Auxiliary Parameter Research Articles

A correspondence between the free and interacting field

We discover a correspondence between the free field and the interacting states. This correspondence is firstly given from the fact that the free propagator can be converted into a tower of propagators for massive states, when expanded with the Hermite function basis. The equivalence of propagators reveals that in this particular case the duality can naturally be regarded as the equivalence of one theory on the plane wave basis to the other on the Hermite function basis. More generally, the Hermite function basis provides an alternative quantization process with the creation/annihilation operators that correspond directly to the interacting fields. As an illustration, we apply this basis to the 3+1 dimensional Yang–Mills theory, where the three-dimensional space being reduced through the Hermite function basis, and an auxiliary parameter omega denotes for string tension. At large omega limit, with then considering only the lowest order Hermite function (Lowest Landau Level), the equivalent action becomes the Banks–Fischler–Shenker–Susskind (BFSS) matrix model. At small omega limit, the perturbative series summed over all orders of Hermite function gives a massive gluon propagator.

Novel approach for nonlinear time-fractional Sharma-Tasso-Olever equation using Elzaki transform

In this article, we demonstrated the study of the time-fractional nonlinear Sharma-Tasso-Olever (STO) equation with different initial conditions. The novel technique, which is the mixture of the q-homotopy analysis method and the new integral transform known as Elzaki transform called, q-homotopy analysis Elzaki transform method (q-HAETM) implemented to find the adequate approximated solution of the considered problems. The wave solutions of the STO equation play a vital role in the nonlinear wave model for coastal and harbor designs. The demonstration of the considered scheme is done by carrying out some examples of time-fractional STO equations with different initial approximations. q-HAETM offers us to modulate the range of convergence of the series solution using , called the auxiliary parameter or convergence control parameter. By performing appropriate numerical simulations, the effectiveness and reliability of the considered technique are validated. The implementation of the new integral transform called the Elzaki transform along with the reliable analytical technique called the q-homotopy analysis method to examine the time-fractional nonlinear STO equation displays the novelty of the presented work. The obtained findings show that the proposed method is very gratifying and examines the complex nonlinear challenges that arise in science and innovation.

New Explicit and Approximate Solutions of the Newton-Schrödinger System

In this paper, we consider the Newton-Schrödinger system ∇2Ψ=γΦ+a(x)Ψ,∇2Φ=∣Ψ∣2,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \\left\\{ \\begin{array}{rcl} \ abla ^{2} \\Psi & =& \\left( \\gamma \\Phi +a(x)\\right) \\Psi ,\\\\ \ abla ^{2} \\Phi & =& \\mid \\Psi \\mid ^{2}, \\end{array} \\right. \\end{aligned}$$\\end{document}which arises in certain quantum transport and chemistry problems. Explicit analytic solutions, which contain an auxiliary parameter, are obtained. An existence and uniqueness theorem to this nonlinear system subject to the boundary conditions is proved. Also, we introduce approximate solutions to the modified Newton-Schrödinger system in the case of spherically-symmetric stationary and time-independence by the Adomian decomposition method.

Application of High-Pressure Gas Expansion Rock-Cracking Technology in Hard Rock Tunnel near Historic Sites

In order to study the applicability of high-pressure gas expansion rock-cracking technology in hard rock tunnel near historic sites, theoretical analysis, field tests as well as vibration monitoring are conducted to obtain suitable rock mass cracking parameters for tunnel excavation. The results show that the ideal effect of rock mass cracking can be achieved with the cutting mode of “central vertical empty hole + double wedge cutting hole” and the auxiliary hole network parameter of “0.8 m × 0.7 m”. The measured vibration velocity is less than 0.1 cm/s at the monitoring point 60 m away from the tunnel face in the field test, which meets the vibration control requirements of the historic sites in the process of tunnel excavation. The research results show that as long as there is a high quality of hole plugging and no punching, the high-pressure gas expansion rock-cracking technology has the advantages of little vibration, low noise and less flying rocks, which provides a technical reference for the excavation of hard rock tunnels near ancient buildings and historic sites.

