1. Magnetic and Electrical Properties of Spinel Copper Ferrite Thin Films

    Kwang Joo Kim , Jongho Park and Jae Yun Park

    Journal of Magnetics, 31 Mar 2018, Vol.23 , No.1, pp.1-4

    Number of citation : 4

    Magnetic and Electrical Properties of Spinel Copper Ferrite Thin Films

    Copper ferrite (CuxFe3-xO4) thin films synthesized on α-Al2O3(0001) substrates exhibited the spinel structure for Cu compositions up to x = 1.0. The substituent Cu ions exhibited charge valence of +2, occupying both the tetrahedral and the octahedral sites of the spinel lattice. Magnetic hysteresis measurements on the CuxFe3-xO4 films revealed gradual loss of saturation magnetization (Ms) with increasing x: Ms is reduced to ~50% that of Fe3O4 for x = 1.0. The electrical resistivity (ρ) of the CuxFe3-xO4 films increased with x: ρ for x = 1.0 is larger by a factor of 30 than that of Fe3O4. The evolution of the magnetic and electrical properties of CuxFe3-xO4 can be explained in terms of the competition between the tetrahedral and octahedral Cu2+ density for ferrimagnetic moment and polaronic conduction.

  2. Influence of Vanadium Substitution on Phase Structure, Magnetic and Dielectric Properties of BiFeO3 Ceramics

    Qiang Li , Shengxiang Bao , Tao Hong , Libo Ai , Yingli Liu , Yulan Jing and Jie Li

    Journal of Magnetics, 31 Mar 2018, Vol.23 , No.1, pp.5-10

    Number of citation : 3

    Influence of Vanadium Substitution on Phase Structure, Magnetic and Dielectric Properties of BiFeO3 Ceramics

    BiFe1-xVxO3 (x = 0.00, 0.03, 0.05, 0.07, 0.09) ceramics were prepared by solid-sate reaction method. The effect of V5+ substitution on phase structure, morphology, magnetic and dielectric properties had been investigated. The Rietveld refinement of the X-Ray diffraction data from the BiFe1-xVxO3 (BFVO) ceramics showed samples with rhombohedral structure (R3c) for x = 0.00-0.07. When x = 0.09, partial phase structural be translated to orthorhombic phase (Pnma). Morphology showed two kinds of crystal and proved the phase to be transition. Magnetic measurements exhibited weak ferromagnetic behavior of sample. BiFe0.93V0.07O3 ceramic exhibited the highest value of saturation magnetization. Due to V5+ substitution, maybe BFVO attributed weak ferromagnetism to structure distortion and phase transition. Dielectric constant kept a stable value in a wide range frequency of 1 MHz to 1 GHz. With V5+ ions increasing, dielectric constant increased significantly, while dielectric loss kept a low value. These results indicated that BFVO may be promising for application in magneto-electric devices.

  3. Validation of Wireless Power Transfer by using 3D Representation of Magnetically Coupled Resonators Considering Peak Efficiency

    Nur Bekiroglu , Ali Agcal and Selin Ozcira

    Journal of Magnetics, 31 Mar 2018, Vol.23 , No.1, pp.11-17

    Number of citation : 2

    Validation of Wireless Power Transfer by using 3D Representation of Magnetically Coupled Resonators Considering Peak Efficiency

    This paper focuses on wireless power transfer system based on magnetic resonance coupling which involves creating a resonance and transferring the power without radiating electromagnetic wave outwith the critical distance. Modelling with Ansys® Maxwell 3D software provides the means to observe the main field quantities with its post-processing capability. Therefore mathematical expressions of optimal coupling coefficients are analyzed by considering mutual coupling model which is presented along with a derivation of key system identifiers such as transmission distance, characteristic impedance and resonance frequency. The effectiveness of the system is analyzed by exciting the resonators with sinusoidal voltage source. Ansys® Maxwell 3D software is utilized to solve equivalent circuit and also to calculate mutual inductance and characteristic impedance according to air gap variations. Resonance frequency is a key parameter in system design whose value can be changed according to distance between resonators. The peak efficiency is analyzed depending on different air gap values for various characteristic impedances at optimum resonance frequency. In this study, modelling resonators in 3D has been constituted correspondingly. The approach demonstrated in this paper allows fixed load receiver to be moved to different orientation within the range of critical coupling distance and approximately efficiency of 70 %.

