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In this study, the ringing phenomenon of gallium nitride‐field effect transistor (GaN‐FET) and silicon‐insulated gate bipolar transistor (Si‐IGBT) inverter excitations in a ring sample was thoroughly measured and analyzed by using a high‐quality oscilloscope with a very high sampling rate of 5 giga‐samples per second (GS/s). Owing to the rapid switching of the GaN‐FET power devices in several nanoseconds and the ringing frequencies in the MHz range, the use of the high sampling rate of 5 GS/s is necessary and useful for accurate measurement. The experimental findings and analysis reveal the following three key points: (i) there are two possible types of high‐frequency resonance phenomena, that is, the first one caused by semiconductor devices and circuits and the other generated by the resonance with loads in use. (ii) The ringing phenomenon because of the resonance under the load is considered to be due to the rising time of pulses that are caused by the rapid switching of the semiconductor devices. (iii) The ability to measure and the two types of ringing phenomena depends on the intensity of the white noise of the measuring instrument [ABSTRACT FROM AUTHOR]

The 3-D polycrystal magnetic field analysis method by means of coordinate transformation is proposed. The local coordinates are fixed in each crystal grain and the global coordinates are defined in the polycrystal steel. Though it is assumed that each crystal grain has the same magnetized characteristics as those of a single crystal grain, the crystal grain shape and its orientations of [alpha], [beta] and [gamma] angles are taken into account. When the proposed model is applied to the real grain oriented (GO) steel with 56 crystal grains in 80-mm x 80-mm, and with 0.35.mm thickness, the calculation results are compared with the grain orientations measured by X-ray diffraction. The GO steel has a higher degree of (110)[001] texture with about 3% silicon. The calculated results of higher magnetic flux density part and lower magnetic flux density part in the real GO steel are explained by the a angle distribution. The calculated inclination angle distribution and the measured [alpha] angle distribution seem to be in good agreement. The calculated normal component of the magnetic flux density reflects the [beta] angle distribution of the real GO steel. It is concluded that the proposed 3-D polycrystal magnetic field analysis is appropriate. Index Terms--Crystal grain shape, finite-element method, GO material, grain orientation, magnetic field analysis, polycrystal.

The authors investigate the effects of double-axis electromagnetic stirring (DAEMS) in continuous casting process, which is composed of a rotational electromagnetic stirrer and a vertical electromagnetic stirrer, using unsteady 3-D hydrodynamic calculation of the molten gallium model. To evaluate the free-surface stability, averaged standard deviation of the free surface is calculated. From the calculation results, it is found that there is an optimum intensity balance between a vertical magnetic stirrer and a rotational magnetic in order to stabilize the free surface. Index Terms--Continuous casting, electromagnetic stirring, free surface, 3-D magnetohydrodynamic calculation.

We propose a new type of magnetic shield structure, in which some closed magnetic paths surround a defined space. Because there are some openings between paths, the freedom in designing and the ease of constructing a shield room are attained. This structure shows better magnetic shield performance than conventional shield structures when openings between magnetic paths, widths of magnetic paths, and weight distribution of magnetic materials are designed appropriately. Index Terms--Electrical steels, magnetic noise, permeability, saturation magnetization, shield coefficient, shield efficiency, soft magnetic materials.

Basic characteristic of electromagnetic force in induction heating application of single-sided linear induction motor (SLIM) which uses electromagnetic AC field is investigated by means of 2-D and 3-D numerical electromagnetic FEM calculation. The electromagnetic force in the normal direction consists of the attractive force caused by magnetization and the repelling force caused by Lorentz force. Although the normal force is canceled by them and becomes zero at crossover frequency, the value is different, which is 2 kHz in 2-D model and is 5 kHz in 3-D one respectively. Since 2-D model expresses only center section of 3-D model and can not express the complex behavior of the eddy current in the whole model, the repelling force caused by Lorentz force is considered to be overestimated when the electromagnetic force value of 2-D model is converted into 3-D one. As a result, the crossover frequency of 3-D model becomes large in comparison with 2-D one. This means that an evaluation by using 3-D model is demanded in order to correctly evaluate the crossover frequency. On the other hand, at low frequency in which the attractive force caused by magnetization becomes dominant, the normal forces of the 2-D and 31D model are in good agreement. This means that the evaluation by using 2-D model is effective at low frequency. Index Terms--Crossover frequency, electromagnetic force, finite element method (FEM), induction heating, linear induction motor, thin steel plate.

