Biquadratic Research Articles

Resonance provocation of improved energy orbit in bi-stable vibration energy harvesters for power enhancement

Bi-stable vibration energy harvesters are advantageous for a wide bandwidth in low frequency ranges, but are confronted with the issue of limited output power. Bi-stability traditionally contains two low- and high-energy orbits; however, this paper reports resonance provocation of the improved energy orbit, which is much higher than the traditional two energy orbits and can be utilized for power enhancement. Theoretically, the enhanced energy orbit is provoked due to an increase in the system’s kinetic energy, achieved by modifying the bi-stable potential energy function from quartic function to quadratic function to utilize the linear resonant restoring force. Experimental results demonstrate that the provocation of the improved energy orbit is frequency selective, and the root mean square voltage is increased by 63.6% in the upward sweep and 188.5% in the downward sweep. For optimal load, the improved energy orbit increases the maximal root mean square voltage by 2.10 times and the maximal average output power by 4.37 times. Meanwhile, the device’s bi-stable bandwidth remains almost unchanged. These results prove that the resonance provocation of the improved energy orbit can refine the power while not sacrificing bandwidth, which is a promising solution to the overall performance improvement for vibration energy harvesters.

Application of Approximate Maximum-Entropy Moment Closure to the Wigner Equation

This paper investigates the potential of moment closures as a possible path to future quantum hydrodynamics models. Moment closures are known to produce accurate predictions of continuum and non-equilibrium classical gas flows while offering modeling and numerical advantages over other commonly used methods. The maximum-entropy hierarchy of moment closures holds the promise of robustly hyperbolic stable moment equations, however, the predicted distribution function in phase space is positive by design, which is in disagreement with the quasi-distribution function described by the Wigner equation. In this paper, predictions made by an interpolative one-dimensional five-moment system are compared to direct numerical solutions of the Wigner equation for a simple low-energy quantum state in unbounded double-well potentials. Numerical solutions for a particle in various potentials described by quartic polynomials are presented. The capacity of moment methods to provide accurate and efficient models for quantum systems is explored.

Command filtered backstepping control of constrained flexible joint robotic manipulator

AbstractHere, an adaptive radial basis function (RBF) neural network (NN) backstepping controller is proposed for a class of input‐constrained flexible joint robotic manipulators represented by strict‐feedback form with unknown terms, external stochastic disturbance, and output disturbance. The proposed approach is robust against both deterministic and stochastic uncertainties and disturbances and copes with the control input amplitude saturation. Moreover, by deploying the minimal learning parameter method and command filter technique, the computational burden of derivative terms and adaptive terms greatly decreases. Considering the mean‐value theorem assists us to avoid the need for having the input saturation bounds in prior. The suggested tracking control scheme mandates the closed‐loop system states to be semi‐globally bounded‐in‐probability. Also, a quartic Barrier Lyapunov function is utilized to force the tracking error to be confined within a pre‐chosen small region around the origin. Eventually, a numerical simulation of a flexible joint robot manipulator with a single link is performed to show the effectiveness and performance of the developed control method.

Exact traveling wave solutions for the (2+1)-dimensional double sine-Gordon equation using direct integral method

In this paper, the direct integral method and complete discrimination system for quartic polynomial in standard form are applied to the (2+1)-dimensional double sine-Gordon equation. All possible exact traveling wave solutions of different types are successfully obtained from nine subcases. These exact solutions include kink solutions, and periodic solutions. Different from traditional methods (the Jacobi elliptic function method, the Exp-function method, extended Tanh method and the algebraic mapping method, etc.), the direct integral method described in this work is very natural and simple, and gives a new idea to obtain exact solutions for the mathematical physics equations considered.