  4. Induced Magnetic Properties of BN Nanotubes by the Adsorption of First-row Adatoms: An ab initio Study

    Fayyaz Hussain , Muhammad Imran , Nimra Fatima , Anwar Manzoor Rana , R. M. Arif Khalil , Arshad Javid and Muhammad Ismail

    Journal of Magnetics, 31 Mar 2018, Vol.23 , No.1, pp.18-26

    Number of citation : 0

    Induced Magnetic Properties of BN Nanotubes by the Adsorption of First-row Adatoms: An ab initio Study

    This work is performed to study the effect of adsorption of various first row adatoms (such as Be, C, F, Li and O) on (8, 0) zigzag boron nitride nanotubes (BNNTs) on their structural, electronic and magnetic properties. These calculations are based on density functional theory using pseudopotentials technique. For this purpose, five different sites namely axial, hexagonal, zigzag, on top of N and/or B (which are the most preferred available sites for adatoms on (8, 0) BNNTs) were utilized. The energetically stable sites for each of the first-row adatoms are found to be different because of their different electronic configurations caused by the charge transfer/rearrangements between s-p or p-p orbitals. The binding energies of all adatoms on (8, 0) BNNTs have been calculated through structural optimization process after adsorbing these five adatoms at the above said sites on the BNNTs and are found to be in the energy range from −2.04 to 2.96 eV. It is further elaborated that F, Be and C adatoms on (8, 0) BNNTs show strong induced magnetization at specific localized sites depending upon the nature of adatom, whereas weak magnetization is noticed for Li and O adatoms on the BNNTs. Such localized induced magnetization could be associated with the hybridization of s-p or p-p orbitals of adatoms and B and/or N atoms.

  5. An Improved Conformal Mapping Method for Static Angular Eccentricity Analysis of Axial Flux Permanent Magnet Machines

    Baocheng Guo , Yunkai Huang and Fei Peng

    Journal of Magnetics, 31 Mar 2018, Vol.23 , No.1, pp.27-34

    Number of citation : 4

    An Improved Conformal Mapping Method for Static Angular Eccentricity Analysis of Axial Flux Permanent Magnet Machines

    This paper presents an improved and simple analytical model to study the static angular eccentricity of single stator single rotor axial-flux permanent-magnet (AFPM) machine. The magnetic flux densities in the air gap under normal and static angular eccentricity are calculated by using a combination of Maxwell’s equations and Schwarz-Christoffel (SC) transformation. The original contribution of the model is that angular eccentricity is obtained without extra transformations. Thus the proposed approach is simpler than existing methods. The calculated back electromotive forces (EMFs) and cogging torque by the proposed method are compared with those obtained from the finite element (FE) model, the results show acceptable accuracy of the proposed method. In this way, the effectiveness of the proposed method is verified.

  6. Interaction Forces and Torques between Two Perpendicular Magnetic Tubes

    Jian-Gang Li

    Journal of Magnetics, 31 Mar 2018, Vol.23 , No.1, pp.35-40

    Number of citation : 2

    Interaction Forces and Torques between Two Perpendicular Magnetic Tubes

    Cylinders, tubes, cuboids, etc. are basic magnet shapes used in permanent magnet machines. The relative positions between magnets include parallel, perpendicular, or inclined. The force and torque between two cuboid magnets of almost any status and two cylindrical magnets with paralleled axes have been solved. Using the theory of magnetic charges and magnetic Coulomb’s law, this study derives a mathematical model for interaction forces and torques between two perpendicular magnetic tubes in three dimensions. Using this model, the effects of tube relative positions on the interaction forces and torques is analyzed by numerical calculation. The model can also express interaction forces and torques between a magnetic tube and magnetic cylinder or between two magnetic cylinders when the inner radius of one magnetic tube is zero or the radii of both tubes are zero. This study provides the theoretical background for magnetic tube and cylinder applications, such as magnetic drive or control across space in mechanical, medical treatment, chemical industry, food production, aerospace, etc.