The numerical model following the equivalent magnetic domain method is proposed to calculate the anisotropy of the magnetic properties of electrical steel. The angle difference between magnetic flux density vector and magnetic field vector, which is observed in the measurement data, is clearly expressed by the proposed model. The angles characteristics of stepwise or lamped shape are shown to be consequences of the strong magnetic anisotropic property. Index Terms--Angle difference, anisotropic steel, finite-element method, magnetic field vector, magnetic flux density vector, rotational magnetic field.

We describe a method to analyze the effects of shrink fitting and stamping on the mechanical stress distribution and iron loss in motor cores. Shrink fitting and stamping are important processes in manufacture of motor cores from electrical steel. The mechanical stress distribution is evaluated by a structural finite-element method, and the iron loss is evaluated by combined analysis of the electromagnetic field (by a finite-element method) and mechanical stress. The method dearly shows that the iron loss becomes larger as the width of the shrink fit increases, an effect borne out by experiment. In regard to the effect of stamping, calculation results again agree well with experimental data. Index Terms--Finite-element method, iron loss, mechanical stress, motor core, shrink fit, stamping effect.

We present a finite-element method for numerical calculation of electromagnetic fields in silicon steel that takes into account the effect of mechanical stress on the steel's mechanical properties. The effect of the mechanical stress is considered in terms of the magnetic permeability in each element. To evaluate the usefulness of the calculation method, we have applied it to an electric motor under uniform and nonuniform mechanical stress distribution. In case of uniform stress distribution, the iron loss distribution is uniform too. The area of increased iron loss corresponds to the area where the mechanical compressive stress is applied. In case of nonuniform mechanical stress distribution, the magnetic flux flows so as to avoid the mechanical compression stress area. The iron loss has a tendency to increase further under mechanical compressive stress because of the increase of the magnetic flux density in the zone of no mechanical stress and the poorer characteristics of the iron loss as a function of magnetic flux density under mechanical compressive stress. Index Terms--Electrical motor, electromagnetic field calculation, finite-element method, magnetic characteristics, mechanical stress, silicon steel.

The free surface velocity strongly influences steel quality in the casting process, so an accurate calculation method is required. The velocity at the free surface is imparted through the wall of the continuous casting mold in an electromagnetic stirring operation. The wall friction in the solidification calculation model is modeled by the Darcy flow coefficient, which was found to be 0.7 from the operation data, according to the oscillation mark made by the free surface deformation. The calculated velocity is in good agreement with the operational velocity. Index Terms--Continuous casting, Darcy flow, electromagnetic stirring, magnetohydrodynamics, solidification, steel making.

A high-response inductive electromagnetic sensor can be made by arranging a conductive and/or magnetic material between the primary coil and the secondary coil. Compared with the conventional inductive electromagnetic sensor, the new sensor has a larger responsivity index (used here to evaluate its characteristics), though it also has a smaller induced voltage at the secondary coil. Index Terms--Electromagnetic sensor, high responsiveness, level sensor, linkage magnetic flux, magnetic flux density.

It is made clear why the pulse electromagnetic casting (EMC) makes the surface steel quality good from the point of view of fluid dynamics by means of magnetohydrodynamic calculation with shadow method. In order to obtain good surface quality, the free surface profile should follow the pulse electromagnetic force and fluid dynamics are stable and uniform for the rectangular axis. By means of the pulse mode in EMC operation, the fluid dynamics make stable and uniform the unstable flow in continuous EMC operation and the free surface profile is maintained as convex. Index Terms--Continuous casting, electromagnetic application, free surface, magnetohydrodynamic, magnetohydrodynamic calculation, pulse electromagnetic casting (EMC), shadow method, stability.

We evaluate the verification of combined system ac and dc electromagnetic field using magneto hydrodynamic calculation. For the effect of level magnetic flow (LMF) that gives the molten steel the breaking force in proportion to the velocity using dc magnetic field, we confirm that the velocity at meniscus becomes stabilized in the time domain and the space domain, though the conventional dual electromagnetic stirring is difficult to realize the stabilization of the meniscus flow dynamics. In the proposed process, it is also confirmed that the velocity at the inner mold is constant in spite of dc magnetic field. Index Terms--Continuous casting, electromagnetic analysis, electromagnetic stirring, magneto hydrodynamics calculation.

