Order Polynomial Research Articles

Optical, electrical, and thermal performance enhancement for a concentrating photovoltaic/thermal system using optimized polynomial compound parabolic concentrators

Performance of a concentrating photovoltaic/thermal system directly depends on the solar irradiation gathered by concentrators. Few studies tackled the systemic and general optimizations of optical efficiency and uniformity of energy distribution for two-dimensional compound parabolic concentrators (CPCs). In this paper, a polynomial CPC is proposed. To evaluate the optical efficiency and uniformity of the concentrated irradiation, an interpolation method is also proposed. Using genetic algorithm, the optimized polynomial CPCs with different polynomial orders are determined. With fourth order, the concentrating efficiency reaches the theoretic limit, and the concentrated irradiation is relatively uniform. Accordingly, the optimized polynomial CPCs for concentration ratios not larger than 10 are determined. Using a double-pass spectral beam splitting photovoltaic/thermal system model, the electrical and thermal performance using the determined optimized polynomial CPCs is calculated. For concentration ratios not larger than 10, the optimized polynomial CPC is able to provide high concentrating efficiencies with good uniformity. Moreover, the maximum temperature of the photovoltaic cell is smaller than 325 K. And then, the optimized polynomial CPCs for multiple incident angles are presented, along with the system performance. For multiple incident angles, the optimized polynomial CPC also shows good performance, but the size increases.

Succinylated starch emulsified Eugenol and Carvacrol nanoemulsions improved digestive stability, bio-accessibility and Salmonella typhimurium inhibition

The ultrasonically processed Eugenol (EU) and Carvacrol (CAR) nanoemulsions (NE) were successfully optimized via response surface methodology (RSM) to achieve broad spectrum antimicrobial efficacy. These NE were prepared using 2 % (w/w) purity gum ultra (i.e., succinylated starch), 10 % (v/v) oil phase, 80 % (800 W) sonication power, and 10 min of processing time as determined via RSM. The second order Polynomial method was suitable to RSM with a co-efficient of determination >0.90 and a narrow polydispersity index (PDI) ranging 0.12–0.19. NE had small droplet sizes (135.5–160 nm) and low volatility at high temperatures. The EU & CAR entrapment and heat stability (300 °C) confirmed by Fourier transform infrared spectroscopy (FTIR) and thermogravimetric analysis (TGA). Further, the volatility of EU & CAR NE was 18.18 ± 0.13 % and 12.29 ± 0.11 % respectively, being lower than that of bulk/unencapsulated EU & CAR (i.e., 23.48 ± 0.38 % and 19.11 ± 0.08 %) after 2 h at 90 °C. Interestingly, both EU & CAR NE showed sustained release behaviour till 48 h. Their digest could inhibit Salmonella typhimurium (S. typhimurium) via membrane disruption and access to cellular machinery as evident from SEM images. Furthermore, in-vivo bio-accessibility of EU & CAR in mice serum was up to 80 %. These cost-effective and short-processed EU/CAR NE have the potential as green preservatives for food industry.

Contactless in-vivo temperature sensing in spinal cord based on magnetically bistable microwire

We have employed a magnetically bistable glass coated microwire as a passive contactless sensing element for in-vivo temperature monitoring in the rat’s spinal cord. The single piece (1 cm long) of Fe76Cr2Mo6B15Cu1 microwire was epidurally implanted into the adult female Wistar rats. The magnetization switching was measured in-vivo within the temperature range of 34.5–41.0 °C. Results show a monotonous temperature decrease of the switching time whose fitting to a second order polynomial dependence allows one to conclude a sensitivity down to 0.01ºC within the measured interval. Biocompatibility study shows that cells have a high affinity to the glass-coated microwire, and their viability is not influenced by the experimental condition under which the microwire’s response is measured. Finally, a histology study reveals that no histopathological changes or tissue reactions were observed even after 9 months of implantation.

Asymptotic approximations of Apostol-Frobenius-Euler polynomials of order α in terms of hyperbolic functions

Asymptotic approximations of Apostol-Frobenius-Euler polynomials of order <i>α</i> in terms of hyperbolic functions

On Stirling and bell numbers of order 1/2

The Stirling numbers of order 1/2 (of the second kind) introduced by Katugampola are discussed and it is shown that they are given by a scaled subfamily of the generalized Stirling numbers introduced by Hsu and Shiue. This allows to deduce in a straightforward fashion many properties of the Stirling and Bell numbers of order 1/2, for example, recurrence relations, generating functions, Dobi?ski formula, and Spivey formula. The even Bell polynomials of order 1/2 are shown to be closely related to generalized Laguerre polynomials of order ?1/2. Generalized Stirling numbers of order 1/2 of the first kind are defined and studied. An analog of the Weyl algebra is introduced and proposed as a natural algebraic setting where the Stirling numbers of order 1/2 of both kinds appear as ordering coefficients. This algebra contains the Weyl algebra as a subalgebra.