  7. Prediction of the Upper and Lower Bounds of Magnetic Vector Potentials in a Linear Magnetostatic Field with Uncertain-but-Bounded Parameters

    Pengbo Wang and Jingxuan Wang

    Journal of Magnetics, 31 Mar 2018, Vol.23 , No.1, pp.41-49

    Number of citation : 1

    Prediction of the Upper and Lower Bounds of Magnetic Vector Potentials in a Linear Magnetostatic Field with Uncertain-but-Bounded Parameters

    Uncertainty is ubiquitous in practical engineering and scientific research. The uncertainties in parameters can be treated as interval numbers. The prediction of upper and lower bounds of the response of a system including uncertain parameters is of immense significance in uncertainty analysis. This paper aims to evaluate the upper and lower bounds of magnetic vector potentials in a linear magnetostatic field efficiently with uncertain-but-bounded parameters. The uncertain-but-bounded parameters are represented by interval notations. By performing Taylor series expansion on the magnetic vector potentials obtained from the equilibrium governing equation and by using the properties of interval mathematics, we can calculate the upper and lower bounds of the magnetic vector potentials of a linear magnetostatic field. In order to evaluate the accuracy and efficiency of the proposed method, two numerical examples are used. The results illustrate that the precision of the proposed method is acceptable for engineering applications, and the computation time of the proposed method is significantly less than that of the Monte Carlo simulation, which is the most widely used method related to uncertainties. The Monte Carlo simulation requires a large number of samplings, and this leads to significant runtime consumption.

  8. On-Chip Spiral Inductors and On-Chip Spiral Transistors for Accurate Numerical Modeling

    M. Dhamodaran , R. Praveen Kumar and S. Jegadeesan

    Journal of Magnetics, 31 Mar 2018, Vol.23 , No.1, pp.50-54

    Number of citation : 2

    On-Chip Spiral Inductors and On-Chip Spiral Transistors for Accurate Numerical Modeling

    This paper presents a new model for designing on-chip spiral inductor and on-chip spiral transistors. For this, the coupling between on-chip inductors and transistors has been implemented. The electromagnetic coupling between the inductors and the transistors and the mutual inductance are modeled by presenting the magnetic vector potential to study the coupling effect. It changes the surface integral of the magnetic field into the loop integral of the magnetic vector potential to calculate the coupling. In this method, the partial mutual inductance idea to compute the mutual inductance between two conductor sections instead of conductor loops can be developed. The inductance classification is applied to an on-chip environment to characterize interconnects and integrated inductors. The investigative model is reconsidered to incorporate the semiconductor substrate losses and the skin effect. The numerical solutions of the investigative model are also presented. To simulate the proposed model ADS Momentum software is used.

  9. Rotor Open-Rib Design for Power Density Improvement in Synchronous Reluctance Motor

    Jae-Kwang Lee , Dong-Hoon Jung , Jongsuk Lim , Ye Jun Oh , Ki-Doek Lee and Ju Lee

    Journal of Magnetics, 31 Mar 2018, Vol.23 , No.1, pp.55-60

    Number of citation : 1

    Rotor Open-Rib Design for Power Density Improvement in Synchronous Reluctance Motor

    MEPS are an efficiency regulation policy for induction motors, which are being implemented primarily in developed countries. Induction motors are the most commonly used type of motor in industry, owing to their simple structure and pricing advantages. Research on the efficiency improvement of induction motors has become saturated; therefore, studies to replace induction motors with SynRM have been actively conducted. SynRM is an electric motor driven by the inductance difference between the d-axis and the q-axis of the rotor, and has advantages of being composed of only an iron core and having a simple structure. Herein, we analyze the influence of the rotor shape on the inductance change. Further, the design for improving the output was implemented, and the solution to solve the stiffness problem that occurred as a result was studied. Finally, we confirmed the validity of the data through production and experiments.

  10. Assessing Vascular Changes Associated with Healthy Aging using 7T Magnetic Resonance Angiography

    So-Ra Jang , Chan-A Park , Kyung-Jin Lee , Yeong-Bae Lee , Hang-Keun Kim and Chang-Ki Kang

    Journal of Magnetics, 31 Mar 2018, Vol.23 , No.1, pp.61-67

    Number of citation : 1

    Assessing Vascular Changes Associated with Healthy Aging using 7T Magnetic Resonance Angiography

    Aging is known to produce changes in the cerebral vasculature and circulation. We aimed to quantitatively assess age-related changes in the morphology of small perforating vessels, lenticulostriate arteries (LSAs). LSA images were acquired using ultra-high field 7-Tesla magnetic resonance imaging (7T MRI) from 24 young healthy volunteers (young group: YG) and 25 old healthy volunteers (old group: OG). Vessel-related factors such as curvature and tortuosity were analyzed using two-dimensional images. Our quantitative results demonstrated a fewer in their branches and a significantly more pronounced curvature in the OG compared to the YG. These findings were further confirmed qualitatively using image analysis. Our study findings show that MR angiography utilizing ultra-high field MRI can provide high-resolution images that can identify morphological characteristics of small perforating vessels. Based on these features, it is possible to document ageinduced changes in cerebral small vessels.