In order to improve steel quality in the continuous casting process, it is necessary to make the dynamic behavior of the free surface flows in a mold clear. The estimation of influences of in-mold electromagnetic stirring (M-EMS) electromagnetic force is especially important. We examined the difference of free surface flows by the different M-EMS exciting frequencies, using numerical experiment (magnetohydrodynamic calculation). We introduce a new index, the responsive ratio, to evaluate it. As a result, the free surface flow has different behavior according to exciting frequency and its responsive ratio is higher in low-frequency zone. The free surface flow has also high resonate-ability with natural frequency of the mold. Index Terms--Continuous casting, electromagnetic analysis, electromagnetic stirring, magneto hydrodynamics calculation.

To decrease the cost of low-frequency linear motor such as M-EMS (in-mold electromagnetic stirring) system and to obtain the process characteristics, it is necessary to estimate the maximum current and voltage as well as the distribution of magnetic flux density precisely. According to the measurement result of the M-EMS unbalanced three-phased electrical circuit, we find out that the standard deviation of the voltages is much smaller than that of currents. Then, it makes clear that the voltage source electromagnetic calculation is useful for the M-EMS design to obtain the maximum current and the magnetic flux density, through the comparison data of the experiment and the calculation. Index Terms--Electromagnetic analysis, electromagnetic stirring, end effect, linear motor, phase unbalance.

We evaluate an effect of the dual in-mold electromagnetic stirring (M-EMS) which is arranged in series to control the molten steel velocity distribution using magnetohydrodynamic calculation. A stirring force ratio (SFR) defined as [F.sub.u]/[F.sub.1] where [F.sub.u] is an electromagnetic force of upper M-EMS and [F.sub.i] is the one of the lower M-EMS is introduced as an index of input. The value of SFR at the optimal condition that meniscus velocity is almost zero, but some velocity is realized at lower M-EMS position. Especially, the SFR condition to have no velocity at free surface is extremely rigorous. This means that it is very difficult to be stable at meniscus by the dual M-EMS system. The lower velocity hardly changes when the SFR changes. Index Terms--Continuous casting, electromagnetic analysis, electromagnetic stirring, magneto hydrodynamics calculation.

This article is the first work to carefully investigate the characteristics of iron loss per weight and relative permeability between the flake and spherical powders with a sinusoidal excitation up to a high frequency of 3.5 MHz in experiments using three separate measurement systems. The composition of the considered powder samples contains 0.001 wt% C, 0.012 wt% Si, 0.09 wt% Mn, 0.0004 wt% P, 0.008 wt% S, and 0.06 wt% O. The flake particle has the preferred orientation that the easy axes are normal to the platelet face, and the water atomized iron powder was processed with ball milling with the lubrication. Key objectives of the utilization of the three independent measurement systems with different specialized equipment and probes are to cross-check and overcome unexpected measurement errors of the related devices in use for validating measured results thoroughly. Experimental results demonstrate the much better performances on the iron loss per weight and relative permeability of the flake powder than that of the spherical powder at high frequencies. Physics-based explanations for the measured results are also presented. Furthermore, two estimation functions based on a six-parameter Steinmetz equation for the measured iron loss of the powders are developed by using MATLAB. [ABSTRACT FROM AUTHOR]

The numerical magnetohydrodynamic (MHD) calculation of heat plasma used in heat and welding processes is described. The heat plasma is concentrated in the center area which is of low density and high electrical conductivity.

This study is the first research to present a detailed assessment of core loss, copper loss and magnetic flux density of the interior permanent magnet synchronous motor (IPMSM) with pulse‐amplitude modulation (PAM) inverter under different excitation angles in both no‐load and load conditions. The PAM method automatically controls the amplitude of changeable DC‐link voltage, and the excitation angle for switches in the inverter is varied from 120° to 180° according to a 12‐step switching pattern designed particularly for the PAM‐based inverter of IPMSM. For reference purpose, the pulse‐width modulation excitation with a very high voltage modulation index is performed. Various conditions with changes in speed and torque are examined. Experimental results show that harmonic components produced by the PAM inverter in the IPMSM current, voltage and magnetic flux density have large effects on the motor core and copper losses; physics‐based explanations and insights are also presented. The PAM under 135° excitation angle has an excellent performance in reducing IPMSM core and copper losses since it can significantly decrease the harmonic components in motor current, voltage and magnetic flux density. Furthermore, simulations using the finite element method are conducted to validate the experimental results of IPMSM core loss with the PAM excitations. [ABSTRACT FROM AUTHOR]