An improved hybridization strategy for the fifth-order unequal-sized weighted essentially non-oscillatory scheme

In this paper, a hybrid unequal-sized weighted essentially non-oscillatory (US-WENO) scheme is developed to reduce the computational cost caused by the computation of nonlinear weights and local characteristic decompositions in its procedures. First, an improved discontinuous sensor is designed based on the mathematical properties of the fourth-degree reconstruction polynomial in the US-WENO scheme. The proposed hybridization strategy can automatically and efficiently identify the troubled cells, and does not contain artificial parameters related to the problems. Second, the efficient linear scheme and the existing US-WENO scheme are combined to simulate the inviscid and viscous compressible flow problems. Finally, some benchmark numerical examples are used to verify the performance of the presented hybrid WENO scheme in various aspects, such as computational efficiency, low dissipation characteristics, shock capture ability, etc. The numerical experiments show that the proposed hybrid method can inherit all the features of the existing US-WENO scheme while improving its computational efficiency.

Multi-wavelength imaging with extended depth of field using coded apertures and radial quartic phase functions

This study demonstrates a new multi-wavelength imaging technique with an extended depth of field. The spatial and spectral information of the objects is encoded into a single bipolar function of sparse dots using coded phase masks (CPMs) and a radial quartic phase function (RQPF). Each wavelength produces an intensity response of sparse dots with a unique set of distances between the dots, enabling the decoding of multispectral information. The RQPF is introduced to extend the depth of focus for different wavelengths. A library of point spread holograms (PSHs) is prerecorded with uniquely designed CPMs by placing the point objects of multiple wavelengths at the system input. For reconstruction, the object hologram is cross-correlated with a PSH corresponding to the wavelength of the object. The results are compared with direct imaging and with the conventional technique of interferenceless coded aperture correlation holography. The method is unique because the number of camera shots required for multi-wavelength imaging is the same as for monochromatic imaging.

A Numerical Evaluation of Forming Failure of an Aluminum Sheet due to Splitting Damage in Hole Expansion Process

Abstract The reduction of car body weight is the principal issue of car manufacturers for reducing fuel consumption. Aluminum alloys are attractive materials for the automotive industry because they have low density and adequate strength, but they may exhibit crack formation during manufacturing processes. Generally, crack formations emerge because of tool geometry and material anisotropy. Accordingly, determination of the forming limits of aluminum alloys is essential. The hole expansion test (HET) is a significant formability process used in the automotive industry because it gives information about the stretch-flangeability limits of the material. Edge splitting (edge fracture) is a failure type seen in HET, and it limits the stretch-flangeability of the material. Therefore, the prediction of edge splitting is an essential issue for engineers in the automotive industry. In this work, HET of AA6016-O aluminum alloy was simulated with the finite element (FE) method to assess the influence of yield functions on failure prediction in HET. To this end, Hill48, Yld91, and a homogeneous fourth-order polynomial type yield criteria (HomPol4) were selected to identify the anisotropic behavior of the sheet. Analyses were carried out in Marc commercial FE software, and the Hypela2 user subroutine was incorporated into FE code. Thickness distributions in the rolling direction (RD), diagonal direction, and transverse direction (TD) of the part and around the hole edge were also predicted, and it was observed that only the HomPol4 criterion predicted excessive thinning at two locations near the RD and TD, separately. On the other hand, Yld91 and Hill48 predicted lower strain levels when compared with HomPol4. Finally, plastic work distribution around the hole edge was considered, and the predictions were compared with the experimental damaged sample. This comparison showed that HomPol4 predicted a robust plastic work localization in RD, which is consistent with the damaged sample.

New optical soliton solutions to the (n+1) dimensional time fractional order Sinh-Gordon equation

This article studies and constructs new optical soliton solutions for the (n+1)-dimensional time fractional order Sinh-Gordon equation. First, we change the differential equation into Ordinary differential equation which is connected with a quartic polynomial based on traveling wave transformation. Then using the polynomial complete discrimination system to classify the roots of the fourth degree polynomial, the exact solutions of the Sinh-Gordon equation are classified, and these specific expressions of optical soliton solutions are given. This solution process is simple, fast, and very effective. The characteristics of some exact solutions were given using 3D, 2D, and contour graphs, which help researchers gain a deeper understanding of the physical characteristics corresponding to the model which we discuss in this article.

