Loop Shaping Research Articles

Effects of Salt Content and Freeze-Thaw Conditions on Dynamic characteristics and its microscopic mechanism of Chloride Silty Clay

Generally, artificial ground freezing (AGF) technology is utilized to guarantee tunnel safety during construction. However, the soil structure changes significantly after freeze-thaw, resulting in uneven deformation of the tunnel under traffic loading from subway vibration. To solve this problem effectively, it is necessary to consider the combined impact of freeze-thaw, salt, and traffic loading damage that marine soft soil must withstand simultaneously. For this reason, cyclic triaxial test and NMR test were performed on the silty clay saturated with NaCl solution in this study. The influence of three main factors on dynamic properties has been thoroughly investigated, namely freeze-thaw, salt content, and confining pressure. According to cyclic triaxial test, the shape of the hysteresis loop of the specimens after freeze-thaw changed more significantly with increasing loading cycles. The dynamic elastic modulus was weakened by freeze-thaw, while improved by the addition of NaCl. Damping ratio was consistent with the dynamic elastic modulus law. It was worth noting that the different freezing temperatures (−10 °C, −20 °C and − 30 °C) had only a slight impact on dynamic elastic modulus, as well as damping ratio. Mathematical models were proposed to forecast the dynamic elastic modulus and damping ratio regarding marine soft clay. NMR test indicated that the addition of salt made the internal pore environment of the specimens tend to be consistent and enhanced the water-solid interaction. The increase in porosity resulted in the decrease in dynamic elastic modulus. The results have provided valuable insights into the mechanical characteristics of marine soft clay when AGF technology is applied.

A birdcage transmit, 24-channel conformal receive array coil for sensitive 31P magnetic resonance spectroscopic imaging of the human brain at 7 T.

Phosphorus (31P) magnetic resonance spectroscopic imaging (MRSI) can serve as a critical tool for more direct quantification of brain energy metabolism, tissue pH, and cell membrane turnover. However, the low concentration of 31P metabolites in biological tissue may result in low signal-to-noise ratio (SNR) in 31P MRS images. In this work, we present an innovative design and construction of a 31P radiofrequency coil for whole-brain MRSI at 7 T. Our coil builds on current literature in ultra-high field 31P coil design and offers complete coverage of the brain, including the cerebellum and brainstem. The coil consists of an actively detunable volume transmit (Tx) resonator and a custom 24-channel receive (Rx) array. The volume Tx resonator is a 16-rung high-pass birdcage coil. The Rx coil consists of a 24-element phased array composed of catered loop shapes and sizes built onto a custom, close-fitting, head-shaped housing. The Rx array was designed to provide complete coverage of the head, while minimizing mutual coupling. The Rx configuration had a mean reflection coefficient better than -20 decibels (dB) when the coil was loaded with a human head. The mean mutual coupling ( ) among Rx elements, when loaded with a human head, was -16 dB. In phantom imaging, the phased array produced a central SNR that was 4.4-fold higher than the corresponding central SNR when operating the 31P birdcage as a transceiver. The peripheral SNR was 12-fold higher when applying the optimized phased array. In vivo 3D 31P MRSI experiments produced high-quality spectra in the cerebrum gray and white matter, as well as in the cerebellum. Characteristic phosphorus metabolites related to adenosine triphosphate metabolism and cell membrane turnover were distinguishable across all brain regions. In summary, our results demonstrate the potential of our novel coil for accurate, whole-brain 31P metabolite quantification.

Impact of Weight Functions on Performance of Three-Input Integrated Dc-Dc Converter in H ∞ Control

Many power electronic systems applications namely locomotives, hybrid electric vehicles, and all renewable energy sourced systems are shifting towards Multi-Input Multi-Output (MIMO) integrated DC-DC converters due to their reliability and flexible nature. Designing controllers for MIMO integrated DC-DC converter is complicated due to its integrated structure, presence of common elements, and interactions between the input and output variables of the converter. In this work, a Three-Input Integrated DC-DC (TIID) converter is modeled using state-space analysis, and a Transfer Function Matrix (TFM) is acquired from the small signal continuous time model. A robust controller based on the loop shaping method is designed for the TIID converter. In this loop-shaping method, the desired robustness and the performance of the controller are represented with weight functions i.e., loop-shaping filters. These weight functions are designed using TFM and are frequency-dependent. The robustness of the controller depends on the weight function parameters. The effect of varying the parameters of the weight functions on system dynamics, robustness, and performance are studied and plotted. TIID converter of 288 W, 24V-30V-36V to 48 V is considered and the impact of weight function on closed-loop system dynamics and sensitivity characteristics under varying parameter conditions are analyzed in MATLAB Environment.

