United States

1. Introduction&lt;br/&gt;The realization of the brushless excitation of the machine is important for the industrial application[1,2].In this paper, a Brushless Electrical Excitation Synchronous Generator will be studied. The rotor coils are divided into two parts: The induction coils (Ci) and rotor excitation winding (Wr). They are connected by a half –wave rectifier which only has four diodes. Ci not only can induce the magnetic field produced by stator excitation current (Is), but also can take part in the induction of the stator armature. However, the magnetic distribution of the generator is not symmetrical as the conventional EESG. The magnetic field is studied by the frozen permeance method. A 1.5kVA prototype was fabricated to verify the correctness of the theoretical analysis and Finite Element Analysis.&lt;br/&gt;2. Magnetic field distribution of DEESG&lt;br/&gt;The magnetic field distribution of DEESG under the no-load condition when &lt;i&gt;I&lt;sub&gt;s&lt;/sub&gt;&lt;/i&gt; is 0.8A at 160ms is as shown in Fig.1. The reason for theasymmetry of the magnetic field distribution is studied. It also can be seen that because all the magnetic flux passes through the air gap, the magnetic flux density of air gap is also not symmetrical as shown in Fig.2.&lt;br/&gt;3. Magnetic field Analysis Excited by Different Currents&lt;br/&gt;The frozen permeability method can be used to decompose the magnetic field which is excited by rotor excitation current &lt;i&gt;I&lt;sub&gt;r&lt;/sub&gt;&lt;/i&gt;, Is and the currents of Ci respectively. The magnetic field distribution of DEESG when I&lt;sub&gt;s&lt;/sub&gt;is taken as the example to do analysis. The magnetic field which is only excited by &lt;i&gt;I&lt;sub&gt;r&lt;/sub&gt;&lt;/i&gt; utilizing the frozen permeability method. The magnetic field distribution which is generated by the currents of Ci will also be studied. The function of Is will also be studied. It can demonstrate that the magnetic field produced by ac component of the currents of Ci can weaken the magnetic field produced by &lt;i&gt;I&lt;sub&gt;s.&lt;/sub&gt;&lt;/i&gt;&lt;br/&gt;&lt;sub&gt;4. Experiment&lt;/sub&gt;&lt;br/&gt;A 1.5kVA prototype was fabricated to test the operating characteristics of DEESG. The magntic field can not be tested directly. The output voltage will be tested to demonstrate the magnetic field distribution of DEESG.

![](https://assets.underline.io/uploads/markdown_image/1/image/dce353cb14a130159644d484d36d6585.jpg)

Fig.1 Field distribution of DEESG at the rated speed.

![](https://assets.underline.io/uploads/markdown_image/1/image/fca712f83b796857855f8b3b4aef5065.jpg)

Fig.2. Magnetic flux density of air gap.

2022 Joint MMM-INTERMAG

Magnetic Field Analysis and Operating Characteristics of a Brushless Electrical Excitation Synchronous Generator with DC Excitation

The 15th Joint MMM-INTERMAG Conference (2022 Joint) is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a plenary session, and an evening session, with about 1500 presentations overall. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

The 2022 Joint Conference will offer both in-person and prerecorded on-demand content.

For tickets to the event, please register at the following link: https://magnetism.org/register

Please register for the Joint MMM-Intermag conference to join the event.

This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

1. Introduction The realization of the brushless excitation of the machine is important for the industrial application[1,2].In this paper, a Brushless Electrical Excitation Synchronous Generator will be studied. The rotor coils are divided into two parts: The induction coils (Ci) and rotor excitation winding (Wr). They are connected by a half –wave rectifier which only has four diodes. Ci not only can induce the magnetic field produced by stator excitation current (Is), but also can take part in the induction of the stator armature. However, the magnetic distribution of the generator is not symmetrical as the conventional EESG. The magnetic field is studied by the frozen permeance method. A 1.5kVA prototype was fabricated to verify the correctness of the theoretical analysis and Finite Element Analysis. 2. Magnetic field distribution of DEESG The magnetic field distribution of DEESG under the no-load condition when Is is 0.8A at 160ms is as shown in Fig.1. The reason for theasymmetry of the magnetic field distribution is studied. It also can be seen that because all the magnetic flux passes through the air gap, the magnetic flux density of air gap is also not symmetrical as shown in Fig.2. 3. Magnetic field Analysis Excited by Different Currents The frozen permeability method can be used to decompose the magnetic field which is excited by rotor excitation current Ir, Is and the currents of Ci respectively. The magnetic field distribution of DEESG when Isis taken as the example to do analysis. The magnetic field which is only excited by Ir utilizing the frozen permeability method. The magnetic field distribution which is generated by the currents of Ci will also be studied. The function of Is will also be studied. It can demonstrate that the magnetic field produced by ac component of the currents of Ci can weaken the magnetic field produced by Is. 4. Experiment A 1.5kVA prototype was fabricated to test the operating characteristics of DEESG. The magntic field can not be tested directly. The output voltage will be tested to demonstrate the magnetic field distribution of DEESG.

