Hysteresis Branches Research Articles

Five models of hysteretic water-retention capacity and their comparison for sandy soil

A description of five mathematical models of the water-retention capacity of soil is given, taking into account the hysteresis phenomena. A computational experiment was carried out with these models using data on sandy soil. The experiment consisted of: (i) tuning of the models (parameter identification) by the method of dot-approximation of experimental data on the main drying and wetting branches of the hysteresis loop using an optimizing algorithm; (ii) the predictive calculation of the scanning branches of the hysteresis loop; (iii) a comparison of the errors in tuning results and the predictive calculation using the Williams-Kloot criteria. The commensurate and sufficiently low errors in the adjustment of the models have been achieved. The differences in the calculation of the scanning hysteresis branches are revealed. The practical significance of the mathematical models presented is to ensure the calculation of precision irrigation rates. The application of such rates in irrigation farming will help to prevent excess moisture from flowing beyond the root layer of the soil under the influence of gravity and, thus, to minimize the losses (unproductive consumption) of irrigation water, fertilizers, meliorants and plant protection products, and also reduce the risk of groundwater contamination with agrochemicals and eutrophication of water bodies.

On the adsorbate restructuring induced hysteresis of simple gas adsorption in slit micropores

Simulations of adsorption isotherms for simple gases in homogeneous slit pores with two open ends often show hysteresis, between condensation and evaporation branches. The hysteresis may result either, from the difference in the curvature of the interface separating the adsorbed and gas phases, or from molecular restructuring when the adsorbate is densely packed. The order–disorder transition that occurs in the second case, has also been observed experimentally for adsorption on a graphite surface, and is supported by molecular simulation (Duval and Thomy, 1975; Ustinov and Do, 2012). In this paper we report a comprehensive set of GCMC simulations designed to explore the effects of pore size and temperature on the hysteresis loop induced by adsorbate restructuring. We report isotherms, isosteric heats, and microscopic analyses of the local density distribution, and the 2D and 3D radial density distributions. Local compressibilities reinforce the supposition that adsorbate restructuring is the origin of the ordering hysteresis.

Conductance hysteresis in the voltage-dependent anion channel.

Hysteresis in the conductance of voltage-sensitive ion channels is observed when the transmembrane voltage is periodically varied with time. Although this phenomenon has been used in studies of gating of the voltage-dependent anion channel, VDAC, from the outer mitochondrial membrane for nearly four decades, full hysteresis curves have never been reported, because the focus was solely on the channel opening branches of the hysteresis loops. We studied the hysteretic response of a multichannel VDAC system to a triangular voltage ramp the frequency of which was varied over three orders of magnitude, from 0.5mHz to 0.2Hz. We found that in this wide frequency range the area encircled by the hysteresis curves changes by less than a factor of three, suggesting broad distribution of the characteristic times and strongly non-equilibrium behavior. At the same time, quasi-equilibrium two-state behavior is observed for hysteresis branches corresponding to VDAC opening. This enables calculation of the usual equilibrium gating parameters, gating charge and voltage of equipartitioning, which were found to be almost insensitive to the ramp frequency. To rationalize this peculiarity, we hypothesize that during voltage-induced closure and opening the system explores different regions of the complex free energy landscape, and, in the opening branch, follows quasi-equilibrium paths.

Influence of dipolar interactions on the angular-dependent coercivity of nickel nanocylinders

In this study the influence of dipolar interactions on the orientation-dependent magnetization behavior of an ensemble of single-domain nickel nanorods was investigated. The rods were synthesized by electrodeposition of nickel into porous alumina templates. Some of the rods were released from the oxide and embedded in gelatine hydrogels (ferrogel) at a sufficiently large average interparticle distance to suppress dipolar interactions. By comparing the orientation-dependent hystereses of the two ensembles in the template and the gel-matrix it could be shown that the dipolar interactions in the template considerably alter the functional form of the angular-dependent coercivity. Analysis of the magnetization curves for an angle of 60° between the rod-axes and the field revealed a significantly reduced coercivity of the template compared to the ferrogel, which could be directly attributed to a stray field induced magnetization reversal of a steadily increasing number of rods with increasing field strength. The magnetization curve of the template could be approximated by a weighted linear superposition of the hysteresis branches of the ferrogel. The magnetization reversal process of the rods was investigated by analyzing the angular-dependent coercivity of the non-interacting nanorods. Comparison of the functional form with analytical models and micromagnetic simulations emphasized the assumption of a localized magnetization reversal. Additionally, it could be shown that the nucleation field of rods with diameters in the range 18–29 nm tends to increase with increasing diameter.

