Unequal Width Research Articles

The performance of restricted AIC for irregular histogram models.

Histograms are frequently used to perform a preliminary study of data, such as finding outliers and determining the distribution's shape. It is common knowledge that choosing an appropriate number of bins is crucial to revealing the right information. It's also well known that using bins of different widths, which called unequal bin width, is preferable to using bins of equal width if the bin width is selected carefully. However this is a much difficult issue. In this research, a novel approach to AIC for histograms with unequal bin widths was proposed. We demonstrate the advantage of the suggested approach in comparison to others using both extensive Monte Carlo simulations and empirical examples.

Three-sensor 2ω method with multi-directional layout: A general methodology for measuring thermal conductivity of solid materials

Anisotropic thermal transport plays a key role in both theoretical study and engineering practice of heat transfer, but accurately measuring anisotropic thermal conductivity remains a significant challenge. To address this issue, we propose the three-sensor 2ω method in this study, which is capable of accurately measuring the isotropic or anisotropic thermal conductivity of solid materials. In this method, several three-sensor groups following the design guidelines are fabricated upon the sample along different characteristic directions, and each group consists of three parallel metal sensors with unequal widths and distances optimally designed based on sensitivity analysis. Among the three sensors, the outer two serve as AC heaters and the middle one as a DC detector. The 2ω voltage signals across the detector in each three-sensor group are measured, and then the data are processed by the proposed Intersection Method to derive thermal conductivities along directions of interest. The application of the detector's 2ω instead of the heater's 3ω voltage signals eliminates errors introduced by the uncertainties of thermal resistance in superficial structures (metal layer, insulation layer, interface, etc.). Meanwhile, by replacing the fitting algorithm with the Intersection Method, the local optimum trap of multivariate fitting is avoided. To verify the accuracy and reliability, four typical monocrystalline semiconductors, i.e., Si, GaN, AlN, and β-Ga2O3, are measured, and the results are consistent with the literature. This method will provide a comprehensive and versatile solution for the thermal conductivity measurements of solid materials.

Heat transfer in a vertically integrated semiconductor device with unequal layer widths

Vertically integrated semiconductor devices and interposer-based heterogeneous integration technologies are being commonly investigated for advanced microelectronic chips. Such multilayer structures often integrate layers of unequal lateral sizes. While most of the past literature on thermal modeling of multilayer semiconductor chips considers layers of uniform widths, heat transfer in multilayer systems with unequal widths orthogonal to the thickness direction has not been investigated much. This remains an important challenge towards effective thermal management of vertically integrated ICs and other semiconductor chips. This work presents an analytical model to determine the temperature distribution in a multilayer device with unequal layer widths. A series solution for temperature distribution in each layer is derived, with an independent set of eigenvalues for each layer. The coefficients of the series solutions are determined through the derivation of a set of linear algebraic equations in the coefficients. Results are found to be in good agreement with numerical simulations, and also agree well with past work for special cases. An analysis of the impact of unequal widths on heat transfer and temperature distribution is presented. It is shown that the lower the ratio of the layer widths, the greater is the peak temperature. On the other hand, layer thickness is found to have an interesting, non-monotonous impact on peak temperature, which is explained on the basis of the two-dimensional nature of heat transfer in this problem. It is found that for a representative SiGe-Si device, peak temperature increases by around 9% as the SiGe layer width is reduced to one-third compared to a baseline equal width case. The novelty of the present work is that it presents the thermal modeling of an important multilayer semiconductor architecture, which has not been addressed much in the past. Results presented here may help improve the thermal design of vertically integrated semiconductor devices and other similar multilayer devices.