A new implementation of an iron-loss model for laminated magnetic cores in the MATLAB/Simulink environment is proposed in this paper. The model is based on numerically solving a one-dimensional diffusion problem for the eddy currents in the core lamination and applying an accurate hysteresis model as the constitutive law. An excess loss model is also considered. The model is identified merely based on the catalog data provided by the core material manufacturer. The implementation is validated with analytical and finite-element models and experimentally in the case of a toroidal inductor supplied from a GaN FET full-bridge inverter with 5–500 kHz switching frequencies and a deadtime of 300 ns. Despite the simple identification, a good correspondence is observed between the simulated and measured iron losses, the average difference being 3.3% over the wide switching frequency range. It is shown that accounting for the skin effect in the laminations is significant, in order to correctly model the iron losses at different switching frequencies. Some differences between the measured and simulated results at high switching frequencies are also discussed. The model is concluded to be applicable for designing and analyzing laminated magnetic cores in combination with power-electronics circuits. The Simulink models are openly available. [ABSTRACT FROM AUTHOR]

In this paper, we develop and examine permanent magnet synchronous motors (PMSMs) by use of both stator and rotor cores made of nanocrystalline magnetic materials (NMMs). We report core loss properties of the PMSM with the NMM under inverter excitation. In addition, we compare core losses of the PMSM with conventional non-oriented (NO) steel sheets under inverter excitation to discuss the core loss characteristics of the NMM motor. In average, under inverter excitation, the reduction ratio in core loss of the PMSM made of NMM is about 60% as compared with the core loss of the PMSM with NO sheets. In particular, the average decrease obtained by using NMM rotor core instead of NO rotor core is about 30%. [ABSTRACT FROM AUTHOR]

We calculate an iron loss attributed to semiconductors ON-voltages in an inverter circuit and reveal influence rate of the ON-voltages on whole iron loss. In our previous work, it has been revealed by inverter excitation that the ON-voltages make minor loops in magnetic hysteresis of magnetic material and the loops affect iron loss characteristics. In this paper, it is investigated by a factor analysis how much the on-voltage has an influence on iron loss, quantitatively. We separate whole iron loss caused in a non-oriented electrical steel sheet into three losses: loss by the ON-voltage, loss by fundamental component, and loss by inverter carrier. The rates of these losses are evaluated under several conditions of single-phase pulse width modulation inverter excitation, and the results show that the proportion of loss by ON-voltages is up to around 10% depending on inverter excitation parameter: fundamental frequency, carrier frequency, modulation index, and magnetic flux density. [ABSTRACT FROM PUBLISHER]

We report core loss properties of permanent magnet synchronous motors (PMSM) with amorphous magnetic materials (AMM) core under inverter and sinusoidal excitations. To discuss the core loss properties of AMM core, a comparison with non-oriented (NO) core is also performed. In addition, based on both experiments and numerical simulations, we estimate higher (time and space) harmonic components of the core losses under inverter and sinusoidal excitations. The core losses of PMSM are reduced by about 59% using AMM stator core instead of NO core under sinusoidal excitation. We show that the average decrease obtained by using AMM instead of NO in the stator core is about 94% in time harmonic components. [ABSTRACT FROM AUTHOR]

This paper focuses on an evaluation of core losses in laminated magnetic block cores assembled with a high Bs nanocrystalline alloy in high magnetic flux density region. To discuss the soft magnetic properties of the high Bs block cores, the comparison with amorphous (SA1) block cores is also performed. In the high Bs block core, both low core losses and high saturation flux densities Bs are satisfied in the low frequency region. Furthermore, in the laminated block core made of the high Bs alloy, the rate of increase of iron losses as a function of the magnetic flux density remains small up to around 1.6 T, which cannot be realized in conventional laminated block cores based on amorphous alloy. The block core made of the high Bs alloy exhibits comparable core loss with that of amorphous alloy core in the high-frequency region. Thus, it is expected that this laminated high Bs block core can achieve low core losses and high saturation flux densities in the high-frequency region. [ABSTRACT FROM AUTHOR]

