Magnetic Intensity Research Articles

A modified Pinto-Espinoza magnetization model for studying on motion characteristics of ferromagnetic particles

In this study, a modified Pinto-Espinoza (P-E) magnetization model that has a wider range of applications is proposed based on the conventional magnetization model. This model uses the relative reference frame conversion method to determine the magnetization force experienced by ferromagnetic particles when magnetic fields are applied in any direction. The accuracy of the improved P-E magnetization model is confirmed on the basis of this, and a coupled simulation environment between the discrete element method (DEM) and the finite volume method (FVM) is constructed. Simulated is the motion of ferromagnetic particles under various magnetic field directions and magnetic induction intensities. The particle distribution, particle velocity vector, and particle total energy change were all investigated. It is inferred that the chain formation direction of ferromagnetic particles in the magnetic field is consistent with the magnetic field direction, and they attract each other along the magnetic field direction and repel each other along the vertical magnetic field direction. Changing the intensity of the magnetic induction can effectively ease the particle delamination phenomenon. The faster the chain formation speed increases with increasing magnetic induction intensity, the shorter the time necessary to attain a stable condition.

Development and application of feature engineered geological layers for ranking magmatic, volcanogenic, and orogenic system components in Archean greenstone belts

Geologically representative feature engineering is a crucial component in geoscientific applications of machine learning. Many commonly applied feature engineering techniques used to produce input variables for machine learning apply geological knowledge to generic data science techniques, which can lead to ambiguity, geological oversimplification, and/or compounding subjective bias. Workflows that utilize minimally processed input variables attempt to overcome these issues, but often lead to convoluted and uninterpretable results. To address these challenges, new and enhanced feature engineering methods were developed by combining geological knowledge, understanding of data limitations, and a variety of data science techniques. These include non-Euclidean fluid pre-deformation path distance, rheological and chemical contrast, geologically constrained interpolation of characteristic host rock geochemistry, interpolation of mobile element gain/loss, assemblages, magnetic intensity, structural complexity, host rock physical properties. These methods were applied to compiled open-source and new field observations from Archean greenstone terranes in the Abitibi and western Wabigoon sub-provinces of the Superior Province near Timmins and Dryden, Ontario, respectively. Resulting feature maps represent conceptually significant components in magmatic, volcanogenic, and orogenic mineral systems. A comparison of ranked feature importance from random forests to conceptual mineral system models show that the feature maps adequately represent system components, with a few exceptions attributed to biased training data or limited constraint data. The study also highlights the shared importance of several highly ranked features for the three mineral systems, indicating that spatially related mineral systems exploit the same features when available. Comparing feature importance when classifying orogenic Au mineralization in Timmins and Dryden provides insights into the possible cause of contrasting endowment being related to fluid source. The study demonstrates that integrative studies leveraging multi-disciplinary data and methodology have the potential to advance geological understanding, maximize data utility, and generate robust exploration targets.

Magneto-thermo-elastic coupled free vibration and nonlinear frequency analytical solutions of FGM cylindrical shell

The magneto-thermo-elastic coupled free vibration of functionally graded materials (FGM) cylindrical shell is investigated. Based on the physical neutral surface theory and Kirchhoff-Love theory, the expressions of internal force and internal torque are obtained by considering the constitutive relationship that includes thermal stress. According to the electromagnetic elasticity theory, the model of Lorentz forces of the shell in magnetic field are derived. The expressions of potential energy, kinetic energy and its variational operators are given by introducing geometric nonlinearity, respectively. Based on Hamilton principle, the magneto-thermal-elastic coupled vibration equation of FGM cylindrical shell in multi-physical field is established. The displacement functions under simply supported boundary conditions are solved, which are combined with Galerkin method for derivation of nonlinear ordinary differential equations. The second-order approximate analytical solution of natural frequency is obtained by applying the multi-scale method. The characteristic curves of natural frequency with different parameters are drawn through numerical examples. The results show that reducing the volume fraction index and increasing the initial amplitude can lead to the increase of the natural frequency under transient conditions. With the increase of temperature and magnetic induction intensity, the natural frequency decreases. In addition, the natural frequency is also influenced by the shell size and volume fraction index.