A new approach of friction model for tendon-sheath actuated surgical systems: Nonlinear modelling and parameter identification

Nonlinear friction in tendon-sheath mechanism (TSM) introduces difficulties in predicting the end-effector force inside the human body during surgical procedures. This brings a critical challenge for surgical robots that need high fidelity in haptic devices. This paper presents a new friction model for a TSM in surgical robots. The model considers the TSM as an element disregarding the tendon sheath curvature and permits an arbitrary configuration of sheath. It allows for the accurate modelling of friction force at both sliding and presliding regimes. Unlike existing approaches in the literature, the model employs not only velocity but also acceleration information. It is also able to capture separate hysteresis branches in the large displacement using a unique differential equation. Transition between the two regimes is smooth. To validate the approach, an experimental setup is developed to measure the tensions at both ends of the TSM. The model parameters are identified and experimentally validated using an optimization method and different types of input signals. It assures an accurate prediction of nonlinear hysteresis behavior of TSM, especially at near zero velocities. This model can be used to provide an estimate of the friction force in a haptic feedback device to the surgeons.

Hysteresis Modeling in Li-Ion Batteries

This paper investigates the applicability of the scalar Preisach model to describe the hysteresis in the state of charge versus open-circuit voltage plane of lithium-iron-phosphate batteries. The model is implemented using the Everett function, identified with experimental data related to first-order reversal hysteresis branches. To show the effectiveness of the approach and the predictive capabilities of the Preisach model in this peculiar application, numerical simulations of a major hysteresis loop and a set of minor loops are compared with the experimental data.

Analysis of the carbon anode in carbon conversion cells

Abstract We examine further the electrochemical oxidation of carbon in molten carbonate, based on analysis of published research. Ascending and descending branches of voltage hysteresis found in current sweeps of atomically-ordered graphite and of disordered carbon (coal char) are separated by about 0.20–0.25 V and by 0.10–0.15 V for ordered and disordered forms, respectively, over a wide band of current density, 0.03–0.10 A/cm2. The higher voltage of the descending branch is in rough agreement with prediction of the Y. Li model for the carbon/carbonate electrode in the same current range, for ordered graphite (La = 70–100 nm) and for disordered structures (La = 3–5 nm), respectively. We suggest that the amplitude of the hysteresis represents the difference between the overvoltage requirements for 2- and 4 electron net transfer processes, respectively. The 2 e− reaction (C + CO32− = CO + CO2 + 2e−) dominates the low current segment (LCS) of our previous analysis, and the more hindered 4e− transfer reaction (C + 2CO32− = 3CO2 + 4e−) dominates the high current segment (HCS). The voltage increase separating LCS from HCS is effected by accumulation of CO2 within small, melt-filled pores to form highly supersaturated solutions of CO2, which enhance anode voltage by a concentration overpotential of 0.10–0.25 V. Overpotential increases with reaction extent until (1) overall polarization inhibits the interior reaction and shifts CO2 production to the more accessible exterior surface, or, (2) at a critical concentration (dependent on surface tension and pore diameter) bubbles nucleate and block current flow in the pores. Further support for this picture comes from the often-reported deviation of the gas composition from the CO/CO2 ratio of the Boudouard equilibrium at atmospheric pressure, as open circuit conditions are approached in an electrochemical cell. Our interpretation accounts for the mole fraction of CO2 at open circuit being greater than predicted from the Boudouard equilibrium.

