScO3, Ln = La, Nd, Sm, Gd). In this synthetic method, low water-vapor partial pressures, well below water's gas liquidus, inhibit particle growth, while an excess of water vapor results in undesired rare-earth hydroxide and oxyhydroxide secondary phases. The optimal humidity for high-purity LnScO3 particle synthesis is shown to vary with the lanthanide; DFT is used to calculate the thermodynamics of secondary phase formation for each lanthanide tested such that the role of water vapor may be quantified and used to maintain phase purity (greater than 96 mol %) across the series. The combination of thermodynamic calculation and experimental confirmation with this pressure-controlled reactor provides an opportunity to explore analogous syntheses of other inorganic perovskite nanoparticles.

Study on Townsend first ionization coefficient in a streamer filament of the pulsed electric discharge in water

Streamers in water usually consist of several weakly ionized gaseous filaments. It is important to understand the ionization and excitation processes occurring in a streamer filament. In this paper, we studied the Townsend first ionization coefficient α in a streamer filament. The emission images of streamers in water were acquired by using an ultra-high speed camera system. Based on the emission images, it was found that the luminance of a streamer filament decreased exponentially as the distance increased from the anode tip. The Townsend first ionization coefficient in the streamer filament in water was then estimated by the emission profile method. It was found that the Townsend first ionization coefficient in a streamer filament was 5.3 cm−1 on average and did not depend on the water conductivity or the applied voltage of interest in the present paper. The Townsend first ionization coefficient estimated by the emission profile method is in agreement with that deduced from the electron density profile of the streamer filament in water, indicating that the emission profile method for measuring the Townsend first ionization coefficient can be applicable to the streamers in water. We also estimated the reduced Townsend first ionization coefficient α/N in a streamer filament in water and found that the obtained value for α/N was four orders of magnitude lower than those obtained from the glow discharge in low pressure water vapor, but at least ten orders of magnitude greater than those predicted by the empirical formulas.

Accelerating the reaction kinetics of K2CO3 through the addition of CsF in the view of thermochemical heat storage

Potassium carbonate (K2CO3) is a promising thermochemical heat storage material (TCM). However, it suffers from hysteresis between (de)hydration temperatures and poor reaction kinetics close to equilibrium conditions. Both aspects are caused by a nucleation barrier and low ionic mobility close to equilibrium. This study investigates the impact of caesium fluoride (CsF) incorporated through recrystallisation on the phase transitions. Thecomposition studies show that K2CO3and CsF react during synthesis, forming KF, which points to the formation of Cs2CO3. The secondary phases are not incorporated into the crystal structure but reside between the main phase's grain cracks due to capillary forces. Because the secondary phases are highly hygroscopic, they promote surface mobility by forming a liquid-like layer even at low water vapour pressures. As the effect of their presence, hydration kinetics are enhanced significantly in all investigated conditions, with the most pronounced impact when hydration of K2CO3is inherently inhibited. The benefits manifest themselvesthrough a faster reaction rate and shorter induction period.The dehydration is enhanced by the presence of the additive mainly far away from equilibrium conditions. Close to the equilibrium, the dehydration of the composite proceeds in an unusual 2-step manner, where the second step is much slower than the dehydration of pure K2CO3. The enhancement of dehydration kinetics is ascribed to the formation of defects during recrystallisation. The lowering of dehydration rates close to equilibrium is attributed to diffusion issues due to excess of a deliquescent phase present in the system.

Numerical investigation on shock waves generated by flashing water jet

Numerical study has been conducted to investigate shock waves generated by flashing water jet. This study presents results of a numerical simulation of flash evaporation phenomena occurring when a jet of superheated water is injected through a nozzle into low-pressure water vapor. Due to the sudden pressure drop, flashing takes place, and the sensible heat of the water converts into latent heat of evaporation. The multiphase flow field in the evaporation zone and induced shock waves are explored via a 2D transient investigation in Ansys Fluent. The Mixture model is applied with slip velocities to model the non-homogeneous multiphase flows. Resulting distributions of the fluid properties velocity, Mach number, pressure, liquid volume fraction, density, and in addition to speed of sound inside the flashing chamber at different time steps are presented and discussed. The results show that once the superheated water is injected, it flashes immediately and generates a shock wave. The primary and reflected shock waves are characterized by discontinuous fluid properties in a narrow region across the shock. The generated shock waves are moving shock waves and can be useful to transfer energy directly between fluids without using mechanical components such as pistons or vaned impellers, which can be exploited in industrial and technological applications such as utilizing resulting shock waves in creating useful compression.