High magnetic performance ultra-thin Fe-6.5Si ribbons fabricated by planner flow casting and annealing

Fe-6.5 wt.%Si steel is one of the most attractive soft magnetic materials for making iron cores with low noise and low power loss. The planner flow casting method was regarded as a promising method to obtain ultra-thin ribbons of Fe-6.5Si alloy. In this study, Fe-6.5Si ribbons with a thickness of 0.03 mm were prepared by planner flow casting. Samples were heat-treated at various temperatures. It is revealed that the grain size on the wheel surface and free surface gradually increases with increasing annealing temperature. The initial {100} fiber texture of the wheel and free surfaces is weakened after annealing, transforming to {001} 〈510〉 on the wheel surface and to {229} < 11 2 2 > on the free surface after annealing at 1150 °C for 1 h. The texture parameter and dislocation density are the key factors affecting the magnetic induction intensity, showing an inverse correlation with the texture parameter and dislocation density. Furthermore, the iron loss is mainly influenced by the grain size, with an optimal grain size of 10 μm. Considering the magnetic induction intensity and iron loss, the optimal annealing temperature is determined to be 1100 °C, resulting in a magnetic induction intensity of B8 = 1.26 T and B50 = 1.65 T, and iron loss values of P1/400 = 14.1 W/Kg and P0.2/5000 = 11.1 W/Kg.

Magnetization process of cubic Fe3O4 submicron particles: First-order reversal curves and neutron diffraction studies

We have studied magnetization process of 260 nm sized cubic Fe3O4 particles below and above the Verwey transition temperature Tv∼ 110 K, by measurements of magnetic first-order reversal curves (FORCs) and high-resolution power neutron diffraction. The FORC diagram exhibits two distinct FORC distribution peaks below Tv, which shift towards the origin, merge into a single peak on heating, whereas only a single FORC peak appears above Tv. Neutron diffraction measurements under magnetic fields revealed a minimum of the magnetic intensity at a magnetic field of ∼−300 Oe, being close to the reversal field where the FORC peak is located. These results were interpreted as due to a reorientation and reversal of a spin vortex core, which accompany a large magnetic irreversibility.

Optimized design of permanent magnet for disk permanent magnet governor

To research the magnetic field and mechanical characteristics of the permanent magnet governor, the static magnetic field of the sector permanent magnet is analyzed by the molecular current method in the permanent magnet governor. The magnetic flux distribution is acquired at any spatial position. Comparing the analytical value with the simulation value, the results show that they are basically consistent. Based on the analytical formula, the influence of the radial position, radial length, thickness, and pole number on the magnetic induction intensity of the permanent magnet governor is studied. Thus, it provides the theoretical reference for the structural optimized design. At the same time, a test bench was set up to measure the magnetic induction intensity. The calculation and experimental results show that the magnetic induction strength of the permanent magnet is increased by 27.5%, the axial component of the air gap flux density is increased by 14.3%, and the permanent magnet material is reduced by 7.84%.

Magnetically Modulated Differential Quartz Crystal Microbalances for Rapid, Ultrasensitive, and Direct Probing of Prostate-Specific Antigens Conjugated with Magnetic Beads.

The occurrence and development of diseases are closely related to overexpression of specific biomarkers in the serum of patients. Rapid and sensitive biomarker detection is beneficial for early diagnosis and treatment. However, the current laboratory processes and assays for biomarker detection are expensive and time-consuming, and their operation also requires a large number of professionals. We developed a magnetically modulated differential quartz crystal microbalance (MMD-QCM) method combined with magnetic bead (MB) labels for rapid and highly sensitive quantitative detection of prostate-specific antigen (PSA). Because MBs exhibit magnetized rotation motion under an applied AC magnetic field, a pair of QCMs are utilized to measure the difference between the magnetic motion intensities of the MBs and the MB-PSA immune complex to determine the PSA concentration. Experimental results demonstrate that the proposed method can be adopted to determine the PSA concentration in a wide range of 0.01-1000 ng/mL as well as exhibit a low detection limit of 0.065 ng/mL. In addition, the proposed scheme enables fast detection and low sample consumption. The single detection process takes less than 4 h and requires only 113 μL of sample solution. The proposed detection strategy is superior to the existing detection method and can be effectively used in early screening and prognostic diagnosis of cancer and other related diseases owing to its simplicity, low cost, and high speed.

