Semi-analytical Method For Calculation Research Articles

A 3D Semi-analytical Calculation Method for a Slotless PMSM with End-wrapped FPCB Concentrated Winding

A 3D Semi-analytical Calculation Method for a Slotless PMSM with End-wrapped FPCB Concentrated Winding

Non-volatile MWIR/LWIR beam reconfigurability with all-dielectric metagratings comprising phase-change materials with a high-refractive-index shift

We propose an all-dielectric grating paradigm comprising an optical-phase-change-material (O-PCM), functional in the 5 μm to 10 μm spectral range. This system leverages the capabilities of a newly-discovered O-PCM [Nat. Comm. 10, 4279 (2019)10.1038/s41467-019-12196-4], Ge2Sb2Se4Te1, which can be reliably switched between amorphous and crystalline phases at larger thicknesses close to 1 μm, while exhibiting a high-refractive-index shift of about 1.5 and no optical loss in this spectral range. The amorphous-O-PCM grating predominantly responds as an effectively homogeneous slab, letting light through without perturbing its path. The crystalline-O-PCM grating supports leaky Floquet-Bloch modes, which, at certain wavelengths, can simultaneously interfere destructively into the primary light path and constructively into the back-bent diffraction channel, in transmission. This “accidental” interference effect steers the incident beam in the negative direction. At a slightly detuned wavelength, the output power can be evenly split between the primary light path and the back-bent diffraction channel. Hence, our all-dielectric O-PCM-based metagrating can function as a platform for non-volatile reconfigurable beam steering and splitting. We have designed the metagrating paradigm and predicted its reconfigurable behavior with a semi-analytical calculation method and then verified it with a numerical first-principles experiment. We believe these results are relevant to MWIR/LWIR applications, but can also inspire new means for programmable and reconfigurable photonics across the spectrum as new O-PCMs are being developed.

Extreme Double/Triple Asymmetric Epitaxial Structure Based Diode Lasers for High Powers and High Efficiencies

In edge-emitting high power laser diodes, the longitudinal spatial hole burning (LSHB) effect induced by the inhomogeneous photon and carrier distributions and the non-linear process, two-photon absorption (TPA), are demonstrated to the key causes of power saturation at the high injection level even in the absence of thermal roll-over. Laser diodes based on extreme, double/triple asymmetric (EDAS/ETAS) epitaxial structures show great potentials in high-power and high-efficiency applications owing to the reduced series resistance, low optical loss, and suppressed power saturation. In this paper, a novel semi-analytical calculation method is proposed to systematically analyze the impact of LSHB and TPA effects on the output characteristics of EDAS/ETAS-based broad area lasers (BALs). By leveraging the feature that it is flexible to adjust the confinement factor of ETAS epitaxial structure without compromising the internal loss and resistance level, the laser parameters are first optimized to minimize power saturation of ETAS-based BALs under pulsed and Continuous Wave (CW) operation.

A time-saving method to evaluate the thermal insulation performance of cryogenic vessels

Equivalent mass loss is a critical index used to evaluate the thermal insulation performance of cryogenic vessels. The current test standards for measuring the thermal insulation performance of cryogenic vessels in different countries require a long testing time and waste a considerable amount of working medium. In this study, a method that can shorten the test time of the thermal insulation performance of cryogenic vessels is established. Different from the current test methods that rely entirely on experiments, the method proposed in this paper is a semi-experimental and semi-analytical calculation method. The proposed method is based on the one-dimensional heat transfer analysis of a cryogenic vessel and short-term experimental test data, and it can be used to predict the mass loss over a long period of time. Moreover, the method can predict the mass loss of a cryogenic vessel at a high liquid level when the mass loss at a low liquid level is known. When this method is used to predict the mass loss, the comparison with the experimental data shows that the maximum relative error of the instantaneous mass flow is 21.1% and the relative error of the cumulative mass flow is less than 8%. When this method is used for the calculation of heat leakage between different liquid levels, the results show that the larger the difference between the two liquid levels, the greater the error of leakage heat, and the maximum is 18.9%.