Direct multiple shooting and direct collocation perform similarly in biomechanical predictive simulations

Direct multiple shooting (DMS) and direct collocation (DC) are two standard transcription methods for solving optimal control problems (OCP) in biomechanics and robotics. They have yet to be compared in terms of solution and speed. Through five examples of predictive simulations solved using five transcription methods and 100 initial guesses in the Bioptim software, we showed that no single method outperformed the others systematically. All methods converged to almost the same solution (cost, states, and controls) in all but one OCP, with several local minima found in the latter. Nevertheless, DC based on fourth-order Legendre polynomials provided overall better results, especially regarding dynamics integration accuracy compared to DMS based on a fourth-order Runge–Kutta method. Furthermore, expressing the rigid-body constraints using inverse dynamics was usually faster than forward dynamics. DC with dynamic constraints based on inverse dynamics converged to better and less variable solutions. We recommend starting with this transcription to solve OCPs but keep testing other methods.

A Fast and Reliable Solution to PnP, Using Polynomial Homogeneity and a Theorem of Hilbert

One of the most-extensively studied problems in three-dimensional Computer Vision is “Perspective-n-Point” (PnP), which concerns estimating the pose of a calibrated camera, given a set of 3D points in the world and their corresponding 2D projections in an image captured by the camera. One solution method that ranks as very accurate and robust proceeds by reducing PnP to the minimization of a fourth-degree polynomial over the three-dimensional sphere S3. Despite a great deal of effort, there is no known fast method to obtain this goal. A very common approach is solving a convex relaxation of the problem, using “Sum Of Squares” (SOS) techniques. We offer two contributions in this paper: a faster (by a factor of roughly 10) solution with respect to the state-of-the-art, which relies on the polynomial’s homogeneity; and a fast, guaranteed, easily parallelizable approximation, which makes use of a famous result of Hilbert.

BIF-hosted high-grade magnetite iron ore targeting by hyperspectral wavelength mapping of chlorite: case study of Qidashan Iron Mine, northeast China

There are two kinds of chlorites occurred in Anshan area, among which the hydrothermal Fe-chlorite with longer Fe-OH wavelength is spatially related to the high-grade magnetite ore, meaning that wavelength mapping of chlorites can be used to target the BIF-hosted high grade iron ore. In this article, quadratic polynomial, cubic spline, and quartic polynomial method were used to interpolate the absorption wavelength near 2250 nm of China ZY1-02D satellite hyperspectral image. The result of quadratic polynomial is continuous without data overlapping or intervals, thus most suitable for discrimination of the chlorites. The field truth shows that the spatial distribution of Fe-chlorite, validated by XRD analysis, is not only in accordance with that of high grade magnetite ore bodies, but also consistent with the recently discovered concealed iron bonanza. The study shows that hyperspectral remote sensing techniques can play significant role in the exploration of magnetite iron ore in east Liaoning Province.

Extraction method of nanoparticles concentration distribution from magnetic particle image and its application in thermal damage of magnetic hyperthermia

Magnetic particle imaging (MPI) technology can generate a real-time magnetic nanoparticle (MNP) distribution image for biological tissues, and its use can overcome the limitations imposed in magnetic hyperthermia treatments by the unpredictable MNP distribution after the intratumoral injection of nanofluid. However, the MNP concentration distribution is generally difficult to be extracted from MPI images. This study proposes an approach to extract the corresponding concentration value of each pixel from an MPI image by a least squares method (LSM), which is then translated as MNP concentration distribution by an interpolation function. The resulting MPI-based concentration distribution is used to evaluate the treatment effect and the results are compared with the ones of two baseline cases under the same dose: uniform distribution and MPI-based distribution considering diffusion. Additionally, the treatment effect for all these cases is affected by the blood perfusion rate, which is also investigated deeply in this study. The results demonstrate that the proposed method can be used to effectively reconstruct the concentration distribution from MPI images, and that the weighted LSM considering a quartic polynomial for interpolation provides the best results with respect to other cases considered. Furthermore, the results show that the uniformity of MNP distribution has a positive correlation with both therapeutic temperature distribution and thermal damage degree for the same dose and a critical power dissipation value in the MNPs. The MNPs uniformity inside biological tissue can be improved by the diffusion behavior after the nanofluid injection, which can ultimately reflect as an improvement of treatment effect. In addition, the blood perfusion rate considering local temperature can have a positive effect on the treatment compared to the case which considers a constant value during magnetic hyperthermia.