Exploring the temperature dependence of magnetic properties and magnetoimpedance effect in Co-rich microwires

We studied the temperature dependence of the magnetic properties and giant magnetoimpedance, GMI, effect in as-prepared and annealed Co69.2Fe3.6Ni1B12.5Si11Mo1.5C1.2 glass-coated microwires with nearly-zero magnetostriction. Substantial changes in the GMI ratio, ΔZ/Z, value and magnetic field, H, dependence, and in the hysteresis loops upon heating were observed. The modification in the hysteresis loop shape upon heating correlates with a change in the ΔZ/Z (H) dependencies. In as-prepared and most of the heat treated samples the hysteresis loop transformation from inclined to squared upon heating correlates with the change in ΔZ/Z(H) dependencies from double-peak to single-peak. However, the stress-annealed at 118 MPa samples present better thermal stability of the ΔZ/Z(H) dependencies and hysteresis loops. In all the studied samples an increase in the GMI ratio at 300 °C was observed. The origin of the observed temperature dependences is discussed in terms of the Hopkinson effect, temperature dependence and relaxation of internal stresses, induced magnetic anisotropy, and temperature dependence of the magnetostriction coefficient.

Remagnetization of magnetite-bearing rocks in the Eastern Qiangtang Terrane, Tibetan Plateau (China): Mechanism and diagnosis

Remagnetization is a common yet notorious phenomenon that interferes with paleogeographic reconstruction. Classical paleomagnetic field tests are helpful in detecting remagnetization but their diagnostic power is limited: remagnetization may occur before folding, the tilting age may be ambiguous, or protracted remagnetization may yield dual polarities. Rock magnetic information can provide other constraints on our understanding of the origin of natural remanent magnetization (NRM). Here we focus on the rock magnetic properties of acknowledged remagnetized limestones and unremagnetized rocks of the Zaduo area in the Eastern Qiangtang Terrane, Tibetan Plateau (China). Chemical remanent magnetization is suggested as a more frequent mechanism than the thermoviscous resetting of the NRM. The secondary NRM resides in authigenic magnetite of stable single domain and superparamagnetic (SP) size which grew during post-depositional burial processes. Both high-field and low-field thermomagnetic runs reveal the alteration of existing iron sulfides to magnetite in the remagnetized limestones. NRM decay curves show that the maximum unblocking temperature of the remagnetized samples is significantly lower than that of the unremagnetized samples. Component analysis of acquisition curves of the isothermal remanent magnetization (IRM) reveals a hard component that represents SP magnetite in remagnetized limestones. This component is absent in unremagnetized rocks. End-member modelling reveals a convex curve in the coefficient of determination versus the number of end-members plot for the unremagnetized limestones, whereas the remagnetized rocks exhibit both near-linear and convex shapes. In addition, quantitative analysis of the hysteresis loop shape for different lithologies indicates its validity in detecting remagnetization. Furthermore, we show the differences in the hysteresis data distributions of the two rock types on the Day plot, the Néel diagram, the Borradaile diagram, and the Fabian diagram. Our research emphasizes that rock magnetic properties can serve as tools to diagnose remagnetization in magnetite-dominated rocks. We recommend a comprehensive rock magnetic study to discriminate remagnetization, involving the Day plot, Fabian diagram, thermal demagnetization curves, IRM component analysis and end member modelling.

Novel coarse and fine stage parallel vibration isolation pointing platform for space optics payload

A coarse and fine parallel vibration isolation pointing platform (CFPP) is proposed, which can realize a wide range of motion and active vibration isolation for space optical payload. First the coarse and fine parallel connection scheme is designed based on the Stewart generalized configuration. Kinematic and constraint analyses are performed to determine the two operation modes of the platform. The platform is then structurally designed. System dynamics model is established based on the Lagrange method, and the dynamic disturbance characteristics are analyzed. Next, the active vibration isolation control algorithm based on H∞ loop shaping is designed. The stability of the control system is analyzed. Finally, the prototype is constructed, and the three-axis pointing range test and active vibration isolation experiments in four attitudes are carried out, and the experimental results show that the designed pointing vibration isolation system with coarse and fine stages in parallel can achieve a 7° movement range of the three axes, and it has a maximum vibration isolation capacity of 20 dB for the disturbance in the frequency band of 2–20 Hz. It has great application prospects in the direction of miniaturization and integration of space optical payload in the future.