A new intervention strategy for an HIV/AIDS transmission by a general fractional modeling and an optimal control approach

This study proposes a new mathematical model in a generalized fractional framework for the investigation of an HIV/AIDS transmission dynamics. An auxiliary parameter further prevents the fractional equations from mismatching in the dimension. In order to analyze the general model, the non-negativity of the solution and the stability of the equilibrium points are examined. The model is also implemented by a powerful numerical scheme based on the quadrature rules and the repeated Trapezoidal method; as well, the error discussion and the convergence analysis are established. In addition, an efficient intervention strategy is developed and examined based on the optimal control theories in terms of optimality necessary conditions. Real-life clinical observations from Cape Verde Islands show that the new fractional model outperforms the classical one with ordinary time-derivatives, and enhances the modeling output compared to the previous fractional mathematical results. Further, numerical simulations demonstrate that the proposed optimal control measure leads to a significant reduction in the disease spread. As a result, the general fractional model offers a degree-of-freedom, an efficient tool which is helpful to illustrate the fundamental features of the disease transmission and to increase the efficiency of the proposed treatment strategy.

Assembly and manipulation of responsive and flexible colloidal structures by magnetic and capillary interactions.

The long-ranged interactions induced by magnetic fields and capillary forces in multiphasic fluid-particle systems facilitate the assembly of a rich variety of colloidal structures and materials. We review here the diverse structures assembled from isotropic and anisotropic particles by independently or jointly using magnetic and capillary interactions. The use of magnetic fields is one of the most efficient means of assembling and manipulating paramagnetic particles. By tuning the field strength and configuration or by changing the particle characteristics, the magnetic interactions, dynamics, and responsiveness of the assemblies can be precisely controlled. Concurrently, the capillary forces originating at the fluid-fluid interfaces can serve as means of reconfigurable binding in soft matter systems, such as Pickering emulsions, novel responsive capillary gels, and composites for 3D printing. We further discuss how magnetic forces can be used as an auxiliary parameter along with the capillary forces to assemble particles at fluid interfaces or in the bulk. Finally, we present examples how these interactions can be used jointly in magnetically responsive foams, gels, and pastes for 3D printing. The multiphasic particle gels for 3D printing open new opportunities for making of magnetically reconfigurable and "active" structures.

A New Computational Technique for Analytic Treatment of Time‐Fractional Nonlinear Equations Arising in Magneto‐Acoustic Waves

This paper presents the study of time‐fractional nonlinear fifth‐order Korteweg–de Vries equations by utilizing an adequate novel technique, namely, the q‐homotopy analysis transform method. The fifth‐order Korteweg–de Vries equation has got its importance in the study of magneto‐sound propagation in plasma, capillary gravity water waves, and the motion of long waves under the influence of gravity in shallow water. To justify the effectiveness and pertinence of the contemplated technique, we take a look at three examples of the time‐fractional fifth‐order Korteweg–de Vries equations. The q‐homotopy analysis transform method offers us to modulate the range of convergence of the series solution using ℏ, called the auxiliary parameter or convergence control parameter. The study of the fractional behaviour of the considered equations expresses the originality of the presented work. There is a visible variation in the obtained solutions for different fractional orders and which can lead to different consequences for future work. As a future research direction, readers can use the hybrid methodologies merging with our projected scheme to achieve better consequences. Additionally, to validate the precision and reliability of the proposed method, we organized suitable numerical simulations. The obtained findings show that the proposed method is very gratifying and examines the complex nonlinear challenges that arise in science and innovation.

Analytic Computational Method for Solving Fractional Nonlinear Equations in Magneto-Acoustic Waves

In this article, we employ a useful and intriguing method known as the ARA-homotopy transform approach to explore the fifth-order Korteweg-de Vries equations that are nonlinear and time-fractional. The study of capillary gravity water waves, magneto-sound propagation in plasma, and the motion of long waves under the effect of gravity in shallow water have all been influenced by Korteweg-de Vries equations. We discuss three instances of the fifth-order time-fractional Korteweg-de Vries equations to demonstrate the efficacy and applicability of the proposed method. Utilizing, also known as the auxiliary parameter or convergence control parameter, the ARA-homotopy transform technique which is a combination between ARA transform and the homotopy analysis method, allows us to modify the convergence range of the series solution. The obtained results show that the proposed method is very gratifying and examines the complex nonlinear challenges that arise in science and innovation.

The Homotopy Analysis Method for Solving Differential Equations With Generalized Caputo-Type Fractional Derivatives

Abstract This study expands and modifies the homotopy analysis method to handle differential equations with generalized Caputo-type fractional derivatives. Analytical approximate solutions for such models were successfully provided using the proposed modification. The determination of the valid region of convergence for the proposed method, with respect to the auxiliary control parameter, was discussed when using fractional operators. Then, mainly, the accuracy and effectiveness of the proposed method was verified through illustrative examples and comparisons with the predictor corrector method and RK4 method. Finally, it is expected that the studied generalized operators and the suggested method can be widely applied in the field of fractional calculus.

