Binary Systems Research Articles

Gender representations in school mathematics: a study of primary textbooks in the Republic of Cyprus

ABSTRACT Several studies indicate that gender is often portrayed stereotypically in mathematics textbooks worldwide. Based on the premise that such representations need to be examined with particular attention to the cultural context within which they exist, this study focuses on the upper-primary mathematics textbooks of the Republic of Cyprus, which are nationally produced and mandatory for all public schools. Specifically, the eight individual parts of grades 5 and 6 (four for each grade) were examined. By approaching both written and visual references from a critical discourse analysis perspective, the findings highlight that (a) gender is represented within the binary system, and (b) there are essential differences in depictions of men and women across three dimensions: professional status, everyday activities, and references to real people. These differences allude to stereotypical performative aspects of gender in this specific socio-cultural context. In closing, I make recommendations for future research directions in this area.

Constraints on Neutrino Natal Kicks from Black-Hole Binary VFTS 243.

The recently reported observation of VFTS 243 is the first example of a massive black-hole binary system with negligible binary interaction following black-hole formation. The black-hole mass (≈10M_{⊙}) and near-circular orbit (e≈0.02) of VFTS 243 suggest that the progenitor star experienced complete collapse, with energy-momentum being lost predominantly through neutrinos. VFTS 243 enables us to constrain the natal kick and neutrino-emission asymmetry during black-hole formation. At 68% confidence level, the natal kick velocity (mass decrement) is ≲10 km/s (≲1.0M_{⊙}), with a full probability distribution that peaks when ≈0.3M_{⊙} were ejected, presumably in neutrinos, and the black hole experienced a natal kick of 4 km/s. The neutrino-emission asymmetry is ≲4%, with best fit values of ∼0-0.2%. Such a small neutrino natal kick accompanying black-hole formation is in agreement with theoretical predictions.

Host-Guest Interaction Study of Olmesartan Medoxomil with β-Cyclodextrin Derivatives.

Olmesartan medoxomil (OLM) is a selective angiotensin II receptor antagonist used in the treatment of hypertension. Its therapeutic potential is limited by its poor water solubility, leading to poor bioavailability. Encapsulation of the drug substance by two methylated cyclodextrins, namely randomly methylated β-cyclodextrin (RM-β-CD) and heptakis(2,3,6-tri-O-methyl)-β-cyclodextrin (TM-β-CD), was carried out to overcome the limitation related to OLM solubility, which, in turn, is expected to result in an improved biopharmaceutical profile. Supramolecular entities were evaluated by means of thermoanalytical techniques (TG-thermogravimetry; DTG-derivative thermogravimetry), spectroscopic methods including powder X-ray diffractometry (PXRD), universal-attenuated total reflectance Fourier-transform infrared (UATR-FTIR) and UV spectroscopy, saturation solubility studies, and by a theoretical approach using molecular modeling. The phase solubility method reveals an AL-type diagram for both inclusion complexes, indicating a stoichiometry ratio of 1:1. The values of the apparent stability constant indicate the higher stability of the host-guest system OLM/RM-β-CD. The physicochemical properties of the binary systems are different from those of the parent compounds, emphasizing the formation of inclusion complexes between the drug and CDs when the kneading method was used. The molecular encapsulation of OLM in RM-β-CD led to an increase in drug solubility, thus the supramolecular adduct can be the subject of further research to design a new pharmaceutical formulation containing OLM, with improved bioavailability.

