Samples of Na-saturated, Upton montmorillonite were prepared with different contents of water (H2O or D2O) by: (1) adsorption of water from the vapor phase at a specific value of p/p°, the relative humidity, (2) adsorption of water from the vapor phase at p/p° = 1.0 followed by desorption of the water into the vapor phase at a specific p/p° < 1.0, and (3) adsorption of water from the liquid phase followed by desorption of the water into the vapor phase at a specific p/p° < 1.0. Water adsorbed initially from the vapor phase was called V-adsorbed water, and water adsorbed initially from the liquid phase was called L-adsorbed water. The water contents of these samples were determined by gravimetric analysis, the c-axis spacings by X-ray powder diffraction, the O-D stretching frequencies by IR spectroscopy, and the heats of immersion by differential microcalorimetry. No difference was found between V-adsorbed and L-adsorbed water; however, if the final water content was established by adsorption, the system was in a different state than if the final water content was established by desorption. In particular, hysteresis was observed in the following properties: the relative humidity of the adsorbed water, the O-D stretching frequency in this water, and the degree of order in the stacking of the clay layers. The only property that did not exhibit hysteresis was the heat of immersion. Apparently, hysteresis occurred because the orderliness of the system was not reversible, and, thus, any property that depended on orderliness was hysteretic.

An environmental infrared microbalance (EIRM) cell was used to study H2O sorption on two montmorillonite samples as a function of water content and type of exchangeable cation. The vibrational spectra showed that H2O sorbed to the clay at low-water content was strongly influenced by the exchangeable cation and by the close proximity to the clay surface. At water contents <6 H20 molecules per exchangeable cation, the H-O-H bending mode of H2O (v2 mode) shifts to a lower frequency and is characterized by an increase in molar absorptivity. In contrast, the positions of the asymmetric and symmetric OH-stretching modes of sorbed water (v1 and v3 modes) shift to higher energies. These observations indicate that H2O molecules sorbed to the clay surface at low-water content are less hydrogen bonded than in bulk H2O. In addition, the vibrational-stretching and bending bands of the structural OH groups of the 2:1 layer are also strongly influenced by H2O content and type of exchangeable cation. By using the EIRM cell, the molar absorptivities of the structural OH-bending vibrations were measured as a function of H2O content. The position and molar absorptivity of the structural OH-bending bands at 920, 883, and 840 cm-1 are strongly influenced by H2O content and type of exchangeable cation. The molar absorptivity of the 920-cm-1 band, which is assigned to the AlAlOH group, decreased strongly at low-H2O content. This reduction in intensity is assigned to a dehydration-induced change in orientation of the structural OH groups resulting from the penetration of H2O molecules into siloxane ditrigonal cavities that are not associated with a net negative charge from isomorphous substitutions.

The binary exchange of cations on clays and soils is generally regarded as a thermodynamically reversible process. The literature on soil chemistry and geochemistry, however, abounds with reports on cation exchange reactions that appear to have only limited reversibility, i.e., that exhibit hysteresis. A satisfactory explanation of this phenomenon is still lacking, even though a number of mechanisms have been advocated, e.g., charge or site heterogeneity at the surface, differential hydration of cations, dehydration of the exchanger, crystalline swelling hysteresis, and inaccessibility of sites caused by domain or quasi-crystal formation. In the present article, the relevant literature is reviewed and analyzed critically. On the basis of available evidence, it is shown that exchangeable cations can be classified into three groups, defined in such a way that hysteresis has, in the literature, generally not been observed when exchange reactions involved cations belonging to the same group, but has often been found when the reactions involved cations from different groups. Furthermore, it is argued that none of the five mechanisms mentioned can, in and of itself, account fully for the observed exchange hysteresis. A conceptual model is proposed that combines elements of these five mechanisms and is able to describe, at least qualitatively, the effects of factors such as clay type, electrolyte concentration, and extent of dehydration.

Adsorption-desorption of Cd to Ca montmorillonite (SAz-1) was studied at concentrations ranging from 44.5 to 266.8 μM. An adsorption model was employed in the analysis of the data. The procedure consists of solving the electrostatic Gouy-Chapman equations and calculating adsorbed amounts of the cations as the sum of the cations residing in the double-layer region, and the cations chemically bound to the surface, in a closed system. The model also accounts explicitly for cation complexation in solution. The model yields good predictions for the adsorbed amounts of Cd, Ca and Mg, by employing binding coefficients from previous studies for the divalent cations and for Na, K and CdCl+. The model calculations also yield good predictions for the apparent hysteresis observed in the adsorbed amounts of Cd after each of 3 cycles of desorption. The apparent hysteresis is explained by the reduction in the total concentrations of Ca and Mg in desorption cycles, and the corresponding increase in the magnitude of the surface potential. Our estimates indicate that adsorption of Cd is mostly to planar, rather than edge sites of the clay mineral.