  11. Experimental Assessment of Unbalanced Magnetic Force according to Rotor Eccentricity in Permanent Magnet Machine

    Jeong-Jin Yoo , Seung-Han Lee , Kyung-Hun Shin and Han-Wook Cho

    Journal of Magnetics, 31 Mar 2018, Vol.23 , No.1, pp.68-73

    Number of citation : 1

    Experimental Assessment of Unbalanced Magnetic Force according to Rotor Eccentricity in Permanent Magnet Machine

    The manufacturing errors of machine tools are usually due to the imperfect of bearings, stiffness of spindle, assembly errors, and so on. In addition, the rotor eccentricity of the permanent magnet (PM) machine affects to the constant torque and speed characteristic of mechanical loads. The errors due to rotor eccentricity is caused by manufacturing process and rotor eccentricity generate unbalanced magnetic force (UMF). The sources of UMF are generated by the interaction between the rotor magnets and the stator core. Firstly, we suggested that the characteristic analysis results due to rotor eccentricity are calculated by using finite-element (FE) analysis. Moreover, we proposed experimental set to measure the UMF on the PM machines. Finally, we verified the validity of the proposed UMF measurement system by comparison with the measured results and simulation results due to the rotor eccentricity in the PM machine.

  12. Experimental and Analytical Study of Surface-Mounted Type Variable Flux Permanent Magnet Motor Considering Controllable Magnet Properties

    Kyu-Seok Lee , Sung-Ho Lee , Jung-Hyung Park and Jang-Young Choi

    Journal of Magnetics, 31 Mar 2018, Vol.23 , No.1, pp.74-78

    Number of citation : 0

    Experimental and Analytical Study of Surface-Mounted Type Variable Flux Permanent Magnet Motor Considering Controllable Magnet Properties

    A variable flux permanent magnet motor (VFPMM) alters its characteristics at low and high-speeds by changing the magnetic flux of a variable magnet. In this paper, a motor capable of varying its magnetic flux based on the slot/pole structure is proposed. In addition, the variation characteristics of flux density and field intensity of a variable magnet in the VFPMM under magnetization/demagnetization conditions are analyzed using the finite element method (FEM) and experimentation. A prototype was tested for the magnetization/demagnetization characteristics, and it was confirmed that the value of the measured back EMF was nearly identical to the corresponding values obtained by an FEM analysis. Finally, the characteristics of the VFPMM for each magnetization/demagnetization state were evaluated at both low- and high-speed ranges. To verify the effect of variable flux, experimental results are also presented.

  13. Tailoring the Impact Toughness of Sintered NdFeB Magnets via Surface Coating

    X. G. Cui , J. X. Pan , C. Y. Cui , P. Mei , X. H. Wang , C. Fang , T. Y. Ma , C. Wang and X. C. Peng

    Journal of Magnetics, 31 Mar 2018, Vol.23 , No.1, pp.79-85

    Number of citation : 1

    Tailoring the Impact Toughness of Sintered NdFeB Magnets via Surface Coating

    Metallic coating by electroplating is commonly attractive for improving the corrosion resistance of sintered NdFeB magnets. However, its tailoring of mechanical characteristics for sintered NdFeB magnets has been seldom concerned. Herein, the impact toughnesses of sintered NdFeB magnets with various metallic coatings (Ni or Ni/Sn) were comparatively investigated. The results indicate that the impact toughnesses of sintered NdFeB magnets are both improved by Ni coating and Ni/Sn bilayer coating. And Ni/Sn bilayer coating exhibits more enhancement of the impact toughness, increased by 41.6% compared with the original magnet. Moreover, the microstructural observations of the metallic coatings and the fracture were conducted, and the enhanced mechanism of impact toughness for the magnet is analyzed. These findings may provide a reference for toughening the brittle materials.