H.E.S.S. observations of the 2021 periastron passage of PSR B1259-63/LS 2883

is a gamma-ray binary system that hosts a pulsar in an eccentric orbit, with a 3.4 year period, around an O9.5Ve star (LS 2883). At orbital phases close to periastron passages, the system radiates bright and variable non-thermal emission, for which the temporal and spectral properties of this emission are, for now, poorly understood. In this regard, very high-energy (VHE) emission is especially useful to study and constrain radiation processes and particle acceleration in the system. We report on an extensive VHE observation campaign conducted with the High Energy Stereoscopic System, comprised of approximately 100 hours of data taken over five months, from p -24$ days to $t_ p +127$ days around the system's 2021 periastron passage (where $t_ p $ is the time of periastron). We also present the timing and spectral analyses of the source. The VHE light curve in 2021 is consistent overall with the stacked light curve of all previous observations. Within the light curve, we report a VHE maximum at times coincident with the third X-ray peak first detected in the 2021 X-ray light curve. In the light curve -- although sparsely sampled in this time period -- we see no VHE enhancement during the second disc crossing. In addition, we see no correspondence to the 2021 GeV flare in the VHE light curve. The VHE spectrum obtained from the analysis of the 2021 dataset is best described by a power law of spectral index $ stat sys $, a value consistent with the spectral index obtained from the analysis of data collected with H.E.S.S. during the previous observations of the source. We report spectral variability with a difference of $ stat sys $ at $95 <!PCT!>$ confidence intervals, between sub-periods of the 2021 dataset. We also detail our investigation into X-ray/TeV and GeV/TeV flux correlations in the 2021 periastron passage. We find a linear correlation between contemporaneous flux values of X-ray and TeV datasets, detected mainly after $t_ p +25$ days, suggesting a change in the available energy for non-thermal radiation processes. We detect no significant correlation between GeV and TeV flux points, within the uncertainties of the measurements, from $ t_p-23$ days to $ t_p+126$ days. This suggests that the GeV and TeV emission originate from different electron populations.

A Sustainable Approach for Enhancing Cationic Dyes Adsorption in Single and Multiple Systems using Novel Nano Ferrites Modified with Walnut Shell

AbstractWalnut shell has been used in various experimental studies for different dyes removal, but it is exciting to study the adsorption behaviour of bio‐waste (walnut shell) in combination with spinel zinc ferrite which resulted in the formation of a novel material having magnetic properties and help in easy separation after the wastewater treatment. Novel magnetic walnut shell zinc ferrite (WSZF) composite has been synthesized and used to remove Malachite Green and Methylene Blue from aqueous solution in single and binary dye systems. Different techniques have been used to characterize the composite such as Fourier Transform Infrared Spectroscopy, X‐Ray Diffraction, Field Emission Scanning Electron Microscopy, Energy Dispersive Spectroscopy, Thermogravimetric Analysis and pHzpc. Adsorption of dyes were studied to see the effect of time, pH, adsorbent dose, dye concentration and temperature. The Lagergren pseudo second order model fitted well among various kinetic models employed. Langmuir adsorption isotherm best fitted with maximum adsorption capacities of 86.20 and 169.5 mg/g in single dye and 23.92 and 18 mg/g respectively in binary dye system for Malachite Green and Methylene Blue. Process was spontaneous and ΔH° were found positive, confirmed endothermic process of adsorption. The composite‘s regeneration capacity was studied for five cycles and at the end of five cycle the efficiency of the material was found to be around 80 % for both single as well as binary dye systems. It is concluded that the chosen WSZF will be the optimum solution for cationic dyes removal.

Equation-of-state-based lattice Boltzmann model of multicomponent adsorption onto fluid–fluid interfaces

In diffuse interface models, such as the lattice Boltzmann method (LBM), interfacial physics plays an important role. An example of an important interfacial phenomenon is adsorption onto a fluid–fluid interface. In the context of LBM, adsorption studies have traditionally only focused on adsorption onto a solid surface. The studies on adsorption onto fluid–fluid interfaces have been qualitative in nature, suffer from restrictions on the number of components, or are based on simple thermodynamic models designed for fully immiscible phases. Our recently published fugacity-based LBM model introduces a platform for the accurate modeling of multiphase fluids unrestricted by the number of components, and governed through accurate equations of state (Soomro and Ayala, 2023). In this study, we utilize the fugacity-based LBM to capture interfacial adsorption. This paper begins by simulating adsorption in a binary system with a flat interface, and shows that the amount of adsorption, quantified by relative adsorption measures, is in exact agreement with Gibbs theory. Next, the analysis is continued for a ternary system with two species adsorbing onto the interface. The binary and ternary simulations are then repeated for the case of a droplet and finally a five component case is presented. The study shows that the fugacity-based LBM can capture adsorption in full agreement with Gibbs adsorption theory. This provides a path for a generalized LBM model for adsorption, based on robust thermodynamic models for the fluids and unrestricted by the number of components, marking a significant contribution to the LBM literature.