Toroidal seawater conductivity sensors and instrumentation for anti-submarine warfare

This paper describes the development of toroid-based seawater conductivity sensors and instrumentation for 0 to 60 mS/cm conductivity range and 50 bar hydrostatic pressure operational capability which is equivalent to 500 metres of ocean depth. Double core toroidal transformer concept was used and investigated for Mn-Zn and Fe based nanocrystalline cores, turns ratio and temperature dependence. Different excitation and sense coil turn numbers were fabricated by keeping the turn&#x2019;s ratio 1:2, 1:4, 1:6 and 1:8. Optimum frequency of Mn-Zn based conductivity sensors with lower and higher turn numbers were observed for turn ratio 1:8 and 1:4 respectively at 120 kHz and obtained voltage responses of 952 and 1567 mV. Fe based Nano crystalline core with turn ratio 1:8 shows an optimum frequency of 70 kHz and giving a voltage difference of 830 mV. Two dimensional polynomials of order 2 were presented for temperature dependence of conductivity for Mn-Zn core based sensors. Sensor responses of Fe based nanocrystalline core sensors in &#x2018;lower turn number&#x2019; configuration with same turn ratio is presented and observed linear temperature dependence compared to Mn-Zn based sensors. The mechanical design and frequency of operation of developed conductivity sensors gives inherent immunity to ASW band of frequency interference. The efficacy of conductivity sensor with measuring electronics and commercial standard sensors profiling was proved experimentally compared up to 500 metres in sea profiling and obtained a root mean square error of 0.42 for profile data.

Random walks on a line and algebraic curves

This work is devoted to the studying the generating function of the first hitting time of the positive semi-axis under the homogeneous discrete integer random walk on a line. In the first part of the work the increments are supposed to be independent. Recurrent relations for the probabilities allow us to write the system of equations for the sought generating function. Applying the resultants technique, we succeed to reduce this system to a single equation. Then we can study it by calculating the genus of the correposponding plane algrebraic curve via analyzing its singularities. In the work we write the sought equations for some random walks and we show that if the increments take all integer values from $-2$ to $2$, or from $-1$ to $3$ with equal probabilities or they take equally probable values $-1$ and $4$, then the curve is rational, while this is not true in the first case. In the second part of the work we consider a symmetric process, the increments take the values $-1$, $0$, $1$, but then we suppose a non-zero correlation of each next increment with the previous one. For such process the equation for the generating function defines an elliptic curve depending on the square of the correlation coefficient for neighbouring increments if all increments are non-zero and it defines a hyperelliptic curve of genus $2$. The degeneration criterion of the latter is the presence of multiple roots of a sixth order polynomial under general symmetrically distributed conditional probabilities.

УСУНЕННЯ ЗАВАД У ДИНАМІЧНИХ СПЕКТРАХ ЗА НАЯВНОСТІ ПОТУЖНОГО СИГНАЛУ. Частина 2. ВУЗЬКОСМУГОВІ ЗАВАДИ УМОВНО-СТАЦІОНАРНОГО ХАРАКТЕРУ

Subject and Purpose. A new method for detecting narrow band interferences is discussed, with the use of an example record of Jovi- an Io-C decametric radio storm as obtained with the UTR-2 array on April 10, 2020. We aimed at developing an efficient and simple algorithm based on a detailed analysis of the effect the radio interference environment and the frequency response of the telescope may have on the efficiency of the interference mitigation procedure. Methods and Methodology. The ‘orthogonal detection’ method proposed for identifying linear interference patterns in dynamic spectra of powerful radio sources has been adapted for application to narrow band interferences of various spectral widths and variable brightness, which often happen to be located close to (or intersect with) the signal of interest. In order to minimize the impact of the telescope’s frequency response, a discretized frequency-scanning technique is used, which permits a steady approximation of the averaged spectrum by low order polynomials, as well as removal of the frequency trend which hinders distinguishing between the low-level interference signals and those coming from the source. Results. An efficient approach to the problem of detecting long lasting, narrowband interferences in dynamical spectra (con- ditionally stationary interferences) is proposed. The algorithm has been tested on the example of a powerful storm of Jovian radio emission. The proposed technique can be especially useful in situations where the signal of interest overlaps with the interference in the time-frequency domain. Conclusions. The new approach to the problem of interference mitigation, based on the development of combined algorithms of signal separation in the time-frequency domain, has been shown to offer an effective method of signal processing. In contrast to the previously used methods based on calculation of statistical moments for amplitudes, the new approach allows avoiding use of the same statistical indicators for both interference detection and subsequent steps of data analysis intended for building physical models and interpreting the observational data.