Limiting factor of dew formation changes seasonally in a semiarid crop field of northwest China

Understanding how seasonal and annual variations in dew formation are controlled by environmental elements of a crop field is necessary for utilizing dew as a water resource for agricultural production. Radiative cooling intensity, wind speed, and water vapor pressure are the key environmental elements for the dew formation. However, a detailed investigation of how seasonal and annual variations in these environmental elements affect the variation in dew formation is unexplored. We examined the relationship between dew characteristics (frequency, amount, and duration) and environmental elements of a semiarid crop field during the cultivation period of corn (April–September) for three years. In spring (April–June), though large nighttime negative net radiation, which indicates strong radiative cooling intensity, was observed, dew rarely occurred and only in small amounts. Conversely, in summer (July–September), dew frequently occurred and in larger amounts despite the lower radiative cooling intensity. In spring, lower water vapor pressure was observed, and thus dew formation was limited by the lack of water source of dew. In summer, water vapor pressure was high, and dew formation was predominantly limited by the radiative cooling intensity. The dew amount during the cultivation period accounted for 5.4% of the rainfall amount on average over the 3 years. However, dew occurred more frequently than rainfall at 53% of the days comprising the cultivation period. Additionally, the occurrence of dew wet the leaves for approximately 10 h indicating the significant impact of leaf wetting by dew on plant eco-physiological functions. The results of this study should advance the understanding of how dew formation is controlled by variations in the environmental elements of a semiarid crop field, which will contribute to improving the utilization of dew as a water resource for agricultural production.

An experimental study on oxygen isotope exchange reaction between CAI melt and low-pressure water vapor under simulated Solar nebular conditions

Calcium-aluminum-rich inclusions (CAIs) are known as the oldest high-temperature mineral assemblages of the Solar System. The CAIs record thermal events that occurred during the earliest epochs of the Solar System formation in the form of heterogeneous oxygen isotopic distributions between and within their constituent minerals. Here, we explored the kinetics of oxygen isotope exchange during partial melting events of CAIs by conducting oxygen isotope exchange experiments between type B CAI-like silicate melt and 18O-enriched water vapor (PH2O = 5 × 10−2 Pa) at 1420 °C. We found that the oxygen isotope exchange between CAI melt and water vapor proceeds at competing rates with surface isotope exchange and self-diffusion of oxygen in the melt under the experimental conditions. The 18O concentration profiles were well fitted with the three-dimensional spherical diffusion model with a time-dependent surface concentration. We determined the self-diffusion coefficient of oxygen to be ∼1.62 × 10−11 m2 s−1, and the oxygen isotope exchange efficiency on the melt surface was found to be ∼0.28 in colliding water molecules. These kinetic parameters suggest that oxygen isotope exchange rate between cm-sized CAI melt droplets and water vapor is dominantly controlled by the supply of water molecules to the melt surface at PH2O < ∼10−2 Pa and by self-diffusion of oxygen in the melt at PH2O > ∼1 Pa at temperatures above the melilite liquidus (1420–1540 °C). To form type B CAIs containing 16O-poor melilite by oxygen isotope exchange between CAI melt and disk water vapor, the CAIs should have been heated for at least a few days at PH2O > 10−2 Pa above temperatures of the melilite liquidus in the protosolar disk. The larger timescale of oxygen isotopic equilibrium between CAI melt and H2O compared to that between H2O and CO in the gas phase suggests that the bulk oxygen isotopic compositions of ambient gas at ∼1400 °C in the type B CAI-forming region is preserved in the oxygen isotopic compositions of type B CAI melilite. Based on the observed oxygen isotopic composition, we suggest that a typical type B1 CAI (TS34) from Allende was cooled at a rate of ∼0.1–0.5 K h−1 during fassaite crystallization.

Effect of low temperature, low water vapor pressure environments on the fatigue behavior of an Al-Li aerospace alloy

The objective of the study is to evaluate the fatigue crack growth of a third-generation Al-Li-Cu alloy (2199-T86) in environments relevant to high-altitude flight. Reduction of PH2O at 23 °C resulted in a general reduction of crack growth rates. A local minimum in growth rates were observed at intermediate ΔK and PH2O and was attributed to roughness induced impedance of water transport through the crack wake. Decreasing temperature had no effect on growth kinetics down to −15 °C, but decreased crack rates were observed at −30 °C and −50 °C.