Sorption of the herbicide isoxaflutole and its main degradate, diketonitrile (DKN), to natural clays, SAz-1, SWy-2 and SHCa-1, and the organoclay derivatives (octadecylammonium (ODA) and hexadecyltrimethylammonium (HDTMA)) of these clays was investigated. Isoxaflutole hydrolysis to DKN was too rapid in aqueous solutions with organoclays to characterize sorption. No measurable DKN sorption was observed for the natural clays. Sorption of DKN was greater on organoclays with an interlayer paraffin-like complex that were prepared from the high-charge SAz-1 clay than on organoclays with a bilayer or monolayer interlayer complex prepared using lower-charge SWy-2 or SHCa-1 clays. Desorption isotherms indicated that sorption was irreversible. For SAz-1 with HDTMA at ∼100% of the clay CEC, the d001 values suggest that DKN enters the interlamellar space of the organoclay and dissociates into the anion. The DKN anion forms a very stable chelate complex with the residual cations and/or partially-coordinated structural cations. This strong interaction supports the irreversibility of the sorptive process.

In Chen and Liang previous work, a model, together with its well-posedness, was established for credit rating migrations with different upgrade and downgrade thresholds (i.e. a buffer zone, also called dead band in engineering). When positive dividends are introduced, the model in Chen and Liang (SIAM Financ. Math. 12, 941–966, 2021) may not be well-posed. Here, in this paper, a new model is proposed to include the realistic nonzero dividend scenarios. The key feature of the new model is that partial differential equations in Chen and Liang (SIAM Financ. Math. 12, 941–966, 2021) are replaced by variational inequalities, thereby creating a new free boundary, besides the original upgrading and downgrading free boundaries. Well-posedness of the new model, together with a few financially meaningful properties, is established. In particular, it is shown that when time to debt paying deadline is long enough, the underlying dividend paying company is always in high grade rating, that is, only when time to debt paying deadline is within a certain range, there can be seen the phenomenon of credit rating migration.

This study seeks to determine the impact of remittances and nonlabor income on the duration of unemployment, and therefore on the hysteresis phenomenon in Colombia for the period between January 2010 and January 2021. The long-term unemployment rate in Colombia (LAPU) is calculated, and a vector autoregressive (VAR) model is subsequently estimated to evaluate the impact of remittances and nonlabor income on the LAPU. The results suggest that the increase in nonlabor income significantly affected LAPU in Colombia in the period analyzed. The growth of remittances instead turned out to positively and significantly impact LAPU only during the COVID-19 pandemic crisis. This suggests that remittances have become a fundamental income in times of crisis that allow for financing the search for work for a longer period of time, thus increasing the duration of unemployment and generating a hysteresis effect.

Understanding seed moisture desorption and adsorption isotherms is important for seed quality maintenance and better predicting seed storage lifespan. Freshly harvested oilseed rape and barley seeds were dried and then rehydrated twice. Seed equilibrium relative humidity (eRH) and moisture content (MC) were determined at different humidity levels so that two cycles of desorption and adsorption could be constructed. In addition, seeds were dried to 30% RH and then rehydrated to 50% RH for five cycles to determine whether they shift to the adsorption isotherm. Monolayer MC was determined using the Gugenheim-Anderson-de Boer model. Storage experiments were conducted for seeds equilibrated at 30, 40, 50, 60 and 70% RH for two cycles of desorption and adsorption at 45°C. Isotherm curves’ shapes were similar for oilseed rape and barley, although spanning a greater MC range in barley. The hysteresis effect was observed for oilseed rape and barley seeds when dried over silica gel at <10% RH. However, this effect was only observed for barley seeds when dried to 30% RH, but not for oilseed rape seeds. Longevity was greater for adsorbing seeds than desorbing seeds at a given eRH, however, there was no significant difference in σ (the standard deviation of the normal distribution of seed deaths over time)–MC log–log relationship. The relationship shifted for seeds on the second cycle. In conclusion, if seed lots are stored at a specific RH, reaching equilibrium by desorption or adsorption can strongly influence their longevity. Also, when seeds of different species are dried to low RH, they will respond differently to a subsequent increase in RH, which could profoundly affect their longevity.

How do people make decisions between an immediate but small reward and a delayed but large one? The outcome of such decisions indicates that people discount rewards by their delay and hence these outcomes are well described by discounting functions. However, to understand irregular decisions and dysfunctional behavior one needs models which describe how the process of making the decision unfolds dynamically over time: how do we reach a decision and how do sequential decisions influence one another? Here, we present an attractor model that integrates into and extends discounting functions through a description of the dynamics leading to a final choice outcome within a trial and across trials. To validate this model, we derive qualitative predictions for the intra-trial dynamics of single decisions and for the inter-trial dynamics of sequences of decisions that are unique to this type of model. We test these predictions in four experiments based on a dynamic delay discounting computer game where we study the intra-trial dynamics of single decisions via mouse tracking and the inter-trial dynamics of sequences of decisions via sequentially manipulated options. We discuss how integrating decision process dynamics within and across trials can increase our understanding of the processes underlying delay discounting decisions and, hence, complement our knowledge about decision outcomes.