New gas radiation model based on the principle of weighted sum of gray gases. Application to CO2–H2O mixtures at high temperature

A new gas radiation model based on the principle of weighted-sum-of-gray-gases (WSGG) is proposed. It is shown that expressing the weighting factors as linear functions of the temperature is more suitable than the fourth-order polynomial dependence to the temperature that is commonly adopted in the WSGG model. Using an efficient inverse algorithm, it was estimated a set of twelve spatially nonconstant parameters of the new model based on four gray gases, namely the coefficients of the linear functions and the pressure absorption coefficients. The inverse algorithm is based on the adjoint state of the radiative transfer equation (RTE) using as data the total radiative heat source instead of the total gas emissivity data. The parameters are fitted using data generated with line-by-line (LBL) simulations based on HITEMP2010. In the present work, the proposed gas radiation model is applied to determine the parameters of H2O–CO2 mixtures at atmospheric pressure with partial pressure ratio equal to 2, within the range of temperature between 400 K and 1800 K and for thicknesses of the gas layer up to 3.0 m. By applying the inverse algorithm to a given case, the present gas radiation model has the level of accuracy of the LBL method. The application of the same parameters to other test cases does not lead to the same level of accuracy, since the parameters obtained are spatially dependent. However, averaging these parameters in the inverse algorithm results in a gas radiation model with spatially constant parameters. When applied to several (1-D and 3-D) test cases in the conditions for which the parameters were obtained, this led to a significant reduction in the normalized errors on the radiative heat source and, for many of these cases, on the radiative heat flux compared to that obtained with the standard WSGG model.

DETERMINATION OF THE RELIABILITY OF THE GAS GENERATOR OF THE STORAGE SYSTEM AND HYDROGEN SUPPLY

It is noted that as a generalized characteristic of the functional gas generator, which is sensitive to variations in its parameters, it is advisable to use the transfer function, or its analogue - the amplitude-phase frequency characteristic of the gas generator. The amplitude-phase frequency characteristic of the gas generator includes two components - amplitude-frequency and phase-frequency characteristics. During the operation of the gas generator, there will be variations in its parameters - transmission coefficient and time constants, due to aging processes and the influence of external factors. Variations in the parameters of the gas generator lead to variations in its amplitude-frequency and phase-frequency characteristics. Mathematical models for variations in the frequency characteristics of the gas generator are built and it is shown that their frequency range should be limited by the bandwidth of the gas generator. The upper limit of the bandwidth of the gas generator is determined by the root of the biquadratic algebraic equation. For the typical parameters of the gas generator using a hydroreactive sample based on sodium aluminate, graphical dependences of variations of its amplitude-frequency and phase-frequency characteristics are constructed depending on variations of the transmission coefficient, time constants, and frequency. These dependencies are used to determine the parameters of the normal distribution law of variations in the frequency characteristics of the gas generator. In accordance with Lyapunov's rule, a normative law for the distribution of variations in the frequency characteristics of the gas generator is adopted. Due to the symmetry of the distribution of variations in the amplitude-frequency and phase-frequency characteristics of the gas generator, their mathematical expectations are equal to zero. Obtaining estimates of the amplitude and phase reliability of the gas generator is carried out using the Laplace function. The argument of this function is the permissible values of the frequency characteristics of the gas generator and their root mean square deviations. It is shown that with probabilities of 0,9973 and 0,9812, the amplitude-frequency and phase-frequency characteristics of the gas generator will not differ more than when it is turned on. Keywords: gas generator, reliability, frequency characteristics.