Semi-Analytical Solution of Magnetic Force and Torque for a Novel Magnetically Levitated Actuator in Rotary Table

This article proposes a fast and accurate semi-analytical calculation method of magnetic force and torque in the magnetically levitated rotary table. Benefited from the high computation efficiency and accuracy, the solution is suitable for the optimization and real-time control of the magnetically levitated system. Different with the existing harmonic method for modeling the magnetic field produced by the circular magnet array in the rotary table, the gaps in circular permanent magnet array are taken into account for the force and torque computation in this article. With the obtained magnetic flux density distribution, the magnetic force and torque can be acquired via the coordinate transformation and Lorenz integral law. Then, the numerical integral method is used to calculate the exact results of complex Lorentz integrals. Finally, the effectiveness and accuracy of the semi-analytical solution are verified by a boundary element software named Radia. Compared with the existing solutions, the new semi-analytical method is more accurate and suitable for the magnetically levitated actuator in the rotary table.

Semi-Analytical Method for g-Function Calculation of bore fields with series- and parallel-connected boreholes

A semi-analytical method for the calculation of g-functions of bore fields with mixed arrangements of series- and parallel-connected boreholes is presented. Borehole wall temperature variations are obtained from the temporal and spatial superposition of the finite line source (FLS) solution. The FLS solution is coupled to a quasi-steady-state solution of the fluid temperature profiles in the boreholes, considering the piping connections between the boreholes. The dimensionless borehole wall temperatures in the bore field and the inlet fluid temperature are obtained from the simultaneous solution of the heat transfer inside and outside the boreholes. The effective borehole wall temperature (i.e., the g-function) is defined based on the dimensionless inlet fluid temperature and a newly introduced effective bore field thermal resistance. The g-function evaluation method is validated against the DST model and its use is demonstrated in a sample simulation of a seasonal thermal energy storage system.

A Semi-Analytical Method for Calculation of Strongly Nonlinear Normal Modes of Mechanical Systems

A new scheme based on the homotopy analysis method (HAM) is developed for calculating the nonlinear normal modes (NNMs) of multi degrees-of-freedom (MDOF) oscillatory systems with quadratic and cubic nonlinearities. The NNMs in the presence of internal resonances can also be computed by the proposed method. The method starts by approximating the solution at the zeroth-order, using some few harmonics, and proceeds to higher orders to improve the approximation by automatically including higher harmonics. The capabilities and limitations of the method are thoroughly investigated by applying them to three nonlinear systems with different nonlinear behaviors. These include a two degrees-of-freedom (2DOF) system with cubic nonlinearities and one-to-three internal resonance that occurs on nonlinear frequencies at high amplitudes, a 2DOF system with quadratic and cubic nonlinearities having one-to-two internal resonance, and the discretized equations of motion of a cylindrical shell. The later one has internal resonance of one-to-one. Moreover, it has the symmetry property and its DOFs may oscillate with phase difference of 90 deg, leading to the traveling wave mode. In most cases, the estimated backbone curves are compared by the numerical solutions obtained by continuation of periodic orbits. The method is found to be accurate for reasonably high amplitude vibration especially when only cubic nonlinearities are present.

Computationally Efficient Analysis of Double PM-Rotor Radial-Flux Eddy Current Couplers

In this study, a semianalytical calculation method for obtaining 3-D solutions for the torque of radial-flux permanent magnet eddy current couplers is presented. In this way, the use of computationally expensive transient 3-D finite element solutions is avoided, which is very important when it comes to the design optimization of these machines. The proposed analytical method takes the effect of flux density harmonics into account. The 3-D end-effects are taken into account by using Russell's coefficient. The accuracy of the proposed semianalytical calculation method is evaluated against extreme variation of machine dimensions. The Russell end-effect factor is evaluated and found to be inaccurate for axially short and radially large couplers. A prototype coupler with different conductors was tested to validate the proposed semianalytical torque calculation method.