Doppler Tomography of the Circumstellar Disk of the Be Star κ Draconis

κ Draconis is a binary system with a classical Be star as the primary component. Its emission-line spectrum consists of hydrogen lines, notably the Hα line with peak intensity ratio (V/R) variations phase-locked with the orbital period P = 61.55 days. Among binaries demonstrating the Be phenomenon, κ Dra stands out as one of a few systems with a discernible mass of its secondary component. Based on more than 200 spectra obtained in 2014–2023, we verified the physical parameters and constructed the mass function. We used part of these data obtained in 2014–2021 to investigate regions in the circumstellar disk of the primary component that emit the Hα line using the Doppler tomography method. The results show that the disk has a non-uniform density distribution with a prominent enhancement at Vy ≈ 99 km s−1 and Vx≈−6 km s−1 that corresponds to a cloud-like source of the double-peaked Hα line profile. We argue that this enhancement’s motion is responsible for the periodic variations in the Hα V/R ratio, which is synchronised in orbital phase with the radial velocity (RV) of absorption lines from the atmosphere of the primary component.

UNIFAC PREDICTION OF VAPOR LIQUID EQUILIBRIA INVOLVING GAMMA-VALEROLACTONE DERIVATIVE SYSTEMS

Researchers have studied the hydrogenation of Gamma-Valerolactone (GVL) over Ru/C to produce 2-methyltetrahydrofuran (2-MTHF), a biomass-based platform chemical with potential as a biofuel and green solvent. Other byproducts of this reaction include 2-butanol (2-BuOH), 2-pentanol (2-PeOH), and 1,4-pentanediol (1,4-PDO). In this study, UNIFAC activity coefficient models were used to predict the vapor-liquid equilibrium of several systems included in the process to explain the phase behavior which is important in purification process. The accuracy of the UNIFAC model is tested by comparing the experimental boiling points for the binary system of 2-propanol + 1-butanol and the vapor-liquid equi-librium of the GVL + 2-MTHF system. From this comparison, the Root Mean Square Deviation (RMSD) values for the boiling point measurements are obtained to be 3.153%, and for the liquid and vapor phases in the vapor-liquid equilibrium measurements, the RMSD values are 1.934% and 0.298% respectively. These RMSD values indicate the level of accuracy of the UNIFAC model in representing the experimental data for both boiling point measurements and vapor-liquid equilibrium phase behavior. The prediction results of vapor-liquid equilibrium data for GVL derivative systems showed that the 2-BuOH + 2-MTHF system does form an azeotrope when the mol fraction of 2-BuOH is 0.0031 at 79.780C. The calculation was performed using ChemCAD commercial software for chemical process modeling and simulation

Study of Activation Energy for Viscous Flow of Mixtures as a Measure of Dilution Efficiency for Heavy Oil-Diluent Systems

As the demand for crude oil continues to increase in response to the continued global needs for it, the development of unconventional crude oil reserves is the only way to sustain global supply. However, the excessively higher viscosity of heavy crude oil makes it less attractive for conventional pipeline transportation. Therefore, reducing the viscosity of heavy crude oil to meet crude oil transporting pipeline regulations is a necessity. This paper has assessed the dilution efficiency of well-known diluents in the petroleum industry, using different dilution ratios based on a thermodynamic approach involving activation energy and heat of vaporization determination. Based on selected dilution ratios, kinematic viscosities of binary and ternary systems of toluene and natural gas condensate as diluents, and Saudi Heavy crude oil as the base oil were measured, using anticipated field based temperatures reported in the literature, which facilitated the experimental approach. The study shows that although the ternary systems have the lowest activation energy for viscous flow and heat of vaporization in accordance with the thermal activation theory of viscous flow, natural gas condensate binary systems have the lowest cost of transportation per barrel of total fluid in the transporting pipeline. The study further shows that the binary systems for toluene and Saudi Heavy crude oil have higher activation energy for viscous flowed compared to the toluene systems.

Theoretical Investigation of Mechanical and Electronic Properties of Hexagonal BaB2

A comprehensive investigation of the electronic and mechanical properties in the hexagonal BaB2 binary system using state of the art first-principles computational techniques is critical for an in-depth understanding of the fundamental properties unique to this binary system. In this context, we derived elastic constants using the metric-tensor formulation, which allowed us to find important mechanical properties such as Bulk Modulus, Shear Modulus, and Vickers's hardness which are fundamental mechanical quantities. Also, this research includes a detailed analysis of the electronic band structures and a study comparison of Fermi surface topologies. The charge density at the Fermi level (N(EF)), which is very important in superconductivity theories, was found to be 1.43 states/eV.uc. Furthermore, we have explored whether there exists a close relationship between these properties and the superconducting behavior of the BaB2 material. Nevertheless, our calculations unequivocally demonstrate that the information derived from electronic band structures and Fermi surfaces alone is insufficient for a comprehensive explanation of the superconductivity phenomenon observed in such materials.