A consensus algorithm based on multi-agent system with state noise and gradient disturbance for distributed convex optimization

Almost all systems are inevitably subject to various uncertainties or disturbances from the external environment in practical applications. Taking these factors into consideration, in this paper a distributed algorithm with state noise and gradient disturbance is proposed for solving distributed optimization problem with closed convex set constraint based on multi-agent system under weight-balanced graph. Moreover, based on the gradient tracking and projection methods, the proposed distributed algorithm with gradient tracking can improve the convergence rate by introducing a projection error term and an auxiliary parameter. In contrast to some existing constrained distributed gradient algorithms, the proposed one can make the convergence faster and enhance the performance of convergence. The proposed algorithm is illustrated with two simulation examples to show its effectiveness and robustness.

Adaptive Neural Control of a 2DOF Helicopter with Input Saturation and Time-Varying Output Constraint

An adaptive neural control for uncertain 2DOF helicopter systems with input saturation and time-varying output constraints is provided. A radial basis function neural network is used to estimate the uncertainty terms present in the system. The saturation error and the external disturbance are considered as a composite disturbance, and an adaptive auxiliary parameter is introduced to compensate it. An asymmetric barrier Lyapunov function is employed to address the constraint violation of the system output. The closed-loop stability of the system is then demonstrated by Lyapunov theory analysis. Simulation results demonstrate the effectiveness of the control strategy.

NEWTON’S LAW OF COOLING WITH CAPUTO DERIVATIVE: CONSISTENT DIMENSIONALITY TO COMPARE WITH EXPERIMENTS

The dimensional homogeneity of different non-integer order versions of Newton’s law of cooling was studied. The Caputo derivative was considered for the analysis, as well as an auxiliary parameter [Formula: see text] with a time dimension. Usually, in the open literature this auxiliary parameter is arbitrarily defined by restricting its value or the range of values that it can take. In this investigation, many experimental data from different sources were collected and the most probable values of [Formula: see text] parameter and the parameter representing the non-integer order of derivatives were determined using the standard least-squares fitting technique. The results for the typical system in which an amount of hot water in a container is cooled by natural convection show that the order of the derivative takes values smaller but close to one, implying that the fractional behavior of the cooling curves deviates slightly from that perceived in the integer order solutions. It was also confirmed that the auxiliary parameter [Formula: see text] can be represented as the product between a real number n and the inverse of the cooling constant k of the classic model. Thus, the parameter [Formula: see text] can be interpreted as a kind of time constant, which can be considered reduced if [Formula: see text] and enlarged if [Formula: see text].

Determination of inorganic tracers in agave plants and agricultural soils as an auxiliary parameter to ensure the authenticity of the region that grants the Denomination of Origin of Tequila

To find authenticity parameters in agricultural soils belonging to the region that grants the Denomination of Origin of Tequila (DOT) 26 samples belonging to Jalisco (sub-regions: Valles, Altos Sur, Ciénega, Lagunas, and Sur), Michoacán, Nayarit, and, Sinaloa were characterized. The characterization consisted of determining texture, apparent density, color, pH, humidity, organic matter, total carbon, and trace metals analyzed by ICP-MS and X-ray fluorescence (XRF). The results obtained were studied through statistical analysis using a one-way ANOVA. For the case of apparent density (0.95 ± 0.10 g mL −1 ), pH (5.8 ± 1.13), humidity (11.29 ± 5.73%), organic matter (0.81 ± 0.18%) and total carbon (9.70 ± 2.45%), no significant differences were detected. Also, color characterization showed that Jalisco regions soils are mostly reddish, associated with mineralogical matrix composition. The characterization of metals by XRF shows that trace metals are associated with micro and macronutrients in soils. Finally, to achieve groups classification, ternary graph using a combination of Cr-Ba-Zr was constructed. The presence of these minerals is due to the DOT region is within the volcanic region of western Mexico. These metals migrate to the agave plant (3995 ± 1279 mg Ba g −1 , 75.75 ± 24.64 mg Cr g −1 , and 7.54 ± 4.67 mg Zr g −1 ) and remain in traces until final product (Tequila 100% agave silver-class, 5.34 ± 4.77 μg Ba L −1 , 13.3 ± 2.2 μg Cr L −1 ) being useful as auxiliary tracers to determine soil authenticity and agave belonging to DOT region. • Soils and plants from the Denomination of Origin of Tequila were characterized. • DOT regions soil properties provide inorganic tracers to the beverage. • Cr, V, Sr, Ba, and Zr traces are useful for classifying soil groups in the region. • Metals can be attributed to the mineralogy of the volcanic soils of the region. • Geochemical fingerprints can be useful as authenticity criteria for Tequila.