Data assimilation finite element method for the linearized Navier-Stokes equations with higher order polynomial approximation

In this article, we design and analyze an arbitrary-order stabilized finite element method to approximate the unique continuation problem for laminar steady flow described by the linearized incompressible Navier–Stokes equation. We derive quantitative local error estimates for the velocity, which account for noise level and polynomial degree, using the stability of the continuous problem in the form of a conditional stability estimate. Numerical examples illustrate the performances of the method with respect to the polynomial order and perturbations in the data. We observe that the higher order polynomials may be efficient for ill-posed problems, but are also more sensitive for problems with poor stability due to the ill-conditioning of the system.

Nonlinear Gradient Field Mapping Using a Spherical Grid Phantom for 3 and 7 Tesla MR Imaging Systems Equipped with High-performance Gradient Coils.

Recent high-performance gradient coils are fabricated mainly at the expense of spatial linearity. In this study, we measured the spatial nonlinearity of the magnetic field generated by the gradient coils of two MRI systems with high-performance gradient coils. The nonlinearity of the gradient fields was measured using 3D gradient echo sequences and a spherical phantom with a built-in lattice structure. The spatial variation of the gradient field was approximated to the 3rd order polynomials. The coefficients of the polynomials were calculated using the steepest descent method. The geometric distortion of the acquired 3D MR images was corrected using the polynomials and compared with the 3D images corrected using the harmonic functions provided by the MRI venders. As a result, it was found that the nonlinearity correction formulae provided by the vendors were insufficient and needed to be verified or corrected using a geometric phantom such as used in this study.

Design Method for Polynomial Orders in ARX-Based Model-Free Predictive Controllers

Design Method for Polynomial Orders in ARX-Based Model-Free Predictive Controllers

Numerical investigation of the flow characteristics involving dissipation and slip effects in a convectively nanofluid within a porous medium

Abstract The aim of the present research is to discuss the numerical aspects of heat-mass transfer in power-law nanofluids on an stretched surface. In addition, the novelty in this research lies in its thorough exploration and incorporation of parameters such as viscous dissipation, slip velocity, and convective boundary conditions into the analysis. This distinguishes the study from previous work and underscores its originality. For non-Newtonian fluids, a power-law model is employed, while the nanofluid system associate the influences of thermophoresis and the Brownian motion. The fluid’s thermal conductivity is considered to change based on temperature, while the concentration of nanoparticles at the surface is maintained at a constant level. A heated fluid situated beneath the lower surface can act as a heat convection mechanism source. A process of similarity transformation is employed to simplify the equations related to the mass, momentum, thermal energy, and nanoparticle concentration into nonlinear ordinary differential equations. These equations are then treated numerically with the help of the shifted Chebyshev polynomials of the sixth order and the spectral collocation method. The proposed technique reduces the existing problem into a system of algebraic equations formulated as a constrained optimization challenge. Subsequently, the optimization technique is applied to determine the unknown coefficients of the series solution. Graphical representations depict the impacts of nanofluid parameters. A quantitative assessment is presented in a tabular format to illustrate a comparison with previously published results for specific scenarios, revealing a notable level of agreement.

The Significance of Cross-Sectional Shape Accuracy and Non-Linear Elasticity on the Numerical Modelling of Cerebral Veins under Tensile Loading.

Traumatic brain injury (TBI) is a serious global health issue, leading to serious disabilities. One type of TBI is acute subdural haematoma (ASDH), which occurs when a bridging vein ruptures. Many numerical models of these structures, mainly based on the finite element method, have been developed. However, most rely on linear elasticity (without validation) and others on simplifications at the geometrical level. An example of the latter is the assumption of a regular cylinder with a constant radius, or the geometry of the vein acquired from medical images. Unfortunately, these do not replicate the real conditions of a mechanical tensile test. In this work, the main goal is to evaluate the influence of the vein's geometry in its mechanical behaviour under tensile loading, simulating the real conditions of experimental tests. The second goal is to implement a hyperelastic model of the bridging veins where it would be possible to observe its non-linear elastic behaviour. The results of the developed finite element models were compared to experimental data available in the literature and other models. It was possible to conclude that the geometry of the vein structure influences the tensile stress-strain curve, which means that flattened specimens should be modelled when validating constitutive models for bridging veins. Additionally, the implementation of hyperelastic material models has been verified, highlighting the potential application of the Marlow and reduced polynomial (of fourth and sixth orders) constitutive models.