Synthesis of Wideband All-Frequency Absorptive Filtering Power Divider with High Selectivity and Flat Output Port Distributions

In this paper, a wideband absorptive filtering power divider (AFPD) which features the characteristics of high selectivity and flat output distributions is proposed. It is composed of one unequal width three-coupled line (TCL), two coupled lines (CLs), two stepped open-circuited stubs, two kinds of isolation resistors, and two types of absorptive branches. The design equations of the proposed AFPD are derived using an even-odd decomposition method, and parametric investigations are also performed. It is found that the passband bandwidth can be adjusted by the stepped open-circuited stub which generates two transmission zeros (TZs). By combining the TCL with the CLs, the passband bandwidth is effectively enlarged. In addition, two isolated resistors are utilized for achieving good isolation and output-port matching performance. Without affecting the passband responses, the input port absorptive feature within the whole frequency band can be obtained by loading the absorptive branches both on the input and output ports. For validation, an example operating at the center frequency of 2 GHz was modeled and tested. Results exhibit that the passband FBW reaches 72% under 1 dB criterion, which illustrates flat output port distributions. In addition, for 10 dB return loss, the input and output impedance matching bandwidths are 250% and 78%, respectively. The features of good filtering responses are demonstrated by realizing the rectangle coefficient of 1.24 and the out-of-band suppression of more than 20 dB.

Thrust Ripple Reduction of Dual-Side Toroidal-Winding Linear Permanent Magnet Vernier Machine by Unequal End-Teeth Width

The linear permanent magnet vernier machines have attracted more and more attention last several years due to its high thrust density at low speed, which is very suitable for the direct-drive applications. A dual-side toroidal-winding linear permanent magnet vernier machine (DSTWLPMVM) with the unequal end-teeth width is proposed in this paper to reduce the detent force and thrust ripple. The low detent force in DSTWLPMVM is achieved by combination of two single-side detent forces with the opposite phase angle, which is obtained by optimizing the unequal end-teeth width of the primary two-sides. In the proposed machine, the symmetry three-phase flux linkage of the toroidal winding also can be obtained by optimizing the unequal end-teeth width. Therefore, the low thrust ripple of DSTWLPMVM is achieved by optimizing the unequal end-teeth width for obtaining the low detent force and symmetry three-phase flux linkage. The vertical magnetic force in the proposed LPMVM is also considered by finite element analysis (FEA) in this paper. Via optimizing the unequal end-teeth width, the detent force is reduced by 90% while the peak-to-peak thrust ripple is reduced by 69% than that of DSTWLPMVM with the equal end-teeth width, respectively. In this paper, the thermal and PM demagnetization behavior of the proposed machine are also analyzed by FEA.

Positioning Method of Four-Wheel-Steering Mobile Robots Based on Improved UMBmark of Michigan Benchmark Algorithm

To reduce the error of the odometer positioning system and improve the positioning accuracy of four-wheel-steering mobile robots, three types of coupling errors are considered, based on the University of Michigan Benchmark (UMBmark) method: unequal track width, unequal wheel diameter, and speed difference of ipsilateral wheels. A “dual direction square path experiment” is designed to decouple the error, a new system error model is defined, and an improved UMBmark method for a four-wheel mobile robot is proposed. In the mobile robot positioning system, a laser tracker is used to measure the absolute positions of the starting and ending points of the robot. The positioning test results of the robot using the improved UMBmark method show that the odometer system error is 69.103 mm, which is 2.6 times less than that in the traditional UMBmark method. Hence, the improved UMBmark can better compensate for the system error of four-wheel-steering mobile robots.

Three-sensor 3ω-2ω method for the simultaneous measurement of thermal conductivity and thermal boundary resistance in film-on-substrate heterostructures