![](https://assets.underline.io/uploads/markdown_image/1/image/dce353cb14a130159644d484d36d6585.jpg)

Fig.1 Field distribution of DEESG at the rated speed.

![](https://assets.underline.io/uploads/markdown_image/1/image/fca712f83b796857855f8b3b4aef5065.jpg)

Fig.2. Magnetic flux density of air gap.

poster

Transcranial Magnetic Stimulation (TMS) coils often are specific to deep brain or focal stimulation. A new technique is used which allows for deep and focal stimulation using temporal interference (TI). TI is a method that allows for steerability, focality, and depth of penetration. TI TMS operates based on the frequency difference of two different electric fields [1]. The TI stimulation frequencies would be in at 10kHz and is filtered by the brain’s inherent lowpass [4] behavior [2]. The frequency difference between the two induced electric fields results in an envelope which allows for a more focal stimulation. By using a coil assembly with several coils (as seen in figure 1), two areas of the brain could be selected and stimulated, focally for use in dual site TMS. Dual site TMS allows for the stimulation of two parts of the brain, which enforces or interferes with brain signals. Dual site TMS stimulation is currently done with two independent coils which are placed on the head and allows for error when placing [3]. The use of a single TI TMS coil for dual site stimulation could allow for a more focused and consistent stimulation for use with dual site TMS.

![](https://assets.underline.io/uploads/markdown_image/1/image/b4e1798b44486dc72cdc09d88679fc02.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/ac996f625495b00087f051deb8cd6da7.jpg)

Temporal Interference for Dual Site Transcranial Magnetic Stimulation

Microplastics (MPs) in ocean environment are a kind of environmental pollution. Many papers have reported potential influences on the ocean and even terrestrial environment [1], [2]. MPs are plastic fragments with diameter smaller than 5 mm. Since chemicals easily stick to MPs, MPs work as a carrier of harmful substances such as Poly Chlorinated Biphenyl (PCB). Small fish or crustaceans eat the polluted MPs, and this may result in bad digestion or deterioration of health conditions. Since the number of MPs has been increasing [3], the development of MP collection method from the ocean is an urgent task towards the United Nations (UN) Sustainable Development Goals (SDGs) [4]. Several methods for MP collection have been proposed, such as collections by floatation, ultrasonic, and filter. However, these methods are not capable of processing a large amount of seawater, and the collection is intermittently conducted. One promising solution is using a strong magnetic field and its high gradient, i.e., a magnetic separation [5]. When a strong magnetic field with high gradient is applied to water including MPs, MPs experience a large magnetic force compared to water. Meanwhile, recently, the performances of high-temperature superconducting (HTS) magnets have been increasing. Currently, &gt;15-T class magnets are easily available, and they can be applied to MP collectors from ocean. In this research, we propose a conceptual idea of MP collector from ocean environment using a high field HTS magnet. Fig. 1(a) shows the schematic view of the proposed MP collector. To evaluate the performance, we developed a fluid simulation code based on a particle method, coupled with magnetic field analysis. Fig. 1(b) shows one simulation case where the magnetic field with constant gradient of 12.5 T/m was applied to the tank of MP collector. As shown in Fig. 2, the proposed device gathers approximately 90 percent of the injected MPs. The details related to the optimal magnetic field or force acting on the magnets are presented at the conference.