Modeling and Applying Implicit Dormant Features for Recommendation via Clustering and Deep Factorization.

E-commerce systems experience poor quality of performance when the number of records in the customer database increases due to the gradual growth of customers and products. Applying implicit hidden features into the recommender system (RS) plays an important role in enhancing its performance due to the original dataset's sparseness. In particular, we can comprehend the relationship between products and customers by analyzing the hierarchically expressed hidden implicit features of them. Furthermore, the effectiveness of rating prediction and system customization increases when the customer-added tag information is combined with hierarchically structured hidden implicit features. For these reasons, we concentrate on early grouping of comparable customers using the clustering technique as a first step, and then, we further enhance the efficacy of recommendations by obtaining implicit hidden features and combining them via customer's tag information, which regularizes the deep-factorization procedure. The idea behind the proposed method was to cluster customers early via a customer rating matrix and deeply factorize a basic WNMF (weighted nonnegative matrix factorization) model to generate customers preference's hierarchically structured hidden implicit features and product characteristics in each cluster, which reveals a deep relationship between them and regularizes the prediction procedure via an auxiliary parameter (tag information). The testimonies and empirical findings supported the viability of the proposed approach. Especially, MAE of the rating prediction was 0.8011 with 60% training dataset size, while the error rate was equal to 0.7965 with 80% training dataset size. Moreover, MAE rates were 0.8781 and 0.9046 in new 50 and 100 customer cold-start scenarios, respectively. The proposed model outperformed other baseline models that independently employed the major properties of customers, products, or tags in the prediction process.

AMFlow: A Mathematica package for Feynman integrals computation via auxiliary mass flow

AMFlow is a Mathematica package to numerically compute dimensionally regularized Feynman integrals via the recently proposed auxiliary mass flow method. In this framework, integrals are treated as functions of an auxiliary mass parameter and their results can be obtained by constructing and solving linear differential systems with respect to this parameter, in an automatic way. The usage of this package is described in detail through an explicit example of double-box family involved in two-loop tt¯ hadroproduction. Program summaryProgram title:AMFlowCPC Library link to program files:https://doi.org/10.17632/nrkrw83bw5.1Developer's repository link:https://gitlab.com/multiloop-pku/amflowLicensing provisions: MITProgramming language:Wolfram Mathematica 11.3 or higherExternal routines:Wolfram Mathematica [1], FiniteFlow [2], LiteRed [3], Kira [4], FIRE [5]Nature of problem: Automatically obtaining high-precision numerical results for dimensionally regularized Feynman integrals at arbitrary points in phase-space.Solution method: The program implements recently proposed auxiliary mass flow method, which introduces an auxiliary mass parameter to Feynman integrals and solves differential equations with respect to this parameter to obtain physical results.

Path Following for Unmanned Combat Aerial Vehicles Using Three-Dimensional Nonlinear Guidance

An effective path-following guidance algorithm for unmanned combat aerial vehicles by pursuing a look-ahead target-point along the desired path is devised. The concept of look-ahead pursuit for 3-D path-following was extended from the planar <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\mathcal {L}_1}$</tex-math></inline-formula> guidance, which has been widely adopted in the application of lateral guidance of fixed-wing drone. Decoupled implementation of the planar guidance action on each of the longitudinal (vertical) and lateral (horizontal) planes supplies longitudinal-lateral acceleration commands in two perpendicular planes which is well accepted by aviation engineers. The computation of the look-ahead point utilizes a finite and iterative numerical search method by introducing an auxiliary path-related parameter. Furthermore, additional implementation-specific details such as the modification of adaptive <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\mathcal {L}_1}$</tex-math></inline-formula> length and the protection strategies ensuring wide applicability of the algorithm indeed guarantee certain necessity to be considered in real implementation of the guidance law. The improved schemes eliminate complicated coordinate transformations and are built on the path-independent assumption, thus making them easier to be adjusted between various types of paths, including discrete optimal trajectories. Monte Carlo simulations and real-world flight tests have confirmed the effectiveness of the nonlinear guidance algorithm.