Solid heterostructures composed of substrates and epitaxial films are extensively used in advanced technologies, and their thermophysical properties fundamentally determine the performance, efficiency, and reliability of the corresponding devices. However, an experimental method that is truly appropriate for the thermophysical property measurement of solid heterostructures is still lacking. To this end, a three-sensor 3ω-2ω method is proposed, which can simultaneously measure the thermal conductivities of the film and the substrate, along with the film-substrate thermal boundary resistance (TBR) in a single solid heterostructure without any reference samples, showing broad applicability for miscellaneous heterostructures with film thickness ranging from 100 nm to 10 μm. In this method, three parallel metal sensors with unequal widths and distances conforming to guidelines for the three-sensor layout design are fabricated on the sample surface, in which the two outer sensors serve as heaters and the middle sensor as a detector. The respective 3ω signals of the two heaters and the 2ω signal of the detector are measured, and then the thermophysical properties of the sample are fitted within 3D finite element simulations. To verify this method, two typical wide bandgap semiconductor heterojunctions, i.e., GaN on SiC (#SiC) and GaN on Si (#Si) with ∼2.3 μm GaN epilayers, are measured. The thermal conductivity of the GaN film, the thermal conductivities of the SiC and Si substrates, and the GaN/substrate TBRs are derived, exhibiting good agreement with the literature. The proposed method will provide a comprehensive solution for the thermophysical property measurements of various solid heterostructures.

Influence of Electrostatic Force Nonlinearity on the Sensitivity Performance of a Tapered Beam Micro-Gyroscope Based on Frequency Modulation.

Electrostatic force nonlinearity is widely present in MEMS systems, which could impact the system sensitivity performance. The Frequency modulation (FM) method is proposed as an ideal solution to solve the problem of environmental fluctuation stability. The effect of electrostatic force nonlinearity on the sensitivity performance of a class of FM micro-gyroscope is investigated. The micro-gyroscope consists of a tapered cantilever beam with a tip mass attached to the end. Considering the case of unequal width and thickness, the motion equations of the system are derived by applying Hamilton's principle. The differential quadrature method (DQM) was used to analyze the micro-gyroscope's static deflection, pull-in voltage, and natural frequency characteristics. We observed that from the onset of rotation, the natural frequencies of the drive and sense modes gradually split into a pair of natural frequencies that were far from each other. The FM method directly measures the angular velocity by tracking the frequency of the drive and sense modes. Then, based on the linear system, the reduced-order model was used to analyze the influence of the shape factor and DC voltage on the sensitivity performance. Most importantly, the nonlinear frequency of system was obtained using the invariant manifold method (IMM). The influence of electrostatic force nonlinearity on the performance of the FM micro-gyroscope was investigated. The results show that the different shape factors of width and thickness, as well as the different DC voltages along the drive and sense directions, break the symmetry of the micro-gyroscope and reduce the sensitivity of the system. The sensitivity has a non-linear trend with the rotation speed. The DC voltage is proportional to the electrostatic force nonlinearity coefficient. As the DC voltage gradually increases, the nonlinearity is enhanced, resulting in a significant decrease in the sensitivity of the micro-gyroscope. It is found that the negative shape factor (width and thickness gradually increase along the beam) can effectively restrain the influence of electrostatic force nonlinearity, and a larger dynamic detection range can be obtained.

A Hybrid Pulse Frequency Modulation Control Strategy for L-LLC Resonant Converter

The traditional control strategy for the L-LLC resonant converter is the synchronous unequal width pulse frequency modulation (SUW PFM). However, this strategy causes a large circulating power in the forward buck and reverse boost modes, especially when the voltage gain deviates from 1. To solve the limitations of the SUW PFM, a novel constant width PFM (CW PFM) is proposed in this article, which can reduce the circulating power and improve the converter efficiency in the forward buck and reverse boost modes. Furthermore, a hybrid PFM control strategy is proposed by merging the appropriate working conditions of the CW PFM and the SUW PFM, which can flexibly switch the two modulations depending on the gain and load conditions. Therefore, the L-LLC resonant converter has good soft-switching characteristics in entire load and gain ranges. Finally, a 7.5-kW L-LLC resonant converter prototype is built to verify the validity and superiority of the proposed control strategy.