  14. Selection of Contactless-Power-Supply Housing Material Considering Eddy Current Loss, Thermal Load, and Structure Safety

    Phuong Thi Luu , Jiyoung Lee , Jeongwook Lee , Jongmoo Kim and Byungchul Woo

    Journal of Magnetics, 31 Mar 2018, Vol.23 , No.1, pp.86-92

    Number of citation : 1

    Selection of Contactless-Power-Supply Housing Material Considering Eddy Current Loss, Thermal Load, and Structure Safety

    This paper deals with the selection of the housing material of the contactless power supplier (CPS) used for the field winding power supply in wound field synchronous machine (WFSM). The housing of the CPS encloses the rotary transformer and the converter of secondary side. The housing prevents the damage of ferrite core in the rotary transformer and the secondary converter due to centrifugal force in the highest speed, 10,000 rpm. Therefore, the housing should have been designed considering not only strengthen, but also lighten. Furthermore, efficiency is also one of important characteristics in power transfer to improve the whole system efficiency. Taking account of aforementioned points, the stainless steel (SUS) and aluminum (Al), which are commonly used as housing materials, were under reviewed as CPS housing. After comparing the characteristic of CPSs according to housing material in term of eddy current loss, thermal characteristic, and mechanical stability, the appropriate housing material is suggested. After that, experimental results deriving from tests are presented to confirm the analysis results.

  15. Simulation and Analysis of Magnetic Circuit of Water-cooling Magnetorheological Fluid Transmission Device

    Jinjie Ji , Zuzhi Tian , Xiangfan Wu and Jin Dou

    Journal of Magnetics, 31 Mar 2018, Vol.23 , No.1, pp.93-98

    Number of citation : 0

    Simulation and Analysis of Magnetic Circuit of Water-cooling Magnetorheological Fluid Transmission Device

    Aiming to solve the problem of magnetorheological transmission heat dissipation, this study designs the magnetic circuit of a water-cooling magnetorheological transmission device based on fundamental electromagnetics theory. Finite element method is used to simulate the magnetic field of the measurement device. Results show that the working magnetic induction can reach 0.56 T when the current is 2.0 A, which can satisfy design requirements. The intensity of magnetic induction in the work space increases with the increase of excitation current and permeability of magnetically conductive material, whereas intensity decreases with the increase of work space size. The thickness and cross-sectional dimension of the guidepost group at the heat-dissipating unit have no significant effect on the intensity distribution of magnetic induction of the entire device.

  16. Research on Preparation and Characteristics of a Novel Transmission Magnetorheological Fluid

    Fei Chen , Tian Zuzhi , Wu Xiangfan , Wang Shuyou and Li Hao

    Journal of Magnetics, 31 Mar 2018, Vol.23 , No.1, pp.99-105

    Number of citation : 4

    Research on Preparation and Characteristics of a Novel Transmission Magnetorheological Fluid

    On the basis of orthogonal experiment, a novel transmission magnetorheological fluid with synthetic ester chain oil as carrier fluid is prepared. The effect of single additive content on the apparent viscosity and settling stability of magnetorheological fluid is analyzed, and the characteristic evaluations are also carried out. The results indicate that the magnetorheological fluid containing 60 wt% carbonyl iron powder has an apparent viscosity of 2.15 Pa·s and can attain the shear yield stress of 36 kPa when the magnetic field strength is 0.5T. Furthermore, the settlement rate of the MRF is less than 3% after two weeks. In comparison with the silicone oil and mineral oil, the synthetic ester chain oil-based magnetorheological fluid has the lowest thermal expansion rate.

  17. Structural and Magnetic Properties of Aluminium-Substituted Cobalt-Ferrite Nanoparticles Synthesised by the Co-precipitation Route

    Budi Purnama and Anisa Khoiriah

    Journal of Magnetics, 31 Mar 2018, Vol.23 , No.1, pp.106-111

    Number of citation : 10

    Structural and Magnetic Properties of Aluminium-Substituted Cobalt-Ferrite Nanoparticles Synthesised by the Co-precipitation Route

    The crystal structure and magnetic properties of aluminium-substituted cobalt-ferrite nanoparticles synthesised by the co-precipitation are reported in this study. The single phase nanoparticles are obtained. Magnetic property Changes in these properties are clarified mainly by changes in parameters such as the crystalline constant, crystallite size and crystalline density. An increase of saturated magnetisation with annealing temperature is also observed. Results for the change in saturated magnetization at several elevated temperatures indicate that the available non-magnetic aluminium ions support redistribution of cation-trivalent Fe3+ during the annealing process at octahedral sites.