The Stiffness Field Modeling and Analyzing of Tool Position and Orientation of Five-Axis NC Machining System

The transformation of tool position and orientation has impact on processing performance of the system when processing complex surface. Five-axis NC machine center was taken for example in this article. Semi-analytical calculation method was taken for stiffness field of system. Based on virtual-work principle, the composite stiffness field modeling of system was built by methods of Jacobian matrix, point transformation matrix and finite element, etc. For the key point of workpiece surface which is needed analyzed, 3D space force ellipsoid was introduced, composite stiffness field was modeled and composite stiffness performance of system was analyzed by force ellipsoid with different tool position and orientation. Guiding conclusion was obtained for following works by analyzing influence of tool position and orientation on stiffness performance.

Response sensitivity analysis of the dynamic milling process based on the numerical integration method

As one of the bases of gradient-based optimization algorithms, sensitivity analysis is usually required to calculate the derivatives of the system response with respect to the machining parameters. The most widely used approaches for sensitivity analysis are based on time-consuming numerical methods, such as finite difference methods. This paper presents a semi-analytical method for calculation of the sensitivity of the stability boundary in milling. After transforming the delay-differential equation with time-periodic coefficients governing the dynamic milling process into the integral form, the Floquet transition matrix is constructed by using the numerical integration method. Then, the analytical expressions of derivatives of the Floquet transition matrix with respect to the machining parameters are obtained. Thereafter, the classical analytical expression of the sensitivity of matrix eigenvalues is employed to calculate the sensitivity of the stability lobe diagram. The two-degree-of-freedom milling example illustrates the accuracy and efficiency of the proposed method. Compared with the existing methods, the unique merit of the proposed method is that it can be used for analytically computing the sensitivity of the stability boundary in milling, without employing any finite difference methods. Therefore, the high accuracy and high efficiency are both achieved. The proposed method can serve as an effective tool for machining parameter optimization and uncertainty analysis in high-speed milling.

A semi-analytical calculation method of bending loss for large-mode-area fibers with arbitrary refractive-index profile

Predicting mode-dependent bending loss is important for large-mode-area (LMA) fibers to strip out unwanted modes. In order to seek a reasonable calculation method, a new bending loss formula that allows for both mode field distortion and weaker mode confinement was derived in detail. Based on the formula, a semi-analytical method was introduced to calculate the mode bending loss for LMA fibers. By combining the applications of the finite element method, discrete Fourier transforms and numerical integral, the method is valid for LMA fibers with arbitrary refractive index profile. The obtained loss characteristics are basically consistent with the previous results. This accordance demonstrates the feasibility and generality of the semi-analytical method.

Radiation- and Bound-Mode Propagation in Rectangular, Multimode Dielectric, Channel Waveguides With Sidewall Roughness

This paper calculates and displays accurate radiation modes for rectangular, multimode dielectric, channel waveguides, for the first time, and introduces the new semianalytical calculation method used to find them, the radiation-mode Fourier decomposition method (RFDM), which is an extension of the Fourier decomposition method (FDM) for finding bound propagating modes. The optimum choice of non-linear conformal transformation parameters is discussed for achieving highest accuracy. Once the radiation modes are known, the coupling coefficients can be found between the bound and radiation modes, as well as those between the bound modes themselves, andhence, the propagation loss can be found. The paper adapts Marcuse's coupled power theory, for the first time, to enable it to model propagation in rectangular, multimode dielectric, channel waveguides suffering from one dimensional sidewall roughness enabling the equilibrium distance to be calculated, at which rate of loss to radiation modes becomes constant, and to find that equilibrium propagation loss, and the dependence on the statistical properties of the wall roughness. This leads to the conclusion that at sufficient distance there exist two uncoupled modes, a symmetric and an asymmetric lowest order mode.

Polarization mode conversion in an optical microdisk resonator vertically coupled to a waveguide bus

Due to the existence of non-zero, and asymmetrics cross-polarization coupling coefficients between a microdisk and a waveguide bus, high Q (∼10,000) overcoupled microdisks with minimal internal losses and sharp bending curvature (small radii) vertically coupled to a narrow-width ridge waveguide can be engineered as a proper candidate for a narrow-band polarization rotator. A semi-analytical calculation method is presented to realize microdisk–waveguide system as a polarization rotator.