Revisiting Fisher-KPP model to interpret the spatial spreading of invasive cell population in biology

In this paper, the homotopy analysis method, a powerful analytical technique, is applied to obtain analytical solutions to the Fisher-KPP equation in studying the spatial spreading of invasive species in ecology and to extract the nature of the spatial spreading of invasive cell populations in biology. The effect of the proliferation rate of the model of interest on the entire population is studied. It is observed that the invasive cell or the invasive population is decreased within a short time with the minimum proliferation rate. The homotopy analysis method is found to be superior to other analytical methods, namely the Adomian decomposition method, the homotopy perturbation method, etc. because of containing an auxiliary parameter, which provides us with a convenient way to adjust and control the region of convergence of the series solution. Graphical representation of the approximate series solutions obtained by the homotopy analysis method, the Adomian decomposition method, and the Homotopy perturbation method is illustrated, which shows the superiority of the homotopy analysis method. The method is examined on several examples, which reveal the ingenuousness and the effectiveness of the method of interest.

Optimized PIDD2 controller for AVR systems regarding robustness

The novel method for tuning proportional-integral-derivative controller with second order derivative term (PIDD2) for the automatic voltage regulator (AVR) of synchronous generator is presented. The design method minimizes load disturbance response regarding constraints on sensitivity functions: maximum sensitivity Ms, maximum complementary sensitivity Mp and measurement noise sensitivity Mn. Simple solution is obtained by shifting PIDD2 controller in a new parameter space and by employing an iterative procedure. In each iteration the five controller parameters are obtained by solving the constrained optimization problem concerning sensitivities Ms and Mn for the fixed value of controller zeros damping factor ξ. The robustness index Mp is calculated subsequently. In that manner, maximum of complementary sensitivity Mp is met by means of auxiliary parameter ξ. The performance improvements are achieved in comparison with traditional PID controller, while robustness is retained. Further, the comparison is made with an optimization method using amplitude optimum principle that also minimizes load disturbance response with different optimality criterion. Experiments are carried out on a small lab synchronous generator setup in order to demonstrate practical potential in real noisy environment of the proposed method and to justify the increased order of AVR controller.

Gas-PM2.5 partitioning, health risks, and sources of atmospheric PAHs in a northern China city: Impact of domestic heating

The diurnal variation, gas-particle partitioning, health risks, and sources of polycyclic aromatic hydrocarbons (PAHs) were investigated in a northern basin city of China in winter, 2020. The mean concentrations of particulate and gaseous PAHs were 87.90 ng m−3 and 69.65 ng m−3, respectively, and their concentrations were considerably enhanced during the domestic heating period. The relationship between the gas-particle partitioning coefficient of PAHs (KP) and subcooled liquid vapor pressure of PAHs (PL0) indicated organic absorption as the mechanism for this partitioning. However, the dual sorption model confirmed adsorption onto elemental carbon (EC). The health risks indicated by several equivalent parameters showed an important health effect of PAHs, especially of particulate PAHs bound onto PM2.5 during the heating period. Environmentally persistent free radicals (EPFRs) were also studied as an auxiliary parameter to evaluate the health impact of PAHs. According to the diagnostic ratios of PAHs and PMF model results, petroleum volatilization and coal combustion were the dominant sources of particulate PAHs during the non-heating and heating periods, respectively. The source apportionment results can help efficiently control PAHs and their health risks.

Adaptive neural fault‐tolerant control of an uncertain 2‐DOF helicopter system with actuator faults and output error constrains

AbstractThis paper develops an adaptive neural fault‐tolerant control for an unknown two‐degree of freedom helicopter nonlinear system with output error constraints, actuator fault, and unknown external disturbances. A neural network disturbance observer is used to estimate system uncertainties and actuator gain failures. The tan‐type barrier Lyapunov equation is used to solve the system's output error constraint. To compensate for actuator bias failures and unknown external disturbances in the system, an adaptive auxiliary parameter is established. Furthermore, rigorously analyzing the chosen Lyapunov function, the system's stability is ensured. Finally, the numerical simulation results prove the rationality and effectiveness of the proposed control strategy.