The use of geometric morphometry and traditional methods to analyze intraspecific variability of the first lower molar (m1) of Alexandromys fortis (Arvicolinae) in island and continental populations of Primorye, Russia

The complexity of the structure of the dental surface of the first lower molar (m1) of mainland and island populations of the reed vole Alexandromys fortis (Büchner, 1889) was assessed using two different methods. Using the traditional approach and methods of geometric morphometry (GM), the morphological variability of the anteroconid m1 of this species of the mainland (the south of Primorsky Krai) and the islands of the Peter the Great Gulf was analyzed. The traditional approach was based on describing the folding of the occlusal surface using three features: 1) folding of the lingual side of the anterior unpaired anteroconid loop (AC); 2) the shape of the labial side of the AC; 3) the shape of the fourth lingual reentrant angle. On the mainland part of the species' range, the highest occurrence was shown by morphotype III-C-a, which also predominated in the Late Pleistocene samples of the species in Primorye. The research revealed increased morphotypic diversity in island populations of the reed vole, which is probably due to the phenotypic and genotypic characteristics of the founders of island populations, as well as inbreeding, which can cause the release of hidden diversity and an increase in the number of rare morphotypes. The most numerous morphotype on the De Livrona – Durnovo Islands was II-C-a, rare for the mainland. In general, the most complex forms are present on the islands. Using a geometric morphometry approach, the anteroconid was divided into two separately studied structures: the anterior unpaired loop of the anteroconid (AC) and the base of the anteroconid (AB). The distribution of AC configurations in the space of the two principal components took on an arcuate shape, revealing a “forbidden zone.” The main changes occur on the lingual side of the AC. Regression analysis showed a direct relationship between the length of the contour (mm) and the complication of the shape of the anterior unpaired loop. The base of the anteroconid (AC) also undergoes transformation: it either stretches or contracts, while if the anterior unpaired loop of the anteroconid (AB) is more complex, then simplification and compression of its base is observed (negative regression). Analysis of the results of using two approaches, traditional and GM methods, in the analysis of the variability of the anteroconid section m1 of A. fortis showed extreme subjectivity in the use of the first one and the wide possibilities of the second one for identifying different aspects of molare transformation using mathematical methods.

Experimental and numerical study of grooved gusset plate damper for cross-braced frames

An innovative grooved gusset plate damper (GGPD) is further developed in this study by conducting cyclic tests and numerical analysis. The proposed damper is installed in X-Concentrically Braced Frames (X-CBFs) for enhancing the seismic performance and energy dissipation of such a system. To investigate the performance characteristics of the system, three 2/3-scale specimens are constructed that are different only in the details of the damper. The damper consists of a gusset plate in which a number of slits are cut around the diagonal braces. The steel between the slits undergoes large plastic deformations under in-plane double curvature, which provides a good level of ductility and energy dissipation. Low cycle fatigue is observed at drift ratios over 1.5% in the first specimen. Thickness of the middle part of the gusset plate is increased in the third specimen as a remedy which turns out to be successful to postpone degradation of stiffness and strength to the drift ratios larger than 3%. Furthermore, a detailed nonlinear 3D finite element model is developed and validated against the results of laboratory tests. The nonlinear finite element model is shown to be successful in predicting failure and fracture due to low cycle fatigue and showing the superiority of the modified specimens in preserving the stable shapes of the hysteresis loops and the cyclic energy dissipation.

Synthesis Methodology for Discrete MIMO PID Controller with Loop Shaping on LTV Plant Model via Iterated LMI Restrictions

This paper presents a methodology for synthesizing discrete MIMO PID controllers through iterative solutions of LMIs. It justifies the necessity of direct synthesis of discrete controllers in digital control systems. The proposed methodology allows for synthesizing an LTI controller for an LTV plant model, ensuring the robust stability of the synthesized system. Robustness is further ensured by the small-gain theorem and a novel approach to loop shaping, enabling the use of arbitrary shape functions. As a result, this methodology provides a broad statement of the problem with performance criteria necessary for practical application in control systems. Numerical examples are used to illustrate the methodology, which is implemented using the MATLAB toolbox, freely available for use.