Binary black holes and quantum off-shell recursion

The quantum off-shell recursion provides an efficient and universal computational tool for loop-level scattering amplitudes. In this work, we present a new comprehensive computational framework based on the quantum off-shell recursion for binary black hole systems. Using the quantum perturbiner method, we derive the recursions and solve them explicitly up to two-loop order. We introduce an indicator that enables straightforward distinguishing diagrams and deriving integral families in the context of off-shell recursions. By employing the soft expansion technique, we remove irrelevant terms from the loop integrands and express them in terms of master integrals. We classify the one-loop and the two-loop classical diagrams, and their loop integrands are represented by linear combinations of the master integrals. Finally, we explicitly calculate the classical scalar 2 → 2 amplitudes in the potential region up to the 3PM order and reproduce the known results.

Quasinormal modes in noncommutative Schwarzschild black holes

We investigate the quasinormal modes of a massless scalar field in a Schwarzschild black hole, which is deformed due to noncommutative corrections. We introduce the deformed Schwarzschild black hole solution, which depends on the noncommutative parameter Θ. We then extract the master equation as a Schrödinger-like equation, giving the explicit expression of the effective potential which is modified due to the noncommutative corrections. After that, we solve the master equation numerically. The significance of these results is twofold. Firstly, our results can be related to the detection of gravitational waves by the near future gravitational wave detectors, such as LISA, which will have a significantly increased accuracy. In particular, these observed gravitational waves produced by binary strong gravitational systems have oscillating modes which can provide valuable information. Secondly, our results can serve as an additional tool to test the predictions of GR, as well as to examine the possible detection of this kind of gravitational corrections.

Calculations of solubilities of pure noble gases and He–CO2/CH4/N2 gas mixtures in aqueous solutions with accurate thermodynamic models

Determining solubilities of pure noble gases and He–CO2/CH4/N2 gas mixtures in aqueous solutions is essential for various applications of noble gases in geological processes and for understanding the migration and accumulation of helium. This study developed two thermodynamic models for calculations of solubilities of five pure noble gases (i.e. He, Ne, Ar, Kr, and Xe) and He–CO2/CH4/N2 gas mixtures in water and in aqueous NaCl solution. The first model is constructed by extending the improved SAFT-LJ equation of state (EOS) to five binary H2O-noble gas systems and four ternary systems (i.e. H2O–He–NaCl, H2O–He–CO2, H2O–He–CH4, and H2O–He–N2). Both the non-ideality of aqueous phase and that of vapor phase of these systems were described using the improved SAFT-LJ EOS (φ-φ model). The second model is developed by modifying the gas solubility model proposed by Duan and his coworkers (one type of γ-φ model). The Pitzer theory was used to describe the non-ideality of aqueous phase and the improved SAFT-LJ EOS was used to describe the non-ideality of vapor phase. Both binary adjustable parameters of the improved SAFT-LJ EOS and parameters of the modified solubility model for pure gas were evaluated from experimental solubility data for pure gas. Both models are predictive for solubilities of gas mixtures since there is no need to evaluate their parameters from solubility data of gas mixtures.Comparisons of calculations of two models with experimental data show that both models can well represent solubilities and Henry's coefficients of five noble gases in pure water, as well as the solubility of He in aqueous NaCl solutions over a wide P-T range (273–600 K, 1–2000 bar for the solubility of He in water). The absolute average deviation of the improved SAFT-LJ EOS from experimental solubility data for five noble gases in pure water is 3.14% and that of the modified solubility model is 2.21%. Predictions of the improved SAFT-LJ EOS for Henry's coefficients for He in the He–CO2–H2O system are consistent with available experimental data. According to predictions of the improved SAFT-LJ EOS, Henry's coefficient for He in the He–CO2–H2O system is always lower than that in the He–H2O system at the same depth. Within 0–5 km depth, He solubility of He–CO2 gas mixture is much greater than that of pure He at the same depth and He partial pressure, He solubility of He–N2 mixture is a little greater than that of pure He, and He solubility of He–CH4 mixture is between that of He–CO2 mixture and that of He–N2 mixture. A computer program for calculations of solubilities of pure noble gases and He–CO2/CH4/N2 gas mixtures in pure water and in aqueous NaCl solutions can be obtained from the corresponding author via email.