  18. Synergy of Build up Effect from Application of Magnetic Bolus in Radiotherapy Area

    Jeong-Ho Kim , Seok-Hwan Bae , Se-Jong Yoo and Myeong-Cheol Park

    Journal of Magnetics, 31 Mar 2018, Vol.23 , No.1, pp.112-116

    Number of citation : 0

    Synergy of Build up Effect from Application of Magnetic Bolus in Radiotherapy Area

    In radiotherapy, bolus is used for the superficial tumor, but there in limitation in the dose distribution control. Therefore, the changes in the dose distribution according to the application of the magnetic bolus are to be evaluated. In the case of not applying the bolus, and in applications of the magnetic bolus and the non-magnetic bolus, OSLD (Optically Stimulated Luminescence Dosimeter) was used to measure the dosage for each depth for comparison. In the case of not applying the bolus and applying the non-magnetic bolus, the difference according to the depth correction was a maximum of 2.17%, and the difference according to applying the nonmagnetic bolus and the magnetic bolus was a maximum of 4.39 %. In addition, the changes in the dose value according to the application of magnetic bolus showed average increase of 2.39 from the surface to 7 mm, and there was average decrease of 0.43% in the depth of 8 cm-15 cm. Therefore, in the radiotherapy, it is considered that the increase in therapeutic effect and normal organ protective effect can be expected according to the application of the magnetic bolus.

  19. Preliminary Validation of Robotic Control of Magnetic Particles for Targeted Hyperthermia

    Haye Min Ko and Sung Hoon Kim

    Journal of Magnetics, 31 Mar 2018, Vol.23 , No.1, pp.117-124

    Number of citation : 4

    Preliminary Validation of Robotic Control of Magnetic Particles for Targeted Hyperthermia

    In this paper, we present a new method for targeted hyperthermia using an electromagnetic navigation system. Typically, Fe3O4 magnetic nanoparticles (MNPs) are utilized by injection methods. However, the study demonstrated that the proposed method provides active locomotion for targeting a destination within a three-axis Helmholtz coil, and generates heat through a high-frequency heating coil. To realize these two functions, the entire system combined the electromagnetic navigation system and a high-frequency heating system. The Fe3O4 MNPs were prepared via chemical synthesis. Using vibrating sample magnetometer (VSM) and X-ray diffraction (XRD), we observed the magnetic properties and structure of the crystals. Through various experimental tests, we investigated the controllability, mobility, and steering ability of the MNPs. In particular, we confirmed the heating characteristics of the fabricated MNPs according to the changes in the magnetic field strength at 205 kHz. On average, the particle cluster generated a temperature of 73.12 ℃ at 58 kA/m.

  20. Enhancement of Hydrodynamic Properties of Blood Pump Using Multiple Pumps Based on Synchronous Magnetic Radial Coupling

    Chang-Ho Yu , Seong Woo Kim and Sung Hoon Kim

    Journal of Magnetics, 31 Mar 2018, Vol.23 , No.1, pp.125-131

    Number of citation : 0

    Enhancement of Hydrodynamic Properties of Blood Pump Using Multiple Pumps Based on Synchronous Magnetic Radial Coupling

    Multiple pump systems are generally able to enhance pressure and flow rates through parallel and serial connections. However, the use of multiple pumps has various drawbacks, including their high power consumption, complex configuration, and large volumes. These problems make these systems unsuitable as blood pumps. To avoid these issues, we propose a new method of multiple-pump system for use with VADs (Ventricular Assist Devices) and BiVADs (Bi Ventricular Assist Devices). In particular, we focus on enhanced hydrodynamic performance through the use of a magnetic pump. The system employs synchronous magnetic radial coupling, thereby controlling up to four pumps through a single pump driver. Through serial and parallel configurations, the multiple pumps are able to extend the operating range of pressure and flow rate for use in blood pumps. The enhanced hydrodynamic performance was verified through various experimental analyses.