Application of High-Resolution Aeromagnetic and Gamma-ray Spectrometry Surveys for Litho-Structural Mapping in Southwest China

Airborne geophysical surveys serve as an effective tool for litho-structural mapping, providing extensive and high-resolution underground information. They offer vital data support for the interpretation and analysis of lithologies and structures, complementing surface geological mapping. In the study area of the Nanpanjiang-Youjiang metallogenic belt in southeast China, we obtained high-resolution aeromagnetic and gamma-ray spectrometry data covering an area of approximately 27,000 km2, which facilitated the conduct of litho-structural mapping. The total magnetic intensity, reduction to the pole, and directional derivative maps generated from the aeromagnetic data, efficiently identified concealed rocks and faults. Additionally, the total count, potassium, thorium to potassium ratio, and ternary maps generated from the airborne gamma-ray spectrometry data demonstrated advantages in distinguishing carbonate rocks from clastic rocks. They also provided more comprehensive geological information, refining the structural strike and location interpreted by the aeromagnetic data. The litho-structural map produced in this study significantly contributes to our understanding of the structures in the Nanpanjiang area and offers valuable guidance for successful mineral exploration endeavors.

EVALUATION OF UPWARD CONTINUATION AND REDUCTION TOEVALUATION OF UPWARD CONTINUATION AND REDUCTION TO MAGNETIC EQUATOR ON AIRBORNE MAGNETIC DATA MAGNETIC EQUATOR ON AIRBORNE MAGNETIC DATA

This research work is aimed at interpreting the airborne magnetic data of the study area for mapping the basement geologic structures using magnetic image enhancement filters. It focus on performing filtering techniques to expose and identify the magnetic properties of the basement structures at various continuation distances. The procedure applied to Total Magnetic Intensity (TMI) data of the study area using Oasis MontanjTM software were Reduction to Magnetic Equator (RTME) to remove the inclination effect as well as positioning the peak of the anomalies over their sources so as to improve the orientation of the magnetic sources, separation of regional and residual magnetic anomalies. These was followed by application of upward continuation at 500 m, 1000 m, 2000 m and 3000 m height. The results of the RTME shows the amplitude of the magnetic anomalies ranging from -37.577 nT to 27.398 nT. High magnetic anomaly is dominated in the northwest, southeast through southern part of the study location. Furthermore the results of the Upward Continuation (UC) revealed a wider wavenumber anomalies as well as height above the near surface. Hence the results of this research has displayed an enhanced geological magnetic structures located in the study area and also shows an improved quality of magnetic anomalies as the continuation distances increases.

Iron ore to lodestone: With lightning assist

A lodestone is a piece of magnetite or titanomagnetite iron ore having an extremely intense remanent magnetization; it is nature's only permanent magnet. This magnetization intensity is larger than could be acquired in any iron ore by any known natural mechanism through exposure to just the Earth's magnetic field. This is revealed by the large ratio (REM) of the measured (NRM) - natural remanence, to the (SIRM) - saturation remanence.We describe new details of the mechanism by which part of an iron ore body becomes a lodestone: Exposure to lightning bolt related electric discharge's magnetic fields is required.While the lightning bolt related magnetic fields are necessary, they are not sufficient for creation of a lodestone. We show that the iron ore must be previously magnetically “hardened” into what we term a “latent lodestone iron ore” condition before the transformation to lodestone can be achieved.A magnetic hardness continuum (characterized with magnetic hysteresis loop parameters) for a range of magnetite and titanomagnetite iron ores demonstrates how the hardening is created by alteration; in magnetite through oxidation scenarios and in titanomagnetite by solid state exsolution and oxidation.Large REM (evidence of lightning), the *Polarity signature (which we identify with iron powder patterns) reflecting the large REM, and the location on the magnetic hardness continuum (latent lodestone state resulting in largest possible magnetization), provides important details to the lodestone story.