On the existence of a hysteresis loop in open and closed end pores

We have studied the adsorption of argon at 87 K in slit pores of finite length with a smooth graphitic potential, open at both ends or closed at one end. Simulations were carried out using conventional GCMC (grand canonical Monte Carlo) or kMC (kinetic Monte Carlo) in the canonical ensemble with extremely long Markov chain, of at least 2 × 108 configurations; selected simulations with much longer Markov chains do not show any change in the results. When the pore width is in the micropore range (0.65 nm), type I isotherms are obtained for both pore models and for both simulation methods. However, wider pores (1, 2 and 3 nm in width) all exhibit hysteresis loops in the GCMC simulations, while in the canonical ensemble simulations, the isotherms pass through a sigmoid van der Waals type loop in the transition region. This loop locates the true equilibrium transition. For the pores with one closed end, this transition is close to, or coincides with, the adsorption branch of the GCMC hysteresis loop, but for the open-ended pores, it is more closely associated with the desorption branch. In a separate study of adsorption hysteresis in an infinitely long slit pore, using both simulation techniques, the van der Waals loop follows the adsorption branch of the GCMC isotherm to the transition, then reverts to a long vertical section that falls midway between the two hysteresis branches and finally moves to the desorption transition close to the evaporation pressure. An examination of molecular distributions inside the pores reveals two coexisting phases in the canonical simulations, whereas in the grand canonical simulations, the molecules are uniformly distributed along the length of the pores.

Synthesis and characterization of pure and stabilized mesoporous anatase titanias

The effects of dopants Al, La, Si, and Zr on the stability, surface area, and porosity of anatase were investigated. Anatase materials stabilized with 0–14mol% La, Si, Zr, or 0–85mol% Al were studied. Materials were characterized using XRD, TEM and N2 adsorption. Results show that (1) dopants increased the surface area and thermal stability of anatase through structural modifications and grain growth inhibition, (2) due to structural modifications it was important to select the appropriate hysteresis branch for pore diameter calculations, and (3) a thorough analysis of N2 adsorption and TEM data provided additional insight into how stabilizing agents affected the mesoporous structure. Stabilized titanias produced by this method demonstrated equivalent or higher thermal stability and surface area compared with pure anatase and previously reported materials after treatment at 400°C and 700°C including 22mol% Al–TiO2 calcined at 400°C which had a surface area of 479±39 m2/g, a pore volume of 0.46±0.04 cm3/g, and a pore diameter of 2.9±0.2nm.

Liquid–solid mass transfer distributions in trickle bed reactors

Micro-electrodes with exposed areas ranging from 5 to 30mm2 were placed onto 4.5mm alumina spheres and used for the sub-particle scale quantification of liquid–solid mass transfer. A novel electrochemical technique was applied where the external cathode wetting fraction and liquid–solid mass transfer were simultaneously quantified. Clear bifurcation of the area-specific liquid–solid mass transfer was observed, providing direct evidence of the two-wetted-zone theory previously inferred from tracer response analysis. The lower hysteresis branch (Levec prewetting) exhibited larger fractions of static wetted area compared to the upper branch (Kan prewetting). The static zones were not completely stagnant and the average static mass transfer rate increased with liquid superficial velocity. The spatial position of the static zones varied for a given packing configuration, while no relationship was found between the positioning of static and residual holdup. Static liquid–solid mass transfer coefficients were found to be higher than those obtained from tracer response analyses on porous particles.

When T(LIESST) Meets Thermal Hysteresis – a Theoretical Approach

AbstractWe used a macroscopic master equation for a two‐level system, with simple assumptions, to calculate the kinetic behavior of a spin‐crossover system when the equilibrium temperature interplays with the T(LIESST) temperature (LIESST = light‐induced excited spin state trapping), that is, the thermal return temperature of the low‐temperature metastable state of the system. The leading role of the unstable equilibrium branch is characterized through the crossing of the cooperative energy barrier, which induces a bifurcation of the response of the system in the strongly cooperative case. The results are shown in terms of a kinetic phase diagram, which shows the eventual discontinuities that result from the bifurcation effect. The present study suggests an experimental method for locating the unstable equilibrium branch of the thermal hysteresis, which enables determination of the equilibrium temperature of the hysteretic system, and which is not accessible by usual static measurements.