Measuring source properties and quasinormal mode frequencies of heavy massive black-hole binaries with LISA

The Laser Interferometer Space Antenna (LISA) will be launched in the mid-2030s. It promises to observe the coalescence of massive black-hole (BH) binaries with signal-to-noise ratios (SNRs) reaching thousands. Crucially, it will detect some of these binaries with high SNR in both the inspiral and the merger-ringdown stages. Such signals are ideal for tests of general relativity (GR) using information from the whole waveform. Here, we consider astrophysically motivated binary systems at the high-mass end of the population observable by LISA and simulate their signals using the newly developed multipolar effective-one-body model: pSEOBNRv5HM. The merger-ringdown signal in this model depends on the binary properties (masses and spins) and also on parameters that describe fractional deviations from the GR quasinormal mode (complex) frequencies of the remnant BH. Performing full Bayesian analyses, we assess to which accuracy LISA will be able to constrain deviations from GR in the ringdown signal when using information from the whole signal. We find that these deviations can typically be constrained to within 10% and in the best cases to within 1%. We also show that with this model we can measure the binary masses and spins with great accuracy even for very massive BH systems with low SNR in the inspiral. In particular, individual source-frame masses can typically be constrained to within 10% and as precisely as 1%, and individual spins can typically be constrained to within 0.1 and, in the best cases, to within 0.001. We also probe the accuracy of the SEOBNRv5HM waveform family by performing synthetic injections of GR numerical-relativity waveforms. Using a novel method that we develop here to quantify the impact of systematic errors, we show that, already for sources with SNR O(100), we would measure erroneous deviations from GR due to waveform model inaccuracies. One of the main sources of error is the mismodeling of the relative alignment between harmonics. These results confirm the need for improving waveform models to perform tests of GR with binary BHs observed at high SNR by LISA. Published by the American Physical Society 2024

Spontaneous Liquefaction of Solid Metal-Liquid Metal Interfaces in Colloidal Binary Alloys.

Crystallization of alloys from a molten state is a fundamental process underpinning metallurgy. Here the direct imaging of an intermetallic precipitation reaction at equilibrium in a liquid-metal environment is demonstrated. It is shown that the outer layers of a solidified intermetallic are surprisingly unstable to the depths of several nanometers, fluctuating between a crystalline and a liquid state. This effect, referred to herein as crystal interface liquefaction, is observed at remarkably low temperatures and results in highly unstable crystal interfaces at temperatures exceeding 200 K below the bulk melting point of the solid. In general, any liquefaction process would occur at or close to the formal melting point of a solid, thus differentiating the observed liquefaction phenomenon from other processes such as surface pre-melting or conventional bulk melting. Crystal interface liquefaction is observed in a variety of binary alloy systems and as such, the findings may impact the understanding of crystallization and solidification processes in metallic systems and alloys more generally.

Thermodynamic Evaluation of the Fe-Zn Binary System with Reference to the Latest Experimental Phase Diagram

Thermodynamic Evaluation of the Fe-Zn Binary System with Reference to the Latest Experimental Phase Diagram

Recent collisional history of (65803) Didymos

The Double Asteroid Redirection Test (DART, NASA) spacecraft revealed that the primary of the (65803) Didymos near-Earth asteroid (NEA) binary system is not exactly the expected spinning top shape observed for other km-size asteroids. Ground based radar observations predicted that such shape was compatible with the uncertainty along the direction of the asteroid spin axis. Indeed, Didymos shows crater and landslide features, and evidence for boulder motion at low equatorial latitudes. Altogether, the primary seems to have undergone sudden structural failure in its recent history, which may even result in the formation of the secondary. The high eccentricity of Didymos sets its aphelion distance inside the inner main belt, where it spends more than 1/3 of its orbital period and it may undergo many more collisions than in the NEA region. In this work, we investigate the collisional environment of this asteroid and estimate the probability of collision with multi-size potential impactors. We analyze the possibility that such impacts produced the surface features observed on Didymos by comparing collisional intervals with estimated times for surface destabilization by the Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect. We find that collisional effects dominate over potential local or global deformation due to YORP spin up.