A new anisotropic-asymmetric yield criterion covering wider stress states in sheet metal forming

The stress state-dependent plastic anisotropy of sheet metals has drawn significant attention. Nevertheless, existing phenomenological plasticity models limitedly capture the distinctive yield strengths and plastic flow (r-values) under a wide range of stress states covering uniaxial tension (UT), equi-biaxial tension (EBT), uniaxial compression (UC), plane strain tension (PS), and pure shear (SH). This study aims to propose a new anisotropic-asymmetric plasticity model with enhanced flexibility based on the non-associated flow rule. The yield function is formulated based on the additive coupling of two stress potentials: coupling between a new anisotropic pressure-sensitive fourth-order polynomial function, and an isotropic stress invariant-based function. Then, all the anisotropic/asymmetric parameters of the yield function can be analytically identified from 7 yield stresses measured from UT tests along 0°, 45°, and 90° to the rolling direction (RD), UC tests along 0° and 90° to the RD, EBT test, and SH test along 45° to the RD. Within the scheme of no-associated flow rule, a new asymmetric fourth-order plastic potential function is proposed to analytically describe the plastic flow of sheet metals under UT, UC, EBT and SH. The additively coupled stress invariant-based term is introduced to adjust the yield stresses and plastic flow under biaxial tension including PS, which leads to an independent description of the yield stresses and plastic strain directions under SH and PS states. Various automotive sheet metals such as advanced high-strength steels, aluminum alloy, and magnesium alloy with strong asymmetry and anisotropy are investigated to verify the proposed yield criterion. The results demonstrate remarkable flexibility and accuracy of the proposed yield criterion against other existing models. Evolving yield surface and plastic potential of a quenching and partitioning steel are accurately captured by the proposed anisotropic-asymmetric yield criterion. Besides, the advantages of new model are further discussed in terms of the proof of yield surface convexity, identified parameters, and the regulation between anisotropy and isotropy in comparison with existing multiplicative coupling method.

The development of rowing performance evaluation technique using high-speed imaging

Rowing as an on-river sports has a long history dating back to the 16th century. The deeper understanding of fluid dynamics theory and the development of advanced material and manufacturing science and technology have inevitably fueled the continuous improvement on the world record of the rowing sports. The current paper focuses on the accurate extraction of the kinematics information including the boats location, velocity, and acceleration, resulting from the athletes rowing motion. A consumer-level digital camera is used for imaging the rowing motion at 50 frames per second from a distance, corresponding to a specific field of view ranging from 12 m 36 m. Furthermore, due to large-scale imaging lens distortion, the physical resolution is varying significantly due to imaging location change. A video-specific calibration method using fourth order polynomials are developed to calibrate the physical resolution of each pixel based on the physical length of the boat. The resulting data is pixel-level accurate and provides detailed record for athletes training. The acquired information is extremely useful in gauging athletes performance and can be further analyzed to provide concrete technical improvement advice.

Reducibility of quartic polynomials and its relation to Galois groups

This paper deals with special classes of quartic polynomials and properties pertaining to their Galois groups and reducibility over certain fields. The existence of quartic polynomials irreducible over Q but reducible over every prime field is first proven, after which criteria are established for the Galois group of polynomials with this property. By constructing classes of V4-generic polynomials and comparing them with criteria put forth in previous studies for determining polynomials with this property, it can be shown that a polynomial of the biquadratic form x4 + ax2 + b has this property if and only if it can be written as x^4 - 2(u + v)x^2 + (u -v)^2 with u, v Q such that none of u, v, or uv can be expressed as ratio of two squares, and 2(u+v),(uv)2 Z . The general form for biquadratic polynomials irreducible over Q and reducible modulo every integer n is found to have a general form similar to this one.