Fluctuation of Magnetic Field in Magnetic Nano-Particles Thermometer

In this study, some important factors have been identified for the fluctuation of the magnetic field over time, which provides a basis for improving the temperature measurement accuracy and long-term stability of the magnetic nanoparticles thermometer (MNPT). We improved the mathematical model between the relative error of the magnetic induction intensity and the temperature measurement error of MNPT. The simulation founded that when the relative error of the magnetic induction intensity is kept within the range of &lt;0.01%, the temperature measurement error is less than 0.1 K. Then, the multi-physics (magnetic field, temperature field, and thermal stress field) coupling relationship in the Helmholtz coil is established. During the coupling process, the temperature field of the Helmholtz coil affects the resistance of coil wire, and its thermal stress field is affected by the temperature field, which also changes the coil radius. After the temperature field and thermal stress field change, the magnetic field fluctuates immediately. Further simulation found that the problem of coil temperature rise becomes more serious as the size of the Helmholtz coil increases. The method of forced air cooling can make the fluctuation of the large Helmholtz coil magnetic field &lt; 0.01%, and improve the measurement accuracy of MNPT.

Effect of microstructure modification on magnetic and mechanical properties of high-grade non-oriented silicon steel during annealing treatment

The optimization of magnetic and mechanical properties by microstructure modification is tremendously challenging for high-grade non-oriented silicon steel. In the current study, the microstructure of cold-rolled high-grade non-oriented silicon steel was modified by recrystallization annealing to achieve high strength and good magnetic properties. The results indicate that recrystallization annealing significantly improved the magnetic properties, while negatively impacting its mechanical properties. At the early stage of annealing (<2 min), recrystallization nucleation occurred in the deformation matrix, leading to a significant decrease in dislocation density. This decrease in dislocation density resulted in a notable reduction in coercivity and hence enhancement in magnetic properties. However, the mechanical properties deteriorated due to the elimination of dislocations. With further increasing the annealing time (>2 min), the recrystallization grains grew within the fully recrystallized matrix. There was a slight decrease in both dislocation density and grain boundary density, leading to a slight decrease in iron loss and yield strength. The magnetic induction intensity of the fully recrystallized annealed sheets was primarily influenced by the recrystallization texture. Thus, the critical annealing time was 2 min to meet the demands of both magnetic and mechanical properties for the studied high-grade non-oriented silicon steel.

Magnetic Storm Effects on the Occurrence and Characteristics of Plasma Bubbles

AbstractThe Communications/Navigation Outages Forecast System satellite mission was designed to investigate the ionospheric conditions that lead to the formation of irregularities. Here, we have studied the effect of magnetic storms on the formation and evolution of plasma bubbles during the satellite's lifetime (2008–2015). During this period encompassing solar minimum and maximum conditions, many magnetic storms of varying intensity developed, producing a unique and rich data set of 248 storms (14 intense, 69 moderate, and 165 weak) that occurred during the same timeframe to examine the role of external magnetospheric drivers in the production and dynamics of equatorial plasma bubbles. We have used the Planar Langmuir Probe and Ion Velocity Meter instruments to elucidate the role of magnetic storm intensity on the bubble's depth, internal speed, width, occurrence, and lifetime. The pre‐reversal enhancement (PRE) tends to increase during the main phase and when BZ is southward. New bubbles occur during large excursions of the PRE value. The bubble lifetime extends and remains active during the main and part of the recovery phase. The plasma velocity within the bubbles increases and typically becomes over 100 m/s during significant PRE and BZ negative times. The depth of bubbles reaches values close to 100% during intense storms. In general, the intensity of the storms seems to control and augment the plasma bubbles' depth, width, and internal velocity.

A dose-response characterization of transcranial magnetic stimulation intensity and evoked potential amplitude in the dorsolateral prefrontal cortex

By combining transcranial magnetic stimulation (TMS) with electroencephalography, human cortical circuits can be directly interrogated. The resulting electrical trace contains TMS-evoked potential (TEP) components, and it is not known whether the amplitudes of these components are stimulus intensity dependent. We examined this in the left dorsolateral prefrontal cortex in nineteen healthy adult participants and extracted TEP amplitudes for the N40, P60, N120, and P200 components at 110%, 120%, and 130% of resting motor threshold (RMT). To probe plasticity of putative stimulus intensity dose-response relationships, this was repeated after participants received intermittent theta burst stimulation (iTBS; 600 pulses, 80% RMT). The amplitude of the N120 and P200 components exhibited a stimulus intensity dose-response relationship, however the N40 and P60 components did not. After iTBS, the N40 and P60 components continued to exhibit a lack of stimulus intensity dose-dependency, and the P200 dose-response was unchanged. In the N120 component, however, we saw evidence of change within the stimulus intensity dose-dependent relationship characterized by a decrease in absolute peak amplitudes at lower stimulus intensities. These data suggest that TEP components have heterogeneous dose-response relationships, with implications for standardizing and harmonizing methods across experiments. Moreover, the selective modification of the N120 dose-response relationship may provide a novel marker for iTBS plasticity in health and disease.