Uniqueness of transverse solutions for reaction–diffusion equations with spatially distributed hysteresis

The paper deals with reaction–diffusion equations involving a hysteretic discontinuity in the source term, which is defined at each spatial point. Such problems describe biological processes and chemical reactions in which diffusive and nondiffusive substances interact according to hysteresis law. Under the assumption that the initial data are spatially transverse, we prove a theorem on the uniqueness of solutions. The theorem covers the case of non-Lipschitz hysteresis branches arising in the theory of slow–fast systems.

Fabrication process of intrinsic Josephson junction stacks in Bi2Sr2CaCu2O8+x crystals by double-sided patterning process using dilute hydrochloric acid

We have developed a new double-sided patterning (DSP) process that employs dilute acid (pH=1.65) to fabricate Bi2Sr2CaCu2O8+x (Bi-2212) stacks of intrinsic Josephson junctions. These stacks, which were fabricated from a single crystal of Bi-2212, were surrounded by an acid-treated product. The critical aspect of this process is that the Bi-2212 surrounding the photoresist pattern was converted into a transparent material, BiOCl, which was connected with the Bi-2212 crystal. Consequently, this process provides a simple way to achieve DSP of the surfaces of Bi-2212 crystals. This new DSP process realizes a remarkably improved reproducibility in fabricating Bi-2212 stacks that exhibit good current–voltage characteristics with a large hysteresis and multiple branches at T=77K.

Trickle flow liquid–solid mass transfer and wetting efficiency in small diameter columns

AbstractA novel method to simultaneously measure liquid solid mass transfer and external wetting efficiency was employed at column to particle ratios of 10, 6 and 3. Two prewetting procedures representing the upper (Kan) and lower (Levec) hysteresis branches were used. For a multipoint distributor on a Kan prewetted bed wetting efficiency and the specific mass transfer coefficient were almost unaffected by column diameter. The multipoint distributor on a Levec prewetted bed exhibited a decrease in specific mass transfer with decreasing column diameter. Point source experiments resulted in significantly lower wetting and mass transfer measurements with an increasing trend with respect to decreasing column diameter. The results indicate that with proper distribution and prewetting, the effect of column diameter on averaged wetting and liquid–solid mass transfer is almost negligible, a powerful result considering the importance of these parameters on reaction experiments. © 2012 Canadian Society for Chemical Engineering

Magnetic dipole configurations in honeycomb lattices: order and disorder

Dipolar spin ice has attracted much attention because of its intriguing ground state ordering and elementary excitation properties. We present experimental realizations of magnetic dipolar spin ice on periodic lattices with honeycomb symmetry. We have analyzed in particular the evolution and distribution of excitations with magnetic charges ±3 per vertex as a function of magnetic field and the distance b between the dipoles ranging from b = 0.4 to 1.7 μm. In all the dipole patterns investigated, we observe a surprisingly high abundance of ±3 magnetic charges at coercivity in the descending and ascending branches of the magnetic hysteresis. At the same time, these ±3 vertices form a charge ordered state with large domains, resembling an ionic crystal. Monte Carlo simulations of the magnetization reversal confirm in the framework of a macrospin model an enhanced abundance of ±3 magnetic charges at the coercive field. But much better agreement is achieved by taking into account the micromagnetic reversal mechanism, which proceeds via nucleation and domain wall propagation for dipoles aligned with the field and via coherent rotation for all others.

An Index for Degree of Hysteresis in Water Retention

Direct characterization of hysteresis in water retention (WR) is typically cumbersome and time consuming. Thus, such data are scarce, and even when available are typically ignored in unsaturated flow modeling. One reason for disregard of this ubiquitous and significant feature of WR is lack of a universally applicable index for the degree of hysteresis that allows a priori assessment of its effect on flow. In this note we show that the mismatch between the hydraulic capacity functions of the primary drainage and imbibition curves can serve as generalized index for degree of hysteresis (H). Moreover, we showed that hysteresis indices of a broad range of soils are linearly related with the natural-logarithm of the van Genuchten n parameter (r2 = 0.73). This model allows predicting the degree of hysteresis and the missing hysteresis branch using only wetting or drying water retention data. The robustness of the proposed index was illustrated by comparing it with error in simulated moisture redistribution in a horizontal column that arises from ignoring hysteresis.