A Review of Friction Dissipative Beam-to-Column Connections for the Seismic Design of MRFs

The use of friction-based beam-to-column connections (BCCs) for earthquake-resistant moment-resistant frames (MRFs), aimed at eliminating damage to beam end sections due to the development of plastic hinges, has been prevalent since the early 1980s. Different technical solutions have been proposed for steel structures, and some have been designed for timber structures, while a few recent studies concern friction joints employed in reinforced concrete structures. Research aimed at characterizing the behavior of joints has focused on the evaluation of the tribological properties of the friction materials, coefficient of friction, shape and stability of the hysteresis cycles, influence of the temperature, speed of load application, effects of the application method, stability of preload, the influence of seismic excitation characteristics on the structural response, statistical characterization of amplitude, and frequency of the slip excursion during seismic excitation. Studies aimed at identifying the design parameters capable of optimizing performance have focused attention mainly on the slip threshold, device stiffness, and deformation capacity. This review compiles the main and most recent solutions developed for MRFs. Furthermore, the pros and cons for each solution are highlighted, focusing on the dissipative capacity, shape, and stability of hysteresis loops. In addition, the common issues affecting all friction connections, namely the characteristics of friction shims and the role of bolt preload, are discussed. Based on the above considerations, guidelines can be outlined that can be used to help to choose the most appropriate solutions for BCCs for MRFs.

Frequency-response curves for rate-independent hysteretic mechanical responses of complex shape

We illustrate the performances of a brand new hysteretic model, recently proposed and denominated VRM+D, to characterize the nonlinear response of mechanical systems endowed with quite complex hysteretic behaviors. To this end, we combine the VRM+D with a continuation procedure based on Poincaré maps developed by Lacarbonara et al. in 1999. In this way, the steady-state response, as well as stability and bifurcation, of a large class of mechanical systems can be analyzed. In particular, we show the effectiveness of the VRM+D, in conjunction with the Poincaré map-based continuation procedure, in accurately predicting periodic solutions of the above-mentioned systems independently of the form of the hysteresis loop shapes. Furthermore, we draw some general considerations on the potential applications of the proposed approach in different fields of engineering to get an improved understanding of the dynamics of hysteretic mechanical systems subjected to cyclic loading.

Electrically Controlled Anomalous Hall Effect and Orbital Magnetization in Topological Magnet MnBi_{2}Te_{4}.

We propose an intrinsic mechanism to understand the even-odd effect, namely, opposite signs of anomalous Hall resistance and different shapes of hysteresis loops for even and odd septuple layers (SLs), of MBE-grown MnBi_{2}Te_{4} thin films with electron doping. The nonzero hysteresis loops in the anomalous Hall effect and magnetic circular dichroism for even-SLs MnBi_{2}Te_{4} films originate from two different antiferromagnetic (AFM) configurations with different zeroth Landau level energies of surface states. The complex form of the anomalous Hall hysteresis loop can be understood from two magnetic transitions, a transition between two AFM states followed by a second transition to the ferromagnetic state. Our model also clarifies the relationship and distinction between axion parameter and magnetoelectric coefficient, and shows an even-odd oscillation behavior of magnetoelectric coefficients in MnBi_{2}Te_{4} films.

Defining ferroelectric characteristics with reversible piezoresponse: PUND switching spectroscopy PFM characterization

Detecting ferroelectricity at micro- and nanoscales is crucial for advanced nanomaterials and materials with complicated topography. Switching spectroscopy piezoresponse force microscopy (SSPFM), which involves measuring piezoelectric hysteresis loops via a scanning probe microscopy tip, is a widely accepted approach to characterize polarization reversal at the local scale and confirm ferroelectricity. However, the local hysteresis loops acquired through this method often exhibit unpredictable shapes, a phenomenon often attributed to the influence of parasitic factors such as electrostatic forces and current flow. Our research has uncovered that the deviation in hysteresis loop shapes can be caused by spontaneous backswitching occurring after polarization reversal. Moreover, we’ve determined that the extent of this effect can be exacerbated when employing inappropriate SSPFM waveform parameters, including duration, frequency, and AC voltage amplitude. Notably, the conventional ‘pulse-mode’ SSPFM method has been found to intensify spontaneous backswitching. In response to these challenges, we have redesigned SSPFM approach by introducing the positive up-negative down (PUND) method within the ‘step-mode’ SSPFM. This modification allows for effective probing of local piezoelectric hysteresis loops in ferroelectrics with reversible piezoresponse while removing undesirable electrostatic contribution. This advancement extends the applicability of the technique to a diverse range of ferroelectrics, including semiconductor ferroelectrics and relaxors, promising a more reliable and accurate characterization of their properties.