Efficacy of Tannin Extract from Cape Gooseberry Root Physalis peruviana L. as Egg De-Adhesion Agent during Artificial Propagation of African Catfish Clarias gariepinus Burchell

The study assessed the best immersion period and concentrations of the Cape gooseberry root Physalis peruviana that can efficiently remove egg adhesiveness of Clarias gariepinus. One male and one female C. gariepinus brood stock weighing 1.0 kg and 1.3 kg respectively, were used for the experiment. Three different concentrations (0.5%, 1%, and 2%) of tannin extract from Cape gooseberry root were used. Tannic acid (0.75g) diluted in 1 litre of water was used as reference de-adhesion agent, while water was used as control. The fish eggs were rinsed with the solutions at different durations of 0.5, 1 and 2 minutes. Each concentration and rinsing time was recorded in triplicates. Data generated were subjected to Univariate Analysis of Variance Test, and third order Polynomial regression analysis was then used to determine the best concentration and immersion period that neutralizes adhesiveness in eggs of C. gariepinus. Results of the study showed that there were no significant differences (p≤0.05) in the non-adhesive eggs and hatching of eggs immersed in tannin extract from Cape gooseberry root and Tannic acid solution but significantly different from the control. Therefore, this study showed that tannin extract from Cape gooseberry root at 1% concentration and 1 minute immersion period is more efficient for egg adhesion and increase hatching in C. gariepinus.

A reinforcement learning strategy for p-adaptation in high order solvers

Reinforcement learning (RL) has emerged as a promising approach to automating decision processes. This paper explores the application of RL techniques to optimise the polynomial order in the computational mesh when using high-order solvers. Mesh adaptation plays a crucial role in improving the efficiency of numerical simulations by increasing accuracy while reducing the cost. Here, actor-critic RL models based on Proximal Policy Optimization offer an approach for agents to learn optimal mesh modifications based on evolving conditions.The paper provides a strategy for p-adaptation in high-order solvers and includes insights into the main aspects of RL-based mesh adaptation, including the formulation of appropriate reward structures and the interaction between the RL agent and the simulation environment. The proposed strategy does not require a high-fidelity solution during the training process and the formulation is general for any computational mesh and partial differential equation (PDE), solved in a discontinuous Galerkin solver. We discuss the impact of RL-based mesh p-adaptation on computational efficiency and accuracy. We apply the RL p-adaptation strategy to a one-dimensional inviscid Burgers' equation, focusing our analysis on smooth solutions of the equation to showcase its effectiveness. The RL strategy reduces the computational cost and improves accuracy over uniform adaptation, while minimising human intervention.

The Determination of Dawn Time through Image Processing Camera

Determining the early time prayer is very fundamental for Muslims as it directly relates to the legal requirements of prayer. Prayers are not performed whenever we want, but rather there is a determination of the beginning and end of the prayer time as a guideline for Muslims to carry it out. The Indonesia government sets standards for Muslims to perform the dawn prayer service, by precisely determining the degree of the emergence of the dawn of Sadiq by -200. This study aims to compare the determination of the government's dawn time using different sensors, specifically drone cameras as image sensors. Drones were chosen due to their several advantages. The data generated by the drone is in the form of photos, which are subsequently processed using digital image processing software, called image-J. The data obtained are in the form of mean and standard deviation. All data collected in 1 day is recorded using Excel to form a graph of data which is then carried out by a polynomial approach to find out the cutoff point as the beginning of the dawn of Sadiq which indicates the start of dawn. The method used in this research is using the 4th order polynomial approach and the Sarrus method and the data obtained is the mean value and standard deviation. The conclusions obtained in the image analysis research are that the government's dawn time is 15 minutes too fast, the standard obtained in this study is -14.98° and unlike 2D SQM data, 3D drone data results in more accurate data analysis.