Prandtl–Ishlinskii (PI) model has an excellent compromise to characterize an asymmetric saturated hysteresis behavior of shape-memory-alloy (SMA)-driven systems, but it cannot consider thermomechanical relations between components of SMA-driven systems. On the other hand, constitutive models are composed of these relations, but their precision needs to be improved. In this paper, PI model is proposed to boost constitutive models in two cases. In the first case, PI model is used to characterize martensite volume fraction (MVF) called hybrid model. In the second case, the model is applied as a regulator in the output of a constitutive model called PI-based output (PIO) regulator. Due to simplicity and ability of Liang–Rogers (LR) model in transformation phases, it is considered as an MVF in the original constitutive model. The performance of both proposed models is compared with the original LR-based constitutive model. Unknown parameters of all three models are identified using genetic algorithm in MATLAB Toolbox. The performance of the three models is investigated at three different frequencies of \[\frac{{2\pi }}{8}\], \[\frac{{2\pi }}{{15}}\], and \[\frac{{2\pi }}{{30}}\] Hz because the excitation frequency changes the hysteresis behavior. Results show that the proposed hybrid model keeps the precision of the original constitutive model at different frequencies. In addition, the proposed PIO model shows the best performance to predict hysteresis behavior at different frequencies.

The coexistence of multiple stable states is indicative of self-organising processes occurring in the course of the combustor-inlet interactions in a ramjet engine and give rise to the appearance of various nonlinear phenomena. This paper provides a dynamic model that can describe the multiple stable states and the corresponding nonlinear effects to further investigate the dynamic interactions between combustor and inlet in a ramjet engine. Our study shows the whole engine can display distinct dynamic behaviours ranging from irreversibility to hysteresis and to various mode transitions, depending on different physical parameters. With the model, we also illustrate the role of the instability of the normal shock wave in impacting the whole engine’s nonlinear dynamics. Additionally, we extend the previous studies of the classification of combustor-inlet interactions from a static framework to a dynamic framework, which helps to clarify the transient processes of the nonlinear interactions. This work offers a quantitative illustration of the combustor-inlet interactions in a ramjet engine by revealing its nonlinear dynamics and associated characteristics, therefore advancing our understanding of the nonlinear phenomena that exhibit in ramjet engines.

The aim of the virtual torsion sensor (VTS) is to observe the nonlinear deflection in the flexible joints of robotic manipulators and, by its use, improve positioning control of the joint load. This model-based approach utilizes the motor-side sensing only and, therefore, replaces the load-side encoders at nearly zero hardware costs. For being applied in the closed control loop, the stability and robustness of VTS are most crucial. This work extends the previous analysis by a general case of nonlinear joint stiffness with hysteresis and provides straightforward conditions with respect to the system dynamics. The dissipativity and passivity of the torsion-torque hysteresis map are analyzed and discussed in detail. The absolute stability of VTS inclusion into position control loop is shown based on the equivalent loop transformations and Popov criteria, including the sector conditions. Illustrative numerical examples of the control error dynamics and its convergence are provided.

Turbulent airflow in a supersonic intake model of rectangular cross-section is studied numerically. Instability of shock waves formed in the intake and ahead of the entrance is examined. Solutions of the Reynolds-averaged Navier–Stokes equations are obtained with a finite-volume solver of second-order accuracy. The expulsion and the swallowing of the shocks with a variation of free-stream parameters are studied at both subsonic and supersonic conditions prescribed at the outlet. Hysteresis in the dependence of 2D flow on the free-stream velocity and angle-of-attack is documented. An influence of 3D effects on the flow is examined.

At river bifurcations water and sediment is divided among the downstreambranches. Prediction of the sediment transport rate and division thereof atbifurcations is of utmost importance for understanding the evolution of thebifurcates for short-term management purposes and for long-term fluvialplain development. However, measured sediment transports in rivers rarelyshow a uniquely determined relation with hydrodynamic parameters. Commonly ahysteresis is observed of transport rate as a function of discharge or shearstress which cannot be explained with the standard sediment transportpredictor approach. The aim of this paper is to investigate the causes ofhysteresis at a bifurcation of the lower Rhine river, a meandering riverwith stable banks, large dunes during flood, and poorly sorted bed sediment.The hydrodynamics and bed sediment transport were measured in detail duringa discharge wave with a recurrence interval larger than 10 years.Surprisingly, the hysteresis in bedload against discharge was in theopposite direction upstream and downstream of the bifurcation. The upstreamclockwise hysteresis is caused by the lagging development of dunes duringthe flood. The counter-clockwise hysteresis downstream of the bifurcation iscaused by a combination of processes in addition to dune lagging, namely 1)formation of a scour zone upstream of the bifurcation, causing a migratingfine sediment wave, and 2) vertical bed sorting of the bed sediment by duneswith avalanching lee-sides, together leading to surface-sediment fining andincreased transport during and after the flood. These findings lead tochallenges for future morphological models, particularly for bifurcations,which will have to deal with varying discharge, sediment sorting in thechannel bed, lagging dunes and related hydraulic roughness.