Real Parameters Research Articles

On the Analytic Continuation of Appell’s Hypergeometric Function F2 to Some Symmetric Domains in the Space C2

The paper considers the problem of representation and extension of Appell’s hypergeometric functions by a special family of functions—branched continued fractions. Here, we establish new symmetric domains of the analytical continuation of Appell’s hypergeometric function F2 with real and complex parameters, using their branched continued fraction expansions whose elements are polynomials in the space C2. To do this, we used a technique that extends the domain of convergence of the branched continued fraction, which is already known for a small domain, to a larger domain, as well as the PC method to prove that it is also the domain of analytical continuation. A few examples are provided at the end to illustrate this.

Testing the Instanton Approach to the Large Amplification Limit of a Diffraction-Amplification Problem

Abstract The validity of the instanton analysis approach is tested numerically in the case of the diffraction-amplification problem ∂zψ−(i/2m)∂2 x2 ψ=g│S│2 for ln U>>1, where U=│ψ(0,L)│2. Here, S(x,z) is a complex Gaussian random field, z and x respectively are the axial and transverse coordinates, with 0≤z≤L, and both m≠0 and g>0 are real parameters. We consider a class of S, called the `one-max class', for which we devise a specific biased sampling procedure. As an application, p(U), the probability distribution of U, is obtained down to values less than 10-2270 in the far right tail. We find that the agreement of our numerical results with the instanton analysis predictions in Mounaix (2023 J. Phys. A: Math. Theor. 56 305001) is remarkable. Both the predicted algebraic tail of p(U) and concentration of the realizations of S onto the leading instanton are clearly confirmed, which validates the instanton analysis numerically in the large ln U limit for S in the one-max class.

Comparison of passive and semi-active piezoelectric transducer damping of cantilever oscillation

The aim of this work is the analysis of passive and semi-active damping methods on the model woven beam with a piezoelectric (PZ) layer. The mathematical model of the PZ layer on cantilever beam is derived. For modeling, real product parameters of PZ layer are used, and through simulation find the optimal values to dampen it. The resistive-inductance passive model, and State-Switch Damping SSD semi-active model are used in this work. The models are processed in the MATLAB Simulink environment and the results of the behavior of the models compared to each other. The program involving passive and semi-active systems, where analyze the behavior of the model for different parameters and the damping capabilities of individual methods are compared. The simulation results show the effectiveness of the semi-active system in comparison with the passive systems, also it shows the passive method is not so effective at low frequency as it in high frequency, and the semi-active method is not optimal for high frequency vibration.

U-AEFA: Online and offline learning-based unified artificial electric field algorithm for real parameter optimization

Optimization problems in real-world scenarios require algorithms that effectively balance exploration and exploitation to avoid local optima and achieve global solutions. To address this, we propose a unified artificial electric field algorithm (U-AEFA) that integrates both offline learning (inspired by high-performing metaheuristic algorithms) and online learning (through historical data generated during evolution). U-AEFA introduces a unique three-layer population structure to enhance search efficiency, consisting of the best agent in the first layer, the top-performing agents in the second layer, and the remaining agents in the third layer. Key features of U-AEFA include (i) an effective Coulomb’s constant for improved exploration, (ii) a non-uniform mutation operator to mitigate premature convergence, and (iii) two acceleration coefficients for enhanced performance. These three factors constitute offline learning and have been implemented to improve different design elements of the algorithm. As part of online learning, it employs a difference vector reuse (DVR) strategy to evolve the first-layer agents. The algorithm is evaluated using the CEC 2017 test suite across multiple dimensions (10, 30, 50, 100), where it consistently outperforms seven state-of-the-art algorithms, demonstrating superior accuracy and convergence speed. Moreover, U-AEFA’s robustness is validated on 12 high-dimensional feature selection problems, further highlighting its effectiveness in solving complex optimization tasks. The source code of U-AEFA is available at

Thermal calibration for triaxial gyroscope of MEMS-IMU based on segmented systematic method

With the progress of micro electromechanical system (MEMS) technology, the performance of MEMS inertial measurement unit (IMU) composed of gyroscopes and accelerometers has been improved. Among the inertial sensors, MEMS triaxial gyroscope plays an important role in attitude estimation, navigation and positioning of intelligent mobile terminals such as unmanned aerial vehicles and unmanned vehicles. However, the measured values of low and medium cost MEMS triaxial gyroscopes are mainly affected by temperature (or thermal effect) and random errors. As results, the drift errors correlated with temperature will reduce application accuracy of MEMS triaxial gyroscope. The traditional calibration method for thermal drift errors relies on the expensive equipment, such as turntable and the temperature control system, which increases the cost of calibration. Therefore, an effective thermal calibration method that is available when using low- or high-cost tools for MEMS triaxial gyroscope will be meaningful for majority users. Hence, this paper analyzed and established the thermal drift model of MEMS triaxial gyroscope, and proposed a segmented systematic calibration method based on 24 states according to this model. Simulation shows that the proposed method can obtain the results approaching the real parameter thermal drift curves. Calibration experiments and parameters test show that the max errors of attitude calculation are reduced to 10% of the results using the original parameters, which indicates that the effectiveness of the proposed method.