Molecular polarizability in quantum defect theory: Non-polar molecules

The Green function in the quantum defect theory provides an exact account for the high-excited and continuum electronic states. We modify it by taking into account the ground and low-excited states using their wavefunctions calculated ab initio. As an application we present simple and efficient semi-analytical method for calculation of dynamic polarizabilities of nonpolar molecules. The method is applied to alkali dimers Li$_{2}$, Na$_{2}$ and Rb$_{2}$. The result of benchmark calculation (H$_{2}$ molecule) are in good agreement with experimental data; the accuracy achieved is comparable with that of ab initio calculations. We also calculate Verdet constants of the above molecules in Becquerel approximation.

Semi-Analytical Method for Calculating the Elliptic Restricted Three-Body Problem Monodromy Matrix

R ECENT years have seen a rising interest in launching unmanned spacecraft into libration-point orbits for scientific missions. Past missions such as ISEE-3, SOHO, and Genesis successfully used quasiperiodic orbits about the L1 and L2 collinear libration points of the sun–Earth system. With the embarkation of future NASA and ESA missions such as Darwin, Terrestrial Planet Finder (TPF), and Single Aperture Far Infrared Observatory (SAFIR), to be launched into libration-point orbits, there is an opportunity to design and evaluate novel trajectory planning, simulation, and control schemes. In practical analysis and design of missions around libration points, the circular restricted three-body problem (CR3BP) model is usually adopted [1–4]. Although this model has proven fruitful, it possesses an inherent approximation, assuming that the orbits of the primaries are circular. However, both the motion of the Earth around the sun and the motion of moon around the Earth are eccentric. Incorporating the eccentricity term into the equations of motion renders a more general model, known as the elliptic restricted threebody problem (ER3BP). The ER3BP has significant topological differences compared with the CR3BP. For example, the position of the libration points is not constant, but rather pulsatingwith respect to Earth. Moreover, the Jacobi integral is time(true-anomaly-) dependent. Several works have addressed the problem of finding natural periodic orbits in the planar ER3BP based on specialized regularizations [5,6]. Derivation of such orbits through numerical searches was accomplished in [7,8]. Almost all methods for calculating orbits about the collinear libration points require the monodromy matrix, which is the state-transition matrix evaluated at the orbital period. Moreover, design of stationkeeping maneuvers, whether impulsive [9] or continuous [10], also requires the monodromy matrix. Although the evaluation of the monodromy matrix in the CR3BP is trivial, the problem is more involved in the more general setup of the ER3BP, because the linearized system is nonautonomous. In fact, the linearized system is linear parameter-varying (LPV) and periodic, exhibiting implicit dependence upon time through the true anomaly. It is therefore important to develop reliable algorithms for computing the monodromy matrix. In this work, we develop a new, semianalytical method for calculation of the monodromy matrix. We propose to expand the state-transition matrix into orthogonal Chebyshev polynomials of the first and second kind, shifted to fit the time interval in use. The Chebyshev approximation transforms the nonautonomous differential equations required to calculate the state-transitionmatrix into a set of algebraic equations. This approach can be used as a computationally efficient scheme for computing the state-transition matrix and as a simple check for verifying the accuracy of monodromymatrix calculations using a direct numerical integration.

Shot noise of single-electron tunneling in one-dimensional arrays

We have used numerical modeling and a semi-analytical calculation method to find the low frequency value S_{I}(0) of the spectral density of fluctuations of current through 1D arrays of small tunnel junctions, using the ``orthodox theory'' of single-electron tunneling. In all three array types studied, at low temperature (kT << eV), increasing current induces a crossover from the Schottky value S_{I}(0)=2e<I> to the ``reduced Schottky value'' S_{I}(0)=2e<I>/N (where N is the array length) at some crossover current I_{c}. In uniform arrays over a ground plane, I_{c} is proportional to exp(-\lambda N), where 1/\lambda is the single-electron soliton length. In arrays without a ground plane, I_{c} decreases slowly with both N and \lambda. Finally, we have calculated the statistics of I_{c} for ensembles of arrays with random background charges. The standard deviation of I_{c} from the ensemble average <I_{c}> is quite large, typically between 0.5 and 0.7 of <I_{c}>, while the dependence of <I_{c}> on N or \lambda is so weak that it is hidden within the random fluctuations of the crossover current.