Recently, novel magnetic materials have been developed for high-efficiency and high power density electric motors. In addition, next-generation semiconductor devices, like silicon carbide (SiC) or gallium nitride (GaN), have been introduced for power converters due to their high-frequency operation. Therefore, high-frequency operation of new magnetic materials is possible when they are driven by GaN or SiC inverters. Nevertheless, iron loss characterization of magnetic materials when they are excited by high-frequency signals have not been conducted yet. This paper introduces the iron losses characterization of a magnetic material at high carrier frequency excitation using a GANFET inverter. This characterization was carried out by the experimental evaluation of iron losses at carrier frequencies from 5 to 500 kHz at different deadtimes. As a result of the measurements, iron losses seem to have a trend to increase at high carrier frequencies and large deadtimes. In addition, filtering is introduced and it seems to be an effective technique for reducing iron losses. [ABSTRACT FROM AUTHOR]

This paper presents the results of experimental trials carried out on a permanent magnet synchronous motor (PMSM) that uses a stator core made of a nanocrystalline magnetic material (FINEMET). It is demonstrated that the manufactured stator can reduce the PMSM total iron loss by 64% to 75% compared with an equivalent motor using a stator made of conventional non-oriented silicon steel. The experimental results are confirmed by 2-D finite-element analysis. [ABSTRACT FROM AUTHOR]

The estimate of free surface velocity at the billet mold in magnetohydrodynamic calculation is important for steel surface quality. It is considered that the free surface velocity in the electromagnetic stirring operation is transferred through the wall, a boundary of the molten steel. Then the wall friction phenomena between the wall and the molten steel are modeled so as a wall friction, force is a function of wall velocity. The calculated velocity distribution in consideration of the wall friction in which the friction coefficient is estimated as 0.03 is in good agreement with the measured value. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

This paper proposes an equivalent magnetic hysteresis (B–H) curve for magnetic multiscale problems of complex materials composed of electrical conductors separated by insulating material. The conventional method, which assigns equivalent material constants to each material, cannot properly express the local eddy current loss and the extra magnetic field derived from the local eddy current. To solve this problem, we derive the magnetic hysteresis curve from the volume-averaged magnetic flux density and the surface magnetic field in the micro-model, and apply this curve to the macro-model. The mesh number of the novel macro-model is reduced to around one-tenth that of the micro-model. Magnetic hysteresis is treated by a free energy magnetic hysteresis model, and the macro-model ignores electrical conductivity. The magnetic hysteresis curve and the numerically calculated losses are consistent in the micro- and macro-models. The proposed method well expresses the local eddy current phenomena. [ABSTRACT FROM AUTHOR]

This paper presents an attempt to evaluate the building factor of a stator core made of nonoriented silicon steel laminations. The stator core is used in a synchronous motor with buried permanent magnets driven by a voltage source three-phase inverter with classical pulse-width modulation (PWM) control. The building factor is the ratio between the iron loss density in the stator core and the specific iron loss density of the material. It then gives an evaluation of the impact of the core manufacture and the motor geometrical configuration on the stator iron losses. A first experiment is conducted to measure the iron losses of the inverter-fed motor in no-load condition. The material-specific iron losses are then evaluated by trying to apply similar magnetic flux density conditions in a wound laminated ring. The results show a decrease of the building factor with the PWM carrier frequency. [ABSTRACT FROM PUBLISHER]

Presents a magnetohydrodynamic calculation for free surface used for the design and evaluation of cold-crucible or initial solidification such as stirring phenomena found in the metal processing industry. Changes that take place in the shape of molten metal in a free surface calculation; Demonstration of a magnetohydrodynamic calculation using the direct method; Information on the flow dynamics calculation for a free surface with a fixed mesh.