![](https://assets.underline.io/uploads/markdown_image/1/image/a117d6fb91ae4052000a9a62e3e7f635.jpg)

(a) Schematic view of proposed microplastic collector and (b) simulation result.

![](https://assets.underline.io/uploads/markdown_image/1/image/82add84e06e8a750daaa6a14d37be3c2.jpg)

Simulated MP concentration and collection ratio.

Conceptual Design for Microplastic Collection Device from Seawater with High Field HTS Magnet

In previous works, we presented the results of the dynamics of the air-magnetic fluid interface under the influence of a non-uniform magnetic field of the moving ring magnet [1, 2]. A distinctive feature of the used magnetic systems is the presence of the magnetic levitation area, with the help of which it becomes possible to control the dynamics of non-magnetic inclusions in the magnetic fluid. This work presents the results of further studies, in which the experiments were performed in microchannels of various configurations with injection of a non-magnetic phase using the syringe pump. In addition to the dynamics of gas inclusions in a magnetic fluid in an inhomogeneous magnetic field, the behavior of non-magnetic droplets of various liquids is presented. The influence of the parameters of the magnetic field and the properties of a magnetic fluid on the dynamics of non-magnetic inclusions and the size of detached bubbles and drops is investigated. It was found that the feed rate of non-magnetic inclusions and external hydrostatic pressure do not affect the size of gas bubbles and non-magnetic drops detached from the levitating main volume. The ability to control the size of non-magnetic inclusions is shown using an external magnetic field and concentration of the magnetic fluid. The results presented in the work can be used to develop microfluidic counters and controlled dispensers of non-magnetic inclusions. The investigation was carried out with the support of part of the implementation of the state task for 2020 (No 0851-2020-0035).

![](https://assets.underline.io/uploads/markdown_image/1/image/bbf4b3226914678eaa7b1eb99bd0c3c3.jpg)

Data of video recording of the position of the interphase boundary of the volume of a nonmagnetic fluid in a magnetic fluid before, at and after the detachment of a nonmagnetic drop from it in an inhomogeneous magnetic field of a ring magnet

Dynamics of nonmagnetic inclusions in a microchannel with a magnetic fluid in an inhomogeneous magnetic field

1. Introduction Random numbers are an important resource in a science and engineering, such as numerical simulations, cryptography and machine learning. A Faster and simpler true random number generators (TRNG), which employs physical phenomena as a noise source, is needed. However, the TRNGs that is compact and faster than GHz is not realized yet. We focused on the magnetic-domain patterns in magnetic garnets as a noise source for TRNG. The magnetic domain can be generated repeatedly and chaotically, and converted to digital value at few Gbit/s by image sensors. The random numbers that generated from the labyrinth magnetic-domain patterns were passed the statistic randomness test (NIST SP800-22) [1]. In this study, other types of magnetic domains were investigated as the noise source. 2. Experimental Sputtered-polycrystalline bismuth substituted yttrium iron garnet (Bi:YIG) films on glass and gadolinium gallium garnet (GGG) substrates, and liquid phase epitaxy (LPE) holmium iron garnet (HoIG) film were investigated. About 3,000 magnetic domain images of each garnet were captured using a polarized light microscope, as shown in Fig. 1.The obtained images were processed to random sequence. The data process was composed of binarization, stable-pattern removal, bit-shift, and XOR. A hundred of the 10 Mbit sequences were generated and evaluated by the randomness test (NIST SP800-22) [2]. 3. Result and discussion A hundred of the 10 Mbit sequences were generated and tested. The results of the randomness test is shown in table 1. The NIST SP800-22 includes 15 periodicity tests. The p-value more than 0.01 indicates that the sequence is non-periodic (random). The pass rates on the table 1 is a ratio of the statistically random sequence. The pass rate more than 0.97 is passed the randomness test. The all samples passed almost of all tests. The low-score with the FFT test could be improved by optimization of the data processing. These results suggest that the random sequences could be generated from many types of magnetic domains.