An Updated CLUBB PDF Closure Scheme to Improve Low Cloud Simulation in CAM6

AbstractCloud Layers Unified By Binormals (CLUBB) adopts the joint probability density function (PDF) to close higher‐order turbulence and diagnose the cloud fraction. CLUBB assumes the equal PDF width of vertical velocity () as the default closure scheme, called Analytic Double Gaussian 1 (ADG1). In this study, a new unequal width PDF closure scheme is adopted in CLUBB, in which the PDF width of is assumed to be associated with skewness and kurtosis of vertical velocity. Offline calculation shows that the updated closure scheme improves the tail in the joint PDF and produces the saturation area from the joint PDF of the total water and liquid water potential temperature closer to that derived from large‐eddy simulations than ADG1. The new PDF scheme implemented in Community Atmosphere Model Version 6 is shown to increase low cloud fraction by 20%–30% in most stratocumulus‐to‐cumulus transition regions. The updated closure scheme is found to improve the low cloud simulation by simulating more symmetric turbulence in stratocumulus and stronger turbulent transport in shallow cumulus. Furthermore, the updated closure scheme enhances the cloud fraction near the cloud base by interacting with the microphysical scheme. Our work indicates the importance of continuous improvement in the PDF closures for higher‐order turbulence schemes.

Quantum interference of electrons through electric-field-induced edge states in stacked graphene nanoribbons

In this work, we investigate, by means of numerical simulations, the quantum interference of electrons in stacked graphene structures consisting of two unequal width, armchair-edged graphene nanoribbons. Electronic states residing near the edges of the system are induced when an external electric field is applied normal to the ribbons. By reversing the direction of electric field in the central region, one can create an electronic analogue of the optical Fabry-Pérot (FP) interferometer. Electronic junctions formed at the boundaries between the central region and the left and right ones in the former play the role of the partially reflected mirrors in the latter. The observed conductance oscillations demonstrate that electrons in the edge states transporting through the system experience quantum interference similar to that of light waves passing through an optical FP interferometer. Moreover, electronic states formed at the junctions enhance inter-edge scattering which affects electron transmission significantly. The possibility to control electron transport via electric gates is also considered.

MAGNETOELECTRIC VALVE MOTORS WITH TOOTHED MULTI-POLE WINDINGS BASED ON 6DVM 300

The paper considers valve motors with toothed windings with pole numbers 2, 4, 6, 8, the main dimensions of which correspond to the 6DVM 300 valve motor manufactured by JSC “Cheboksary electrical apparatus plant”. This approach allows us to evaluate the effect of the number of stator teeth on the electromagnetic moment and its harmonic composition. The three adjacent coils of the toothed windings in question belong to three different phases. The paper analyzes the MMF of the windings and magnets of the rotor. The distribution of magnetic induction in the gap, the EMF of the stator winding and the electromagnetic moment are found based on the method of the specific magnetic conductivity of the gap. It is shown that the MMF curve of the stator winding consists of two multipolar rectangles of unequal height and width. Due to the non-sinusoidal distribution of magnetic field sources and the jagged inhomogeneity of the air gap, the curves of the phase EMF of the stator winding are also significantly non-sinusoidal. It is found that with an increase in the number of poles (from 2 to 8 poles) of the stator winding, the maximum induction in the air gap decreases from level 1 to 0.75 Tl, the average value of the electromagnetic moment increases from 120 to 160 Nm, the amplitude of the phase EMF remains unchanged, and the maximum (height of the rectangle) of the MMF of the stator winding is reduced from 2000 to 500 A.

Design optimization of double-sided PMLSM with unequal width Halbach magnet array

Double-sided permanent magnet linear synchronous motor (PMLSM) is used in high precision manufacturing system. Reducing the higher harmonic components of the air gap magnetic flux density can significantly suppress the thrust fluctuation of the linear motor. In this paper, an unequal width Halbach magnet array is proposed. The FEA results shows that the harmonic component can be reduced by the an unequal Halbach magnet array with center aligned. On this basis, the parameters of the permanent magnet poles are optimized based on finite element parametric scanning. The optimization results show that the thrust ripple can be reduced by 89.6% by minimizing the total harmonic component. The new configuration can effectively suppress thrust fluctuation without changing the square shape of the permanent magnet, and has the characteristics of simplicity, effectiveness and low cost.