Modeling of exchange bias in the antiferromagnetic (core)/ferromagnetic (shell) nanoparticles with specialized shapes

Zero-field-cooled (ZFC) and field-cooled (FC) hysteresis loops of egg- and ellipsoid-shaped nanoparticles with inverted ferromagnetic (FM)-antiferromagnetic (AFM) core-shell morphologies are simulated using a modified Monte Carlo method, which takes into account both the thermal fluctuations and energy barriers during the rotation of spin. Pronounced exchange bias (EB) fields and reduced coercivities are obtained in the FC hysteresis loops. The analysis of the microscopic spin configurations allows us to conclude that the magnetization reversal occurs by means of the nucleation process during both the ZFC and FC hysteresis branches. The nucleation takes place in the form of “sparks” resulting from the energy competition and the morphology of the nanoparticle. The appearance of EB in the FC hysteresis loops is only dependent on that the movements of “sparks” driven by magnetic field at both branches of hysteresis loops are not along the same axis, which is independent of the strength of AFM anisotropy. The tilt of “spark” movement with respect to the symmetric axis implies the existence of additional unidirectional anisotropy at the AFM/FM interfaces as a consequence of the surplus magnetization in the AFM core, which is the commonly accepted origin of EB. Our simulations allow us to clarify the microscopic mechanisms of the observed EB behavior, not accessible in experiments.

Bistability and spatial hysteresis in an Nd:GdVO4 laser with an intracavity twisted-nematic liquid crystal

In this study, optical bistability accompanied by spatial hysteresis was demonstrated in an Nd:GdVO4 laser with an intracavity twisted-nematic liquid crystal. The low branch of power hysteresis mainly has the spatial distribution of the fundamental mode as the pump power increases, whereas a four-mode and varying transverse pattern exist in the high branch of power hysteresis as the pump power decreases. The result revealed that the power and spatial hysteresis is controlled by the director axis reorientation and the order parameter modification in twisted-nematic liquid crystals, which is determined by the non-uniform transverse distribution of the intracavity laser intensity.

New Double-sided Patterning Process Using a Dilute Hydrochloric Acid Solution to Fabricate Stacked Intrinsic Josephson Junctions Inside Bi2Sr2CaCu2O8+x Single Crystals

We developed a new double-sided patterning (DSP) process using a dilute acid solution (pH=1.65) to fabricate Bi2Sr2CaCu2O8+x (Bi-2212) stacks of intrinsic Josephson junctions. The stacks, which were fabricated from a single crystal of Bi-2212, were surrounded by an acid-treated product. The critical aspect of this process is that the Bi-2212 surrounding the photo-resist pattern was changed to a transparent material, BiOCl, which was connected with the Bi-2212 crystal. As a result, this process provides an easy way to achieve the DSP of the surface of the Bi-2212 crystal. This new DSP process allows for remarkably improved reproducibility in fabricating the Bi-2212 stacks which show good current-voltage characteristics with large hysteresis and multiple branches at T=77 K.

A modified prandtl-ishlinskii model for modeling asymmetric hysteresis of piezoelectric actuators

Piezoelectric actuators can offer high resolution of displacement and this makes them suitable for precise driving tasks. However, most piezoelectric actuators are made of piezoceramics which have a major drawback related to their natural hysteresis nonlinearity. To compensate the hysteresis nonlinearity of piezoelectric actuators, many hysteresis models have been proposed such as the Preisach model, the classical Prandtl-Ishlinskii model, and so on. This paper provides a new approach to model the asymmetric hysteresis nonlinearity of piezoelectric actuators. Unlike the classical Prandtl-Ishlinskii model, the proposed model is based on a combination of two asymmetric operators which can independently simulate the ascending branch and descending branch of hysteresis. Moreover, the proposed model can be calculated using the recursive least-squares method and this makes the model easy and convenient to be calculated. The validity of the proposed model is demonstrated by comparing its simulation results with experimental measurements. The results show that the proposed model is capable of modeling asymmetric hysteresis of piezoelectric actuators with very high accuracy.