Detection of extragalactic magnetic massive stars

odot $ leave behind neutron stars and black holes by the end of their evolution. The merging of binary compact remnant systems produces astrophysical transients detectable by gravitational wave observatories. Studies of magnetic fields in massive stars with low metallicities are of particular interest because they provide important information on the role of magnetic fields in the star formation of the early Universe. While several detections of massive Galactic magnetic stars have been reported in the last few decades, the impact of a low-metallicity environment on the occurrence and strength of stellar magnetic fields has not yet been explored. Because of the similarity between Of?p stars in the Magellanic Clouds (MCs) and Galactic magnetic Of?p stars, which possess globally organised magnetic fields, we searched for magnetic fields in Of?p stars in the MCs. Additionally, we observed the massive contact binary Cl$*$ NGC\,346\,SSN7 in the Small Magellanic Cloud to test the theoretical scenario that the origin of magnetic fields involves a merger event or a common envelope evolution. We obtained and analysed measurements of the magnetic field in four massive Of?p stars in the MCs and the binary Cl$*$ NGC\,346\,SSN7 using the ESO/VLT FORS2 spectrograph in spectropolarimetric mode. We detected kilogauss-scale magnetic fields in two Of?p-type stars and in the contact binary Cl$*$ NGC\,346\,SSN7. These results suggest that the impact of low metallicity on the occurrence and strength of magnetic fields in massive stars is low. However, because the explored stellar sample is very small, additional observations of massive stars in the MCs are necessary.

Thermodynamic and spectroscopic investigation of the molecular interactions among vitamin B5, calcium salt, and cyclodextrins in aqueous media

The pharmaceutical industry aims to enhance drug development processes by gaining a deeper understanding of the physiochemical properties of drug molecules. This study provides a comprehensive analysis of the volumetric and compressibility properties of the drug, calcium-D-pantothenate (CDP) in aqueous solutions of cyclodextrins (β-CD/HP-β-CD). By measuring the density and speed of sound, we have evaluated various parameters, including apparent molar volume, compressibility, and their corresponding infinite dilution parameters. In addition to this, positive transfer parameters such as ΔtrVs,φo and ΔtrKs,φo of solute provide insights into solute-co-solute and solute–solvent interactions. Also, Hepler’s constant offers valuable information on the structure-breaking characteristics of the studied drug in cyclodextrin medium. The decrease in molar conductance of the binary system after adding cyclodextrin supports our theoretical observation from volumetric and compressibility studies. Positive values of activation energy favor spontaneity and the solubilization process. Furthermore, the 1H NMR study demonstrates that the β-CD molecule interacts more strongly with CDP molecules as compared to HP-β-CD.

A macroscopic model for predicating stepwise crystalline swelling of montmorillonite

Bentonite, as an optimal buffer material in high-level radioactive waste (HLRW) repository, is usually unsaturated and sensitive to relative humidity (RH) conditions. Accurately modelling unsaturated crystalline swelling of bentonite is crucial for estimating the performance of a geological repository. In this study, we attempt to extend Laird model, a classical model for crystalline swelling, from saturated to unsaturated. For this purpose, a binary system that comprising air phase and water phase is introduced into Laird model, then the concept of effective diabattivity for atmosphere with a certain RH is proposed. On the basis, the net hydration repulsions under various RHs conditions can be determined. To calibrate the effective diavattivity, the oriented montmorillonite (Mt) tactoids is prepared and the RH controlled X-ray diffraction test is carried out. Moreover, a coupling approach of molecular dynamics (MD) simulation and fluctuation–dissipation dielectric theorem is employed to gain interlayer dielectric from dipolar fluctuations, which further improves the model accuracy. The novel model is validated by the experimental results for 3 typical buffer materials, including MX-80, Kunipia and FEBEX bentonites. Comparisons between the predicted and measured basal spacings indicate the proposed model can effectively capture the stepwise nature of crystalline swelling. Besides, the model also provides a quantitative approach to track the evolution of interaction energy during hydration process.