Ultimate capacity of SHS X-joints made of normal and high-strength weathering steels

The aim of the current work is to study the static strength properties of welded tubular X-joints made of weathering steel. Quasistatic tensile and compression tests were carried out on welded tubular X-joints made of three weathering steel grades. The X-joints were manufactured from squared hollow section (SHS) tubes of 355WH, 500WH and 550WH weathering steel materials and prepared using gas metal arc welding with a LNM 28 solid wire (diam. 1 mm) as a welding consumable. Both joints with equal and unequal brace width to chord width (β = b1/b0) ratios were studied and a total number of 17 quasistatic tests on the X-joints were conducted, of which four specimens were tested in compression and 13 were tested in tension. In addition, flat coupon specimens were manufactured from the weld sections of the joints with the ratio of β = 1.0 for quasistatic testing, supported by the macrographical investigations, hardness measurement and scanning electron microscopy (SEM) analysis at the joint area. The obtained experimental ultimate capacities exceeded the design resistances for axially loaded joints as per the Eurocode 3 standard and the results thus indicated that the present standard can be used for design purposes of tubular joints made of weathering steels. The investigated high-strength weathering steel grades suffered from the strength reduction due to the welding and the limitations regarding heat inputs should be carefully considered.

Design considerations and stress analysis of helical gear drives with unequal and offset face widths

Design considerations and stress analysis of helical gear drives with unequal and offset face widths

Leftward Spatial Bias in Dialyzed Patients With End-Stage Renal Disease: A Sign of Right Hemispheric Attentional Activation or Impaired Left-Sided Disengagement?

In the horizontal line bisection task, patients with end-stage renal disease (ESRD) treated with dialysis typically have an increase in the normal leftward attentional bias. It is not clear, however, whether this increased bias is related to an increase of attention toward left hemispace or impaired disengagement from left-sided stimuli. Non-demented patients with ESRD who were being treated with dialysis and demographically matched healthy controls attempted to bisect series of horizontal lines composed of two segments of unequal length and width, with the longer segment placed to the right or left. To test for the presence of a global spatial attentional bias, participants attempted to find the middle of the whole line. To test for focal attentional engagement and attentional disengagement, participants were asked to bisect only the longer segment of these compound lines. For the global condition, both patients and healthy controls were biased toward the longer segment and more so to the left. In the focal condition, when the longer segment was on the right side, both groups deviated their bisections toward the shorter segment. However, when in the focal condition the longer segment was on the left healthy controls deviated their bisection significantly more rightwards than did the patients, whereas with the longer segment on the right, the patients and healthy controls did not differ in their bias. These results suggest that the previously recognized dysfunction of the right fronto-subcortical attentional network in dialyzed patients might account for the results of the current study.

New Design Topology of High-Q Factor Printed Base Antenna Having Unequal Width and Pitch Used for Near-Field Wireless Power Transmission

In this article, an unequal printed structure is proposed to obtain high quality factor ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -factor) coil antenna in wireless power transmission systems. In the resonance method wireless power transmission, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -factor is one of the important factors that determine the transmission efficiency. Generally, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -factor is increased by increasing the size of the resonator, but, through the structure presented in this article, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -factor can be maximized without changing the size. In addition, this method can improve the low <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -factor of the “printed antenna,” which was pointed out as a disadvantage. The main idea to achieve a high <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -factor is that pitch and width are not constant along the width. The line pitch and width of the printed pattern are gradually increased in proportion with the outer diameter. By using this design method, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -factor is increased about 21.8% in comparison with the conventionally designed antenna. In addition, it can be confirmed that the antenna performance is substantially superior to that of a typical coil antenna if the size conditions are the same.