![](https://assets.underline.io/uploads/markdown_image/1/image/bbfed28ef748ffa07826d0dfadee0b7a.jpg)

Fig. 1 Polarized microscope image of the garnet films

![](https://assets.underline.io/uploads/markdown_image/1/image/2e23a6fc4c63ad65100ccc4c69f12268.jpg)

Table. 1 Result of SP800-22 for 100×10Mbit sequences

Number Generation from Different Types of Magnetic Domain Images

Aircraft propellers are a constant source producing excessive vibrations and noise due to aerodynamic loads imposed in flight. Such vibrations are transmitted to the cockpit and aircrews are inevitably exposed to the high levels of vibrations during flight. The prolonged exposure to severe vibrations due to extended missions can cause the discomfort and fatigue of the occupants, reducing the ability to make correct judgement and appropriate actions during the flight. One of effective way to provide comfortable work environment to occupants is to design a seat equipped with vibration absorbers that can isolate or reduce the unwanted vibration transmitted from the cockpit floor to occupant body. In this study, the adaptively tunable magnetorheological elastomer (MRE)-based vibration absorber was proposed for achieving better vibration reduction performance of a propeller aircraft seat. Since MREs are one of smart materials that can change their key physical properties by external stimuli, MRE-based vibration absorbers can provide both variable stiffness and damping by adjusting the magnetic field. As a result, MRE-based vibration absorbers have an adaptively tunable capability working at wider frequency range that can overcome the narrow operating frequency limitation of passive vibration absorbers. In this study, the simple but effective design of the MRE-based vibration absorber for a propeller aircraft seat was presented (Figure 1). In order to effectively concentrate the magnetic field generated from the electromagnet into the MRE pad areas, the electromagnetic analysis was also conducted by using a finite element method. Based on this analysis, the MRE-based vibration absorber was fabricated. The damper force characteristics of the MRE-based vibration absorber was experimentally evaluated by using an Instron material testing device. In order to confirm the tunability of the MRE-based vibration absorber, the frequency responses with respect to applied current inputs was experimentally obtained (Figure 2).

![](https://assets.underline.io/uploads/markdown_image/1/image/916bf925ae3a3874b07730e6331d4772.jpg)

Figure 1. MRE-based vibration absorber for a propeller aircraft seat

![](https://assets.underline.io/uploads/markdown_image/1/image/4ece2ead9c2a1228811bea21fba1ab33.jpg)

Figure 2. Frequency responses of the MRE-based vibration absorber

Adaptively Tunable Magnetorheological Elastomer-Based Vibration Absorber for a Propeller Aircraft Seat

Magnetic anomaly detection (MAD) is an important means of detecting the existence and localization of magnetic targets [1-2]. With the improvement of magnetic sensor technology, MAD has very large application prospects [3]. The traditional magnetic signal processing method cannot greatly improve the SNR (signal-to-noise ratio) while also restoring the target’s characteristic [4]. Our research about Full Magnetic Gradient Orthonormal Basis Function [5] solves the problems of the low SNR of the magnetic anomaly signal, the influence of the sway of the magnetic gradiometer platform. But it can only detect the existence of the target and cannot obtain the characteristics of the target. In this paper, based on the full magnetic gradient tensor which contains huge spatial magnetic field information, we analyze the factor of each component in the target magnetic abnormal signal. A target’s moment direction estimation method has been proposed, the flowchart is shown in Fig. 1(a). This method can estimate the target magnetic moment direction in 3-D Cartesian coordinates with a resolution of 30°. We have simulated 100 sets of targets with different magnetic moment sizes and distances, and the accuracy of the estimation of the target magnetic moment direction is 100% (Fig.1 (b)). The SNR is increased by 25.8 times on average (Fig.1 (c)). We put the magnetic moment of the target in 6 different directions and conducted 10 experiments in each direction (Fig.2 (a)). The original signal and the processed signal are shown in Fig. 2(b). The accuracy of the target magnetic moment estimation and the improvement of the SNR are shown in Fig. 2(c). Compared with the traditional signal processing method, the proposed method can estimate the magnetic moment direction of the target while greatly improving the SNR and the performance is not affected by the shaking of the sensor carrier. These are very helpful properties for the fast and large-scale detection of magnetic anomalies, such as aeromagnetic prospecting, medical micro-robot positioning.

![](https://assets.underline.io/uploads/markdown_image/1/image/bf68a5cc9966d2332fdd9e999ddbe513.jpg)

Fig.1. (a) Flowchart. (b) Accuracy of simulation experiment. (c) SNR after processing

![](https://assets.underline.io/uploads/markdown_image/1/image/2bca62b102c9aba3182ee4d796ca8b0e.jpg)

Fig.2. (a) Experimental device. (b) Original and processed signal. (c) Result of field experiment.