Cyclic Loading Test Conducted on the Bottom Joints of a Hybrid Precast Utility Tunnel Composed of Double-Skin Sidewalls and a Precast Bottom Slab

Four full-scale specimens were constructed, including two hybrid precast specimens with a haunch (height: 150 mm, PUT-H) and without a haunch (PUT). Additionally, two cast-in-place (CIP) comparative specimens (referred to as RUT-H and RUT) were included, all of which underwent reversed cyclic loading. The results showed that the four specimens suffered flexural damage at the ends of the sidewall and displayed similar hysteresis loops shapes. The bearing capacity of the PUT specimen was 2.7% higher than that of the RUT, while the bearing capacity of the PUT-H specimen was 8.5% lower than that of the RUT-H. Additionally, the displacement ductility values of the precast specimens PUT and PUT-H were 2.98 and 2.46, respectively, which are 11.3% and 3.53% lower than those of the corresponding CIP specimens. The haunch increases the local stiffness of the component, exerting a notable influence on the bearing capacity and displacement ductility of the specimens, increasing the bearing capacity by 20% and decreasing the ductility by 21%. Moreover, an assessment conducted using the criteria outlined in ACI 374.1-05 indicated that the four specimens exhibit excellent seismic performance.

SEISMIC MITIGATION EFFECT FOR LARGE-SPACE UNDERGROUND STRUCTURES CONSIDERING SPATIALLY VARYING SOIL PROPERTIES

The seismic response of the large-space underground structure (LSUS) is significantly influenced by the physical properties of the surrounding soil media, while the soil owns a strong spatial variability. This study proposes a seismic response analysis process of the soil-LSUS interaction system is proposed, which can consider the characteristic of the spatially distributed soil properties. The proposed process begins with establishing the spatially random field model of the soil properties using the improved latent space method. Then, the model is calibrated based on the real data and Bayesian approach, and the realization of the random field is accomplished. Further, the soil-LSUS interaction finite element (FE) model is established, which incorporating the soil physical properties generated from the random field. Finally, the nonlinear time-history analysis of the soil-LSUS interaction FE model is conducted. As an illustration of the proposed process, a typical LSUS located in Guangzhou is selected as an example, and the seismic mitigation measure which the lead-filled steel tube damper (LFSTD) is installed between the intermediate column and the top beam is adopted for the LSUS. The influence of the spatial variability of soil properties on the seismic mitigation effect of the LSUS is investigated. Results indicate that the spatial variability of the soil properties can cause a minor influence on the force and deformation of the intermediate column and the energy dissipation ratio between the LFSTD and structure, while it can bring a significant influence on the maximum deformation and force and the shape of the hysteresis loop of the LFSTD.

A 2-DOF drag-free control ground simulation system based on Stewart platform

Space-based gravitational wave detection missions use multiple satellites to form a very large scale Michelson laser interferometer in space. This requires extremely high precision displacement measurements at the picometer level between test masses even millions of kilometers apart. Drag-free control is a key technology to ensure the ultra-static and ultra-stable space experiment platform for space-based gravitational wave detection. This paper proposes an innovative ground simulation scheme for drag-free control principle based on the Stewart platform. The kinematics and dynamics modeling of the Stewart platform used in the experiment is presented. A drag-free ground simulation experimental equipment is designed and built. A two-degree-of-freedom (2-DOF) drag-free controller is designed based on the H∞ loop shaping algorithm which outperforms a PID controller in Simulink simulation. A semi-physical simulation experiment is conducted to verify the controller designed using rapid control prototyping technology. The experimental results show that the control performance reaches the limit accuracy of the hardware device, thus verifying the effectiveness of the drag-free control algorithm.