Multiple-effect desiccant-based zero liquid discharge desalination systems

State-of-the-art zero liquid discharge (ZLD) technologies are currently bound with either intensive use of high-grade electrical energy such as mechanical vapor compressors or high capital cost with environmental concerns such as evaporation ponds. The present study aims to address these issues by an innovative desiccant-based ZLD desalination system in which a multiple-effect distillation (MED) unit is uniquely embedded at the heart of an absorption-desorption system. Here, the MED and absorption systems are inherently coupled enabling both heat and mass transfer processes between a hypersaline brine slurry and a desiccant solution. The proposed technology employs an absorption-based thermally-driven vapor compressor concept to pressurize the vaporized brine of the ZLD crystallizer unit from a low-pressure absorber to a high-pressure desorber module. The low water vapor pressure environment required for the ZLD treatment is established by the strong hygroscopic properties of an aqueous lithium bromide (LiBr) salt capturing a large volume of water vapor from the brine slurry. This eliminates the need for energy-intensive electrically-driven mechanical vapor compressors currently employed in advanced brine crystallizers. Comprehensive thermodynamic modeling is performed to evaluate the energy efficiency and size of the system at different thermohydraulic conditions. The detailed analysis indicates that the thermal energy consumption of the proposed desiccant-based ZLD desalination system is 67 kWh of thermal energy per cubic meter of the distillate produced with a gained output ratio (GOR) of 10. This is 63% and 44% reductions in the ZLD energy consumption compared with advanced mechanical vapor compression and thermal evaporation based ZLD systems, respectively. Insights gained from the present study have a high potential to truly transform thermal desalination and, in particular, ZLD treatment industries.

Water vapor adsorption on Mars

Near-surface air moisture observations from Phoenix and Curiosity display diurnal adsorption, which appears insensitive to mineralogy of regolith. To study this, adsorptive column model simulations are made for midsummer at Phoenix, validated against recalibrated TECP water vapor pressures p. Two standard-form (= obeying the van't Hoff equilibrium law) adsorption isotherms with quite different specific surface areas As do produce nearly identical and good matches with the observed p, whereas a widely used non-standard isotherm fails. When made standard, it also produces good results. Adsorbed amounts differ in the three good simulations but their surface fluxes and surface vapor concentrations are nevertheless nearly identical. Properties of regolith except enthalpy are shown to disappear in the model's adsorption term, explaining insensitivity to As. The van't Hoff plot of observed ln p vs. model's 1/Tg during adsorption and desorption suggests enthalpy of about 22 kJ/mol. Enthalpies of the three standard-form isotherms are close to this, explaining their excellent match with each other and with observations. Hence the low-pressure water vapor adsorption to martian regolith appears essentially nonspecific and is associated with low enthalpy, as is typical for physisorption in general.

Atomic-Scale Dynamic Interaction of H_{2}O Molecules with Cu Surface.

Atomic-scale interaction of water vapor with metal surfaces beyond surface adsorption under technologically relevant conditions remains mostly unexplored. Using aberration-corrected environmental transmission electron microscopy, we reveal the dynamic surface activation of Cu by H_{2}O at elevated temperature and pressure. We find a structural transition from flat to corrugated surface for the Cu(011) under low water-vapor pressure. Increasing the water-vapor pressure leads to the surface reaction of Cu with dissociated H_{2}O, resulting in the formation of a metastable "bilayer" Cu─O─H phase. Corroborated by density functional theory and abinitio molecular dynamics calculations, the cooperative O and OH interaction with Cu is responsible for the formation and subsurface propagation of this phase.

Inclusion of solar energy in iraq gas-turbine power plants as a method of solving the country's energy system shortage

At high ambient temperatures, the performance of gas turbine power plants drops significantly. Technical solutions of compensation for losses associated with the constant injection of water into the air intake of a gas turbine. This approach is not acceptable in regions with limited fresh water reserves. Radical solutions are required to reduce the cost of generated energy. Integrated Combined Solar Cycle (ISCCS) technology has proven itself on many projects. The addition of a combined cycle gas cycle with solar energy can significantly increase the overall efficiency of the power plant. Despite the increase in costs during the construction of its solar part, the total cost of operating solar collectors is several times less than a turbine installation. Given the global trend to fight carbon emissions, switching to a hybrid scheme is economically attractive. Trading in carbon credits for CO2 emissions will significantly reduce the payback period for the construction of gas turbine modernization under the ISCCS scheme. This paper presents an option to modernize a gas turbine power plant in the city of Basra (Iraq), using the advantages of solar radiation and recycling of combustion products from gas turbines. It is proposed to equip the existing 200 MW gas turbine plant with two steam turbine units with a capacity of 75 and 65 MW, working in conjunction with solar collectors producing low pressure water vapor. Due to modernization, the efficiency of the power plant should increase from 38% to 55%. The revision of the schematic and technical solutions of Iraq power plants will allow producing sufficient energy for the region.