Magnetic Moment Direction Estimation Method Based on Full Magnetic Gradient Orthonormal Basis Function

Chiral molecules are the building blocks of most biomolecules and underlie many biochemical processes. A novel phenomenon called Chirality Induced Spin Selectivity (CISS) has emerged in recent times wherein electron polarization in chiral molecules translates to spin polarization [1]. It has been observed in DNA, proteins etc.[2]. Due to lack of inversion symmetry in chiral molecules a Rashba type spin orbit coupling (SOC) arises, which causes spin-filtering in chiral molecules. Here, we seek to model CISS in a 2-D channel material with a square lattice within the NEGF formalism, by adding an imaginary component originating from SOC to the Hamiltonian. This is motivated by the idea of chiral artificial receptors for enantioselective electronic noise sensors, capable of distinguishing between enantiomers [3]. The channel, assumed to be chiral, has a chiral electric field from the atoms present, the direction of which is used to probe the chirality of the channel. The chiral molecules break structure inversion symmetry but preserve time reversal symmetry, and so to break the degeneracy of the electrons a direction of propagation must be chosen [4]. The results in Fig. 2 show us that on selecting a direction of propagation by applying a bias we do get a particular spin polarization. The polarization gets reversed on changing the chirality of the channel. The spin polarization in the 2-D channel attests to its chiral nature, which can be utilized to sense chiral molecules. In an attempt to explore CISS in another work, we have included CISS into electron-phonon coupling and studied its effect on inelastic electron tunneling.

![](https://assets.underline.io/uploads/markdown_image/1/image/14fc154d8c83a7e59b3ee6140fbeac08.jpg)

Fig. 1(a) A 2D channel with the spin-orbit coupling; γ is the on-site energy βx, βy are the nearest neighbour coupling in x and y direction respectively. (b) The mirror image of the chiral field used to probe the chirality in the channel.

![](https://assets.underline.io/uploads/markdown_image/1/image/cebc1edc4387fb3cf5bf284472d85f70.jpg)

Fig. 2(a) The transmission of up-spin and down-spin electrons in the channel of right-handedness. The spin polarization in the channel due to difference in the up-spin and down-spin transmission, P= (Tup – Tdown )/(Tup + Tdown), P reverses on changing the chirality.(b) The plot of electron concentration in the channel (sign implies the spin of the electron).

Chirality Induced Spin Selectivity in a 2D Chiral Channel

Abstract—Since the circumferential and axial widths of permanent magnet (PM) pole and stator pole are very sensitive to the back electromotive force (EMF) of linear rotary PM motor with E-shape stator, it is difficult to obtain the optimization value by the traditional design method. The flux calculated model is built and the main flux and side flux variation laws of stator pole are derived by the Schwarz Christoffel method. The analyzed results are consistent with the results analyzed by 3-D finite element method. I.Introduction The calculation of the magnetic field distribution is very important in the motor design. The subdomain method and separation of variables method can be used to calculate the magnetic flux density of slotless segmented-Halbach permanent magnet (PM) synchronous machine and single-cage induction machines [1][2], respectively. The flux calculation model of a linear rotary PM machine (LRPMM) with E-type stator (ES) structure is built by Schwarz Christoffel method (SCM), which can consider the side flux of the stator pole in circumferential and axial directions. II.Flux Calculation in the E-shape Stator pole of ES-LRPMM Fig. 1 shows the topology of ES-LRPMM. SCM is used to obtain the main flux and side flux of the stator pole by building finite-depth and infinite-depth stator slot models of the E-shape stator. Then the flux variation laws of stator pole are derived. Fig. 2 shows the main flux and side flux waveforms. It is seen that the angular velocity of the flux is equal to the angular velocity of the mover while it works in rotary motion, and it is equal to three times of the angular velocity of the mover when it works in linear motion. III.Conclusion In order to reduce the difficulty of the optimization of ES-LRPMM, the flux in the E-shape stator section is analyzed by SCM and the variation law of the flux is deduced and concluded. Taking the cogging torque, detent force, torque and thrust as the optimization objectives, the optimum value of the motor structure is obtained.