Interaction Between Grid-Forming Converters With AC Grids and Damping Improvement Based on Loop Shaping

Grid-forming converters (GFC) are a promising technology for improving the grid inertia and frequency stability via voltage source converters (VSC). However, GFCs could make the ac-side oscillations more complicated since it mimics the dynamics of synchronous generators (SG), and the ac-side oscillations could spread to the dc systems. This paper investigates the mechanism of the interactions between GFCs and ac grids, and proposes an enhanced GFC to improve the damping performance on oscillations. By separating the system model into GFC-related transfer functions (TF) and the ac grid-related TFs, the interaction and stability margin can be investigated by the phase difference of these TFs at the cross-gain frequency (CGF). A lead compensator is designed to reshape the phase characteristic of GFC-related TF for enhancing the damping performance of the GFC. The effectiveness of the enhanced GFC is tested according to the simulations on DIgSILENT/PowerFactory.

Enhancing heating efficiency of magnetic hyperthermia using pulsed magnetic fields

We investigated the magnetization response and heat generation of magnetic particles exposed to high-speed pulsed magnetic fields (PMF) during magnetic hyperthermia cancer treatment. The magnetization measurements exhibited an asymmetric change in the shape of the hysteresis loop, attributable to the rapid and substantial changes in the short-duration PMF (75 mT/μs). We propose a novel parameter to evaluate heat efficiency. The parameter considered disparities in waveforms and served as a valuable metric for evaluating the effectiveness of heat production. Our findings affirmed a substantial enhancement in heat efficiency with the application of PMF. Furthermore, the heat generation stemming from the magnetic energy dissipation within the PMF exhibited direct proportionality to the square of the field amplitude. The heat efficiency is fourfold higher than that generated by conventional waveform.

A frequency domain-based loop shaping procedure for the parameter estimation of the fractional-order tilt integral derivative controller

<p>This paper demonstrates a frequency domain-based loop shaping method for the parameter estimation of a fractional order tilt integral derivative (FOTID) controller for the interval integer and fractional order time-delay systems. Along with the five nonlinear constraints usually considered for the design of the fractional order proportional integral derivative (FOPID) controller, a more flat phase concept signifying an enhanced robustness of the system towards gain variations is adopted as the sixth constraint for the tuning of a six variable tunable FOTID controller. The optimization toolbox fmincon in MATLAB is utilized for the solution process of the above constraint minimization problem. A certain class of fractional order plus time delay process is considered for the implementation and validation of the above procedure. The robustness of the FOTID controller optimized by the proposed method is tested against variations of the system parameters. By considering different numerical examples, the technical superiority of the FOTID controller over the FOPID controller is demonstrated through suitable comparisons in this current work.</p>

Effect of Ca2+ doping and annealing temperature on the structure, morphology and magnetic behavior of CaxCo1-xFe2O4/SiO2 nanocomposites

Co-doped ferrites are promising functional materials for many practical applications and their physical properties can be tailored by changing their composition. This study assesses the structure, morphology and magnetic properties of CaxCo1-xFe2O4/SiO2 (x = 0.0–0.5) nanocomposites (NCs) obtained by sol–gel method and annealed at different temperatures (400, 800 and 1200 °C). The effect of Ca2+ doping on the properties of nano-structured Ca-Co ferrite embedded in the SiO2 matrix was investigated by thermogravimetry and differential thermal analysis, X-ray diffraction (XRD), Fourier-transform infrared spectroscopy, Brunauer-Emmett-Teller surface area, inductively coupled plasma optical emission spectrometry, atomic force microscopy (AFM) and magnetic measurements. The thermal analysis showed the formation of metal succinates up to 200 °C and of ferrite above 280 °C. The presence of poorly crystalline ferrite accompanied by silicates at low annealing temperatures and of highly crystalline ferrite accompanied by SiO2 and Ca silicates at high annealing temperatures was identified by XRD. The increased Ca2+ doping led to a decrease in the structural parameters estimated by XRD and the surface area. The AFM images revealed that the NCs have a crystalline core covered by a layer of amorphous SiO2. The hysteresis loop shape indicated the superparamagnetic-like and ferromagnetic behavior of the obtained NCs. The magnetic properties improved with the increase in annealing temperature and depended on the particle size and dopant content. The NCs with low Ca2+ content annealed at 800 °C still show appreciable hysteresis, but doping with high Ca2+ contents drastically affects the magnetic properties.