Evaluation of Light Falling Weight Deflectometer for In Situ Measurement of Secondary Deformation Modulus of Various Forest Road Pavements

Roads in forests are necessary for proper forest management and active protection of the natural environment. They facilitate tourism and recreation and have a very important function in firefighting. The cost of building roads in forest areas is considerable, even when relatively cheap materials such as aggregates of natural or anthropogenic origin are used. Therefore, any road investment must be well prepared and executed. Bearing capacity and compaction are among the most important and frequently used geotechnical parameters in road construction. The aim of this study was to determine the possibility of predicting the value of the secondary deformation modulus E2 (obtained from measurements with a static plate load test – PLT) based on measurements with a light falling weight deflectometer (LFWD) Zorn, type ZFG 3000 GPS with a drop weight of 10 kg. The regression analysis included 245 results of bearing capacity measurements carried out on 46 forest road sections with various road pavements. Different regression models were tested: linear, logarithmic, polynomial, exponential and power models, excluding polynomials of fourth and higher degree. Prediction of E2 (PLT) values from dynamic deformation modulus Evd (LFWD) values is possible. However, the reported unsatisfactory strength of the relationship between the two parameters is associated with a high risk of error (r=0.73, R2=0.54, Se=80.37 MN·m-2). Neither the use of more complex non-linear regression models nor the use of multiple regression by introducing an additional estimator in the form of the s/v ratio significantly improved the estimation results. The quality of the prediction of E2 values is not constant. It varies depending on the type of forest road pavements, the use of geosynthetic pavement reinforcements and the type of road subgrade. The study also found that the quality of E2 prediction can be improved by limiting the range of tested Evd values upwards. It is advisable to continue this type of research, as the results obtained could be the basis for developing national standards for the application of LFWD to control the bearing capacity and compaction of forest road surfaces in the future.

Quantitative study of the primary ossification centre of the parietal bone in the human fetus.

Detailed morphometric data concentrating on the development of primary ossification centres in human fetuses is critical for the early detection of developmental defects. Thus, an understanding of the growth and development of the parietal bone is crucial in assessing both the normal and pathological development of the calvaria. The size of the parietal primary ossification centre in 37 spontaneously aborted human fetuses of both sexes (16 males and 21 females) aged 18-30 weeks was studied by means of computed tomography, digital-image analysis and statistics. The numerical data of the parietal primary ossification centre in the human fetus displays neither sex nor laterality differences. With relation to fetal age in weeks, the parietal primary ossification centre grew in sagittal diameter according to the quadratic function: y = 16.322 + 0.0347 × (age)² ± 1.323 (R² = 0.96), in projection surface area according to the cubic function: y = 284.1895 + 0.051 × × (age)³ ± 0.490, while in both coronal diameter and volume according to the quartic functions: y = 21.746 + 0.000025 × (age)⁴ ± 1.256 and y = 296.984 + + 0.001 × (age)⁴, respectively. The obtained morphometric data of the parietal primary ossification centre may be considered age-specific references, and so may contribute to the estimation of gestational ages and be useful in the diagnostics of congenital cranial defects.

Study of fluorescent nanodiamonds concentrations in aqueous solutions for biological applications

Commercial fluorescent nanodiamonds constitute a new class of nanoprobes with excellent perspectives for biomedical applications. They produce a broad emission spectrum partially matching the biological window for high tissue penetration, which can be excited in the visible region (380–780 nm) and in the biological window (1000–2500 nm) using two-photon excitation processes, giving a chance for high-resolution multi-photon fluorescence imaging at a sub-cellular resolution scale. Because of their carbon-based structure, nanodiamonds are highly biocompatible and display low toxicity if adequately coated. The nanodiamonds fluorescence spectrum arises due to the so-called Nitrogen-Vacancy (NV) color centers, which are highly photostable and are formed by local charge density compensating defects because of the typical nitrogen presence impurity ions in the host nanocrystals. In this work, a study of different nanodiamonds’ concentrations in terms of their fluorescent activity was investigated in the range of 0.1–10 mg/mL by means of fluorescence spectroscopy with the purpose of determining which concentration of nanodiamonds suspended in milliQ water achieves the maximum intensity, in which it was found that the 5 mg/mL was the most intense in our experimental observations. Additionally, a non-linear fit of the experimental observations of intensity was performed to predict the fluorescence intensity following an expression of a fourth order polynomial with respect to concentration, with a figure of merit, FOM = 0.03–0.04 (3–4%). Based on this effect, the optimal nanodiamonds/aqueous media solution has been determined by means of cell viability assays, finding that concentrations ≤0.1 mg/mL are as biocompatible as milliQ water.