Directional Rebound of Microdroplets on a Magneto-Responsive Micropillar Array Surface.

The manipulation of droplet movement behavior is of scientific importance and has practical applications in many fields, such as biological analysis, water collection, oil-water separation, deicing, antifrosting, and so on. Using the magneto-responsive surface to dynamically change the surface morphology is an effective method to realize droplet manipulation. A replica molding technique was used to fabricate the surface with the magneto-responsive micropillar array, and the direction of the micropillar array could be changed dynamically with the magnetic induction intensity. The mechanism of the droplet directional rebound on the magneto-responsive surface and the implementation of the controllability of droplet movement were investigated. On the magneto-responsive surface, it was achievable to realize the directional rebound of droplets on the micrometer scale. The critical condition for the droplet directional rebound was identified. The force and energy of the droplet during the spreading and retraction stages were analyzed, which lay a theoretical foundation for the precise control of droplet directional rebound.

Enhanced magnetoelectric coupling performance in CoFe2O4 @BaTiO3 multiferroic liquid by tuning the CoFe2O4 morphology

Multiferroic materials are identified as a newly emerging area of research because of their obvious magnetoelectric effects between ferroelectric and ferromagnetic orders. This paper uses the ball milling method to prepare CoFe2O4 @BaTiO3 (CFO@BTO) multiferroic liquids with different CoFe2O4 (CFO) particle morphologies. The settling stability and magnetoelectric properties of the CFO@BTO multiferroic liquids with different CFO particle morphologies have been systematically studied. XRD analysis confirmed that the crystal structure of the powders was consistent with that of standard cards, and the CFO powders exhibited irregular spherical shapes, well-dispersed rectangular shapes, and uniform nanowires. TEM images revealed a core-shell structure of the formed particles. The study found that as the CFO particle morphology changed from spherical to rectangular and then to nanowire, both the residual magnetization intensity (Mr) and saturation magnetization intensity (Ms) of both CFO powder and CFO@BTO composite powder increased gradually. The settling rate of the multiferroic liquids with spherical CFO morphology was observed to be 4.6% with good settling stability after resting for 48 h. The dielectric constant and dielectric loss showed similar trends in the presence and absence of magnetic fields. With the change in CFO particle morphology, the maximum polarization strength (Pmax), residual polarization strength (Pr), and coercivity field strength (Ec) of the multiferroic liquids gradually increased. The magnetoelectric coupling coefficient of the multiferroic liquids was found to be the largest when the CFO morphology was rectangular, measuring 23.93 V/(cm·Oe). The study provides insights into improving the magnetoelectric coupling effect of multiferroic materials and opens up new possibilities for further research in this area.

Geothermal prospective areas in the Northern sector of Bida Basin and environs, North-Central Nigeria

With the deteriorating electrical power supply in Nigeria, it is imperative that more alternative sources are explored. This research work is carried out to assess part of the Bida basin as a possible source of geothermal energy that will help to augment the electric power generation in the country. The study was carried out within the northern sector of the Bida Basin and environs and the area which lies between Longitudes 5000ʹ00ʺ – 7000ʹ00ʺ E and Latitudes 8030ʹ00ʺ – 10030ʹ00ʺ N. Sixteen (16) half degree high resolution aeromagnetic data in a block grid format was utilised for this research. To enhance data for interpretation the total magnetic intensity (TMI) map was subjected to regional-residual separation using Oasis Montaj (version 7.0.1) software. To minimize the effect of frequency noise caused by tiny structures near ground surface, the residual magnetic map was upward continued and further divided into sixteen square blocks with each block windowed and subjected to spectral analysis using Matlab (version R2010a) software. Surfer 11 surface mapping software was used for data contouring. Results obtained from the analysis revealed a Curie point depths ranges from 9 – 17 km over the study area, a geothermal gradient range from 32 – 65 0C km-1, and heat flow ranges from 83 – 163 mWm-2. From interpretation of heat flow map, the prospective areas with anomalous geothermal conditions recommended for geothermal exploitation are areas around Masamagu, Mokwa, Bokani, Lapai, Agaie and Agena.