Shannon entropy of asymmetric rectangular multiple well with unequal width barrier

We present the Shannon entropy of the Schrödinger equation with an asymmetric rectangular multiple well, in which the potential well width is equal but the barrier width is in an arithmetic sequence. When the confined potential is small, we notice that the wave function of the particle is distributed inside the entire interval, but its distribution is mainly confined inside the wells as the confined potential increases. For the higher excited state, we find that the magnitude inside the barrier is always bigger than that inside the well. However, in the double-well case the magnitude is the biggest in the leftmost second barrier for Vconf=1000 meV, but it is in the rightmost barrier in the triple well case. For large confined potential, the momentum entropy density (MED) will be concentrated to the center of the total rectangular multiple well with the increasing confined potential. Likewise, we see that the momentum entropy densities of the ground, first and second excited states are overlapped in the triple well case, but they are all overlapped in the four well case. Particularly, in the double well case, the position entropy densities of ground state and 2nd excited state as well as the 1st and 3rd excited states occupy each well. In the triple well case, however, the position entropy densities of ground state and 2nd excited state occupy each one of three wells, but the 1st and 3rd excited states occupy one of four wells. The position entropy density (PED) of each state in four well case is distributed in each well of them as the confined potential is very large. When the number of wells increases, there exist some additional oscillations in the PED. For the higher excited state, the oscillator frequency of the PED increases inside the well but decreases inside the barrier as the confined potential depth increases. For the lower states, as the potential well depth increases the MED extends outward from the original central distribution, but the main distribution is concentrated to the center of the total system for the higher excited state. We also note that both the position entropy Sx and the momentum entropy Sp do not decrease or increase as the parameter Vconf increases, but their sum always satisfies the BBM inequality.

Experimental Validations of Hybrid Excited Linear Flux Switching Machine

Linear Flux Switching Machines (LFSMs) possess the capability to generate adhesive thrust force, thus problems associated with conventional rotatory electric machines and mechanical conversion assemblies can be eliminated. Additionally, the unique features of high force/power density, efficiency, and a robust secondary structure make LFSMs a suitable candidate for linear motion applications. However, deficiency of controllable air-gap flux, risk of PM demagnetization, and increasing cost of rare earth PM materials in case of PMLFSMs, and inherent low thrust force capability of Field Excited LFSMs compels researchers to investigate new hybrid topologies. In this paper, a novel Double-Sided Hybrid Excited LFSM (DSHELFSM) with all three excitation sources, i.e., PMs, DC, and AC windings confined to short moving primary and segmented secondary providing short flux paths is designed, investigated, and optimized. Secondly, unequal primary tooth width optimization and additional end-teeth at all four corners of the primary equip proposed design with balanced magnetic circuit and reduced end-effect and thrust force ripples. Thirdly, the measured experimental results of the manufactured proposed machine prototype are compared with corresponding simulated model results and shows good agreements, thus validating the theoretical study.

Novel Millimeter-Wave Bandwidth-Controllable Filtering Antenna Based on Composite ESPPs-SIW Structure

A bandwidth-controllable filtering antenna based on composite effective surface plasmon polaritons (ESPPs)-substrate integrated waveguide (SIW) structure is presented. The composite ESPP-SIW structure can support ESPPs at some frequencies. The asymptotic characteristic of ESPPs is employed to form a bandpass filter, which consists of an SIW and an air cavity situated on the top of the SIW. The unequal widths and the different dielectrics of the cavity and the SIW are employed to provide flexible controllability on the dispersion of ESPPs and thus on the cutoff frequencies of the ESPPs-SIW structure. By engineering the structural dispersion of ESPPs, the filter based on ESPPs-SIW structure shows independent controllability on its cutoff frequencies and thus exhibits a controllable bandwidth. Moreover, from effective-medium aspect, an analytical method is provided to guide the filter design. The filter is used to construct a filtering antenna operating at 5G millimeter-wave (MMW). A prototype of the filtering antenna is fabricated by using multilayer printed circuit boards (PCBs). Simulated and measured results show a good skirt selectivity and flat antenna gain in the passband (22–28 GHz) and also a high suppression in the stable wide stopband (30–43 GHz).