An Improved Fractional Moment Maximum Entropy Method With Polynomial Fitting

Abstract The moment method is commonly used in reliability analysis, in which the maximum entropy method (MEM) and polynomial fitting (PF) have been widely used due to their advantages in accuracy and efficiency, respectively. In this paper, we propose a novel reliability analysis method by combining MEM and PF. The probability density function is preliminarily estimated using the fractional moment maximum entropy method (FM-MEM), based on which PF is then used to further improve the accuracy. The proposed method can avoid the phenomenon of the negative probability density and function oscillations in PF effectively. Moreover, the order of the exponential polynomial in the FM-MEM is adaptively selected in the preliminary solution calculation process. An iterative process for the number of exponential polynomial terms is also proposed, using the integral of the moment error function and the integrals of the local and global negative probability density as the convergence criteria. Four numerical examples and one engineering example are tested, and the results are compared with those of the Monte Carlo simulation and the classical FM-MEM results, respectively, demonstrating the good performance of the proposed method.

Numerical treatment of Burgers' equation based on weakly L-stable generalized time integration formula with the NSFD scheme

In this study, we present a weakly L-stable convergent time integration formula of order N1>3 (N1∈Z is odd) to solve Burgers' equation. The time integration formula for the initial value problem w′(t)=f(t,w),w(t0)=η0 is formulated using backward explicit Taylor series approximation of order (N1−1) and Hermite approximation polynomial of order (N1−2). We convert the Burgers' equation into the initial value problem using the nonstandard finite difference scheme for spatial derivatives and implement the derived integration formula. The nonstandard finite difference scheme makes it possible to choose several denominator functions. The method's convergence, stability and truncation error are also discussed. To show the correctness and effectiveness of the proposed technique, we present numerical solutions, ‖e‖2 and ‖e‖∞ error norms in several tables and figures. Additionally, the numerical outcomes are compared with the results of some existing techniques and exact solutions.

High-order finite element method for atomic structure calculations

We introduce featom, an open source code that implements a high-order finite element solver for the radial Schrödinger, Dirac, and Kohn-Sham equations. The formulation accommodates various mesh types, such as uniform or exponential, and the convergence can be systematically controlled by increasing the number and/or polynomial order of the finite element basis functions. The Dirac equation is solved using a squared Hamiltonian approach to eliminate spurious states. To address the slow convergence of the κ=±1 states due to divergent derivatives at the origin, we incorporate known asymptotic forms into the solutions. We achieve a high level of accuracy (10−8 Hartree) for total energies and eigenvalues of heavy atoms such as uranium in both Schrödinger and Dirac Kohn-Sham solutions. We provide detailed convergence studies and computational parameters required to attain commonly required accuracies. Finally, we compare our results with known analytic results as well as the results of other methods. In particular, we calculate benchmark results for atomic numbers (Z) from 1 to 92, verifying current benchmarks. We demonstrate significant speedup compared to the state-of-the-art shooting solver dftatom. An efficient, modular Fortran 2008 implementation, is provided under an open source, permissive license, including examples and tests, wherein particular emphasis is placed on the independence (no global variables), reusability, and generality of the individual routines. Program summaryProgram Title: featomCPC Library link to program files:https://doi.org/10.17632/962fzmm7f7.1Licensing provisions: MITProgramming language: Fortran with command-line interfacesNature of problem: Solution of the Schrödinger, Dirac, and Kohn–Sham equations of density functional theory for isolated atoms.Solution method: A high-order finite element method is used to assemble a generalized eigenproblem that is then solved for eigenvalues and orbitals. The Poisson equation is solved using the finite element method also. Self-consistent field equations are solved using Pulay mixing.Additional comments including restrictions and unusual features: Our solution methodology for the Dirac equation does not suffer from spurious states. We maintain high accuracy even for κ=±1 states. Unlike other methods, our approach is not limited to Coulombic or self-consistent potentials and can handle non-uniform meshes, including exponential meshes.Restrictions: Spherical symmetry.

A p-Refinement Method Based on a Library of Transition Elements for 3D Finite Element Applications

Wave propagation or acoustic emission waves caused by impact load can be simulated using the finite element (FE) method with a refined high-fidelity mesh near the impact location. This paper presents a method to refine a 3D finite element mesh by increasing the polynomial order near the impact location. Transition elements are required for such a refinement operation. Three protocols are defined to implement the transition elements within the low-order FE mesh. Due to the difficulty of formulating shape functions and verification, there are no transition elements beyond order two in the current literature for 3D elements. This paper develops a complete set of transition elements that facilitate the transition from first- to fourth-order Lagrangian elements, which facilitates mesh refinement following the protocols. The shape functions are computed and verified, and the interelement compatibility conditions are checked for each element case. The integration quadratures and shape function derivative matrices are also computed and made readily available for FE users. Finally, two examples are presented to illustrate the applicability of this method.