Quasi-Static Modelling of a Full-Channel Effective Magnetorheological Damper with Trapezoidal Magnetic Rings.

Magnetorheological damper (MRD) has been successfully applied to vehicle suspension systems as an intelligent core component. Most conventional MRDs have closed rectangle-shaped magnetic circuits, resulting in a short effective working length and negligible damping force. To address the above issues, a novel full-channel effective MRD with trapezoidal magnetic rings (FEMRD_TMR) is proposed. The trapezoidal magnetic ring can shunt the magnetic circuit, distributing it evenly along the damping channel and increasing the effective working length. Additionally, which has the same variation trend as the magnetic flux through it, makes the magnetic induction intensity distribution more uniform to reduce the magnetic saturation problem. Theoretically analyzing the damping characteristics of the FEMRD_TMR, a quasi-static model is developed to forecast the output damping force. The structural design of MRD is challenging since conventional quasi-static models rely on the yield stress of magnetorheological fluid (MRF) to reflect the rheological property, which cannot be directly observed and is challenging to calculate. The Takagi-Sugeno (T-S) fuzzy neural network and a unique magnetic circuit computation are offered as a novel quasi-static modeling approach to address the issue. The MRF's yield stress is linearized into magnetic induction intensity functions by the T-S fuzzy neural network and then converted into the MRD's structural size by the special magnetic circuit calculation. Therefore, the proposed quasi-static model can directly reflect the relationship between the damping force and structure size, simplifying MRD's structure design. The novel quasi-static model is shown to be more straightforward and understandable than the conventional Bingham quasi-static model and to have approximately accurate damping force prediction when compared to experimental data.

Optimizing processing performance of Fe-6.5 wt%Si–SiC magnetic abrasive particles by in-situ formation of FexSiy interlayer

The Magnetic Abrasive Finishing (MAF) technology has demonstrated significant potential for precision machining due to its adaptable processing characteristics. However, the current methods for preparing Magnetic Abrasive Particles (MAPs) suffer from issues such as high cost, uneven particle size distribution, and unsatisfactory structure. In this paper, a two-step ball milling method is proposed to address these problems and produce MAPs with a uniform core-shell structure. During the ball milling process, nanoscale iron powder (NIP) is added and forms a coated intermediate bonding layer on the Fe-6.5 Si powder core, increasing the adhesion between the ferromagnetic phase core and the abrasive hard phase. The study found that the addition of 10 wt% NIP as a mass percentage can optimize the MAP structure. During the sintering process at 1169.7 °C, the NIP interface transforms into a metallic interface layer, namely FexSiy (Fe5Si3 and Fe3Si), between the hard phase and the ferromagnetic phase. This intermediate layer combines the hard phase with the ferromagnetic phase, enhancing the magnetic saturation intensity while reducing the coercivity. The developed MAPs were applied to the polishing of Zr alloy tubes and effectively removed localized defects on the outer surface of the tubes. After six polishing cycles, the surface roughness decreased from 0.361 µm to 0.085 µm. This study establishes the correlation between interface behavior and magnetic properties and proposes a new strategy for the preparation of high-performance MAPs.

Study on the motion of single particle chain in the magnetorheological fluid under the action of traveling magnetic field

Magnetorheological fluid (MRF) is a widely used intelligent material that can quickly respond to external magnetic fields. To effectively control the motion of the particle chain inside the MRF, this paper combines the traveling magnetic field (TMF) with the MRF to study the movement of the single particle chain in the MRF under the action of the TMF for the first time and discusses the influence of the moving velocity of the TMF and the magnetic induction intensity on the motion displacement and the velocity of the single particle chain, determines the adjustable range of the single particle chain motion parameters, and builds an experimental platform to observe the motion of the single particle chain. The results show that under the action of the TMF, the single particle chain makes a variable velocity reciprocating motion, and the displacement amplitude of the single particle chain is inversely proportional to the moving velocity of the TMF but directly proportional to the magnetic induction intensity of the TMF. The single particle chain velocity amplitude is only proportional to the magnetic induction intensity and is unrelated to the moving velocity of the TMF. This study shows that adjusting the TMF parameters can effectively control the displacement and velocity of single particle chain motion. This study provides a compelling new method to control the motion pattern of single particle chains in MRF.