Preparation of CaF2 Microspheres with Nanopetals for Water Vapor Adsorption

The hierarchically structured flower-like CaF2 microspheres with nanopetals, named FL-CaF2, were synthesized via a hydrothermal method using calcium acetate Ca(Ac)2 and NaBF4 as calcium and fluorine sources, respectively, assisted by the chelating reagent trisodium citrate (Na3Cit) with the optimal pH of the synthesis solution. Meanwhile, a reference sample, named FL-CaF2-R, was reproduced using ethylenediaminetetraacetic acid disodium salt (Na2EDTA) as the chelating reagent, based on the recipe and synthesis procedure from the literature. Various techniques such as X-ray diffraction, scanning electron microscopy, transmission electron microscopy, Fourier transform-infrared spectroscopy, and N2 adsorption-desorption at 77 K were then used to characterize the synthesized samples. The results show that FL-CaF2 with a larger diameter has a much higher thermal stability than FL-CaF2-R because the larger the nanocrystallite size, the higher the thermal stability. The adsorption of water vapor on CaF2 is irreversible because CaF2 can interact with the adsorbed water molecules strongly. The dual-site Langmuir model was used to describe the measured adsorption isotherms of water vapor on FL-CaF2 at low water vapor pressures and 298, 308, and 318 K. FL-CaF2 has a much higher water-adsorption capacity than those reported in the literature. Furthermore, the isosteric heat of adsorption as a function of loading, derived from the measured isotherms, varies from ca. 46 to 43 kJ mol-1 in the whole loading range investigated. Finally, the applications of FL-CaF2 are anticipated in the dehydration of hydrogen fluoride gas as well as in catalysis.

Performance of transition metal-doped CaCO3 during cyclic CO2 capture-and-release in low-pressure H2O vapour and H2O plasma

The effects of transition metal doping of calcium carbonate on the subsequent performance of the material during CO2 release and recapture have been evaluated for calcination under low-pressure (~0.1 mbar) water vapour and water plasma conditions. The initial samples were prepared by precipitation method from analytical grade carbonate, calcium and transition metal (Fe, Co, Zn, Cu and Ni) containing precursors. The release-recapture properties of the sorbents were monitored over five cycles involving calcination at 1200 K and carbonation at 825 K. The most noteworthy effects were observed for the Zn-doped samples, which exhibited rapid CO2 recapture.Calcination in H2O plasma was tested to evaluate the potential for in-situ material processing as a means to counteract material degradation. The impact of plasma exposure during calcination on the looping performance was mixed and dependent on the specific sample composition. The performance of the Zn-doped CaCO3 was consistently improved by plasma calcination, yielding high uptake and better retention of carrying capacity over the five cycles.All samples exhibited a deterioration in carrying capacity over repeated cycles. The Zn-doped samples also performed best in this respect (least loss of carrying capacity). The beneficial effects of Zn-doping were dependent on the Zn-content of the precursor solutions used for material synthesis.

New kinetic model of the dehydration reaction of magnesium sulfate hexahydrate: Application for heat storage

Magnesium sulfate–water vapor is an interesting working pair of thermochemical materials for compact inter-seasonal heat storage at low temperature. Total dehydration of magnesium sulfate heptahydrate shows a theoretical storage energy density of 2.8 GJ m−3. However, kinetic data are poorly studied up to now making use of this material difficult for a practical storage application. In the present work, a kinetic study of the dehydration of MgSO4·6H2O powder at low temperature (35–60 °C) and at low water vapor pressure (2–21 hPa) is carried out using thermogravimetric analysis in isobaric-isothermal conditions. A mathematical model is developed for this bivariant system and validated representing the mechanism of dehydration: water molecules diffusion in the solid solution followed by transfer of these molecules from the surface to the atmosphere. The transfer of water molecules at the surface during dehydration is identified as rate-determining step. The fractional conversion and reaction rate of the dehydration reaction are calculated and compared to the experimental data.

Humidity observations and column simulations for a warm period at the Mars Phoenix lander site: Constraining the adsorptive properties of regolith

Two recalibrated sets of Phoenix (PHX) near-surface TECP air humidity measurements were compared with results from adsorptive single column model simulations during a warm clear-sky polar midsummer period, PHX sols 50–60. The model's 2 m temperatures were close to the observed values. Relative humidity (RH) is very low during the day but at night RH at 2 m reaches nearly 100% by the Zent et al. (2016) recalibration (Z), and 60–70% by the Fischer et al. (2019) recalibration (F). Model values of RH2m are close to Z and F at night and to F during the day. All three imply low water vapor pressures near the surface at night, 0.03–0.05 Pa, with a rapid increase each morning to 0.3–1 Pa and a decrease in the evening by both F and the model simulation. The model's daily adsorbed and desorbed water is in balance for regolith porosity of 16% (instead of 35% for lower latitudes). The depleted layer of nighttime air moisture extends to only about 200 m above the surface; hence the model's precipitable water content stays around the observed ~30 μm throughout the sol. The model's moisture cycle is not sensitive to tortuosity of the regolith but the in-pore molecular diffusivity should be at least 5 cm2/s for fair agreement with the observations. In the adsorption experiments there is no fog and just a hint of ground frost, as observed during this period. Strong night frosts appear if adsorption is made weak or absent in the model.