The core losses of an interior permanent-magnet synchronous motor (PMSM) have been reduced by about 50% using an amorphous magnetic material (AMM) stator core instead of a nonoriented (NO) steel stator core. Numerical calculation and experimental tests data have been compared to evaluate the reliability of the results. The AMM stator core has been realized using the latest improvements in manufacturing technologies. [ABSTRACT FROM AUTHOR]

SUMMARY In this study, it is demonstrated that the iron loss from the SiC-MOSFET, which represents a new power semiconductor with an extremely low on-voltage for electric machine drives, is almost the same as that from an Si-IGBT, which is a conventional power semiconductor. In order to evaluate the iron loss characteristics when an SiC device is used, two single-phase pulse width modulation inverters were built and used for the excitation of a ring made up of electrical steel sheet. One of the inverter employed an SiC-MOSFET, and the other inverter employed an Si-IGBT. The iron losses for the two inverters are compared. [ABSTRACT FROM AUTHOR]

It is revealed by magnetic field analysis that a difference between an actual reactor loss and a material datasheet loss, which was observed by measurement using an actual reactor with air gaps under high-frequency excitation, is caused by leakage magnetic flux near the air gaps of a reactor. In our previous measurement, an actual reactor loss under high-frequency excitation became large compared with a datasheet loss of the reactor core material. To clarify the reason, we carry out a 3-D magnetic field analysis. As a result, due to the increasing eddy current losses by leakage magnetic flux density near reactor gaps and due to the ununiform distributions of an iron loss caused by leakage magnetic flux, the reactor loss becomes larger than that of the datasheet loss. [ABSTRACT FROM AUTHOR]

The iron losses of a reactor with an air gap are investigated and compared for three different magnetic materials, namely, grain-oriented material (GO230), high performance non-oriented Fe-Si metal (super E ST125), and nanocrystalline soft magnetic material (FINEMET FT-3M). The iron losses of the reactor are measured by the experiments for different voltage supply frequencies and amplitudes. The measured data are compared with the material iron losses that are calculated from the manufacturer’s material datasheets. It is concluded that the air gap is responsible for a large part of the increase between the reactor and material iron losses and that the FT-3M has sensibly higher building factor compared with the other materials. [ABSTRACT FROM AUTHOR]

In this paper, we propose a numerical method for accurately predicting the surge voltage generated in an electromagnetic (EM) clutch, which is the inductive load of a vehicular air conditioner compressor. The EM clutch is expressed by a 2-D transient response model that considers eddy currents and the non-linear magnetization characteristics of the clutch materials. We found that the surge voltage can be calculated exactly using this model. The calculation result differed from the measured value by <5%. [ABSTRACT FROM PUBLISHER]

To evaluate how magnetic properties of magnetic materials are influenced by power semiconductor properties in an inverter circuit, we propose and test a new numerical calculation method. This method combines an electrical circuit analysis for current–voltage properties of power semiconductors with a magnetic analysis based on a magnetic hysteresis model. Previous measurements on an inverter show that magnetic properties, such as B–H curves (B is the magnetic flux density and H is the magnetic field intensity) and iron losses, are affected by ON-voltages of power semiconductors. Those measurements motivate this paper. The magnetic hysteresis model used here is a novel approach that is based on physical thermodynamics theory and can capture the essence of physical magnetic phenomena. Calculations with the proposed method show that measured minor loops in B–H curves are well represented and calculated voltage waveforms properly capture ON-voltage effects. [ABSTRACT FROM AUTHOR]

A new structure for a vehicular electromagnetic (EM) clutch is proposed here that suppresses the surge voltage generated by turning off the ignition switch of a vehicle. Through the theoretical consideration of the EM field, it is found that a larger eddy current in the EM clutch would be able to suppress the surge voltage because it causes a small time change in the magnetic flux passing through the coil. Therefore, the proposed structure has a metal layer with low resistivity surrounding the clutch coil and located between the coil and the coil housing. Numerical calculation of the EM field and electrical circuit, which expresses the measured time-series surge voltage well, shows the suppression effect of the surge voltage with the proposed structure. Therefore, the structure is verified to be useful for suppressing the surge voltage. [ABSTRACT FROM AUTHOR]

A cord pattern, where magnetic flux density distribution is separated into strong and weak parts like the magnetic domain, appears in magnetic anisotropic numerical calculation results. It is obtained in the strong magnetic anisotropic material. The same cord patterns are also found in the measured magnetic domain structure. Fractal structure of the cord patterns is also observed through the partial enlargement of the calculated cord patterns. The similar cord pattern resembled to the magnetically numerical calculation is also obtained in the structural numerical analysis of the metal crystal level. The fractal cord patterns emerge as a fundamental characteristic of anisotropy in numerical calculation and in physical observations. [ABSTRACT FROM PUBLISHER]