![](https://assets.underline.io/uploads/markdown_image/1/image/cd229eb1710e4141e3ba817a05decf7b.jpg)

Fig. 1. Topology of ES-LRPMM


![](https://assets.underline.io/uploads/markdown_image/1/image/2d693b0b9002015642773ceacf064ff5.jpg)

Fig. 2. Main and side flux waveforms, (a) main flux, and (b) side flux of phase A compared with the sum of phase A, D, G stator side flux when it works in rotary or linear motion.

Flux Analytical Calculation in the E-shape Stator Pole of Linear Rotary Permanent Magnet Motor

The wound rotor synchronous machine (WRSM) constitutes a good alternative to PM synchronous machines for electric vehicles propulsion [1,2]. In the design optimization of electric vehicle traction motors a variety of operating points are required when considering the whole vehicle driving cycles [3]. To decrease the CPU time of such an optimization, we present a 2D analytical electromagnetic model of a WRSM capable of predicting airgap field harmonics in order to consider cost functions such as torque ripple and radial force harmonics. This paper proposes: 1 - A linear analytical method for magnetic field calculation in the air gap of WRSM including rotor slotting effect. The analytical method is based on the resolution of Laplace’s and Poisson’s equations in polar coordinates by separation of variables in low permeability subdomains [4]. A magnetic vector potential formulation is adopted. A 2D view of the model is shown in Figure 1 where the stator is represented by an equivalent current sheet. The iron material has an infinite permeability, so the PDEs are solved in the slot carrying a dc coil (region I), the slot opening (region II) and the air gap (region III). In each subdomain, the solution is written as a Fourier series whose coefficients are calculated using boundary conditions and continuity conditions between the different subdomains (normal flux density and tangential magnetic field). 2- A comparison between the analytical and the finite element [5] radial flux density distribution along a circle in the middle of the air gap under load condition and with the same assumptions is shown in Figure 2. The agreement is very good. The analytical computation takes 40 ms while the finite element solution requires 1.3 s. Hence, the analytical model is a very efficient tool to perform WRSM optimization on a driving cycle. In the extended paper, more details regarding the electromagnetic model, further comparison with FE results and the model limit with respect to magnetic saturation, will be given. Furthermore, a thermal model of the machine will serve to evaluate the winding temperatures. Hence, a coupled magneto-thermal optimization on a driving cycle will be presented and largely analyzed.

![](https://assets.underline.io/uploads/markdown_image/1/image/ebcd88fa4091ff06fcb32499dd2c1288.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/cefd69af3e60b2ecf8df59dcf8a7be45.jpg)

Analytical Model of Wound Rotor Synchronous Machine for Electric Vehicle Traction

**Authors list:** 
Guannan Wei, Daniel Lordan, Ansar Masood, Paul McCloskey 

Tyndall National Institure, Cork, Ireland 


**Abstract body:** A series of different thicknesses of amorphous magnetic CoZrTaB films were deposited on Si-substate. Strip domain structures induced secondary peak show up in high frequency imaginary permeability spectra when thicknesses increased to above 100 nm. In order to verify this, biased in-plane magnetic fields was applied during high frequency permeability measurement to eliminate strip domain structure, and at the same time the secondary peak was observed to disappear. Furthermore, OOMMF simulations were done to study strip domain induced high frequency imaginary permeability spectra. As strip domain became wider, the blue shift of the secondary peak shows up in consistent with measurement results.
**References:** 1-Z. Tang, H. Ni, and B. Lu. Journal of Magnetism and Magnetic Materials, Vol. 426, P.444 (2017) 
2-S. Ha, J. Yoon, and S. Lee, Journal of Applied Physics, Vol. 105, P.07D544-1 (2009). 
3- V, Gehanno, R. Hoffmann, and Y. Samson, The European Physical Journal B, Vol. 10, P. 457 (1999). 

![](https://assets.underline.io/uploads/markdown_image/1/image/72e85dd3e96d7a37468a4c8cf94dcfee.png) 
Fig.1 
![](https://assets.underline.io/uploads/markdown_image/1/image/81043aabbc89851b5b47578f763bd6d2.png) 
Fig.2

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