A framework of integrated differential evolution variants based on adaptive relay mode for global optimization

Differential evolution (DE) is highly competitive in single-objective real parameter optimization. However, there are still some problems with differential evolutionary variants in optimizing complex multimode functions, such as poor solution accuracy and slow convergence. To address these problems, an optimization framework of integrated DE variants based on adaptive relay mode (fDE-ARM) is proposed. In this framework, different DE variants are integrated through two adaptive relay mechanisms to give full play to the advantages of the algorithms, thereby improving the performance of the whole algorithm. For the first adaptive relay mode, when the currently executed algorithm is judged to have converged, the population is updated by Gaussian random walk, and then the optimization is continued through the relay algorithm. For the second adaptive relay mode, the relay condition is determined by the average fitness improvement rate. If the condition is met, the relay algorithm takes over the optimization. At the same time, if the diversity is lower than the threshold, to improve the exploration, the roulette wheel method is used to select some individuals to perform the Gaussian random walk. In addition, a feedback mechanism is introduced in the relay process to avoid false switching. To verify the performance of the proposed algorithm, extensive simulations are performed on CEC2005, CEC2014, CEC2017, and CEC2021 benchmark functions. In addition, three engineering problems are used to test the performance. Compared with some newly proposed optimization algorithms, fDE-ARM is statistically superior to the comparison algorithms in terms of solution accuracy, convergence speed, and stability.

Analysis of the influence of brake pipe pressure gradient on heavy haul combined train and optimisation of operation strategy

In this paper, based on the theory of gas flow, the action logic of the control valve, and the principle of multi-rigid-body dynamics, a simulation model of the 20,000 t heavy haul combined train is established to investigate the influence of brake pipe pressure gradient on the braking performance, longitudinal dynamics, braking and release characteristics of trains. Utilizing real railway line conditions, locomotive and vehicle parameters, and train operation monitoring equipment (LKJ) record data of Shuozhou-Huanghua Railway, the cyclic braking condition of the train on the long and steep downhill is simulated, and the control strategy of reducing the coupler force during the cyclic braking is proposed. The results indicate that a larger brake pipe pressure gradient before braking leads to weaker braking capability, and higher coupler forces during braking, but smaller coupler forces during release. As the brake pipe pressure gradient before braking increases, braking synchronicity decreases, while release synchronicity slightly improves. By adjusting the locomotive’s electric braking force during the cyclic braking, it is possible to appropriately increase the brake pipe pressure gradient before braking, effectively reducing coupler forces during release and reducing the number of braking cycles, thus lowering the operational difficulty of the train.

Hybrid building energy modeling method with parameterized prototype models and rapid calibration

Building energy models were widely used in building energy performance analysis and efficiency improvement, such as building demand response assessment and energy system optimization. However, building energy modeling was a time-consuming and complex process. Therefore, this paper proposed a hybrid building energy modeling method based on parameterized prototype models and rapid calibration. The main feature of the method was the rapid generation of target building energy models using the prototype building energy performance database. The parameterized prototype building energy model considered 13 uncertainty parameters. Based on the range of 13 uncertainty parameters, such as wall U-value and solar heat gain coefficient, 1000 simulations were performed by Monte Carlo sampling to generate the prototype building energy performance database. The target building energy model was quickly calibrated by learning from this database. It filtered the models that met the requirements based on the actual building measurement data. Based on this hybrid modeling method, the rapid modeling tool AutoBPS-Hybrid was developed in a ruby environment. Shopping mall buildings located in three different climate zones were selected as case studies for this study. The results showed that if only one building energy model meeting the percentage errors was needed, only 3–4 simulations were required. If it was necessary to match the real uncertainty parameter distributions, an average of about 53 simulations was needed. The building energy models were applied to plug load and lighting control in buildings. The shopping mall buildings in Harbin, Beijing and Chengdu could reduce energy consumption by 10.18–13.33 kWh/m2, 14.43–18.15 kWh/m2 and 11.54–14.69 kWh/m2 per year, respectively.

Rogue-wave structures for a generalized (3+1)-dimensional nonlinear wave equation in liquid with gas bubbles

This study explores the behavior of higher-order rogue waves within a (3+1)-dimensional generalized nonlinear wave equation in liquid-containing gas bubbles. It creates the investigated equation’s Hirota D-operator bilinear form. We employ a generalized formula with real parameters to obtain the rogue waves up to the third order using the direct symbolic technique. The analysis reveals that the second and third-order rogue solutions produce two and three-waves, respectively. To gain deeper insights, we use the Cole-Hopf transformation on the transformed variables ξ and η to produce a bilinear equation. Using the system software Mathematica, the dynamic analysis presents the graphics for the obtained solutions in transformed ξ, η, and original spatial-temporal coordinates x, y, z, t. These visualizations reveal rogue waves’ intricate structure and evolution, capturing their localized interactions and significant presence within nonlinear systems. We demonstrate that rogue waves, characterized by their substantial height and sudden appearance, are prevalent in various nonlinear events. The equation examined in this study offers valuable insights into the evolution of longer waves with smaller amplitudes, which is particularly relevant in fields such as fluid dynamics, dispersive media, and plasmas. The implications of this research extend across multiple scientific domains, including fiber optics, oceanography, dusty plasma, and nonlinear systems, where understanding the behavior of rogue waves is crucial for both theoretical and practical applications.

Modeling Electronic Devices with a Casimir Cavity

The Casimir effect has been exploited in various MEMS (micro-electro-mechanical system) devices, especially to make sensitive force sensors and accelerometers. It has also been used to provide forces for a variety of purposes, for example, for the assembly of considerably small parts. Repulsive forces and torques have been produced using various configurations of media and materials. Just a few electronic devices have been explored that utilize the electrical properties of the Casimir effect. Recently, experimental results were presented that described the operation of an electronic device that employed a Casimir cavity attached to a standard MIM (metal–insulator–metal) structure. The DC (direct current) conductance of the novel MIM device was enhanced by the attached cavity and found to be directly proportional to the capacitance of the attached cavity. The phenomenological model proposed assumed that the cavity reduced the vacuum fluctuations, which resulted in a reduced injection of carriers. The analysis presented here indicates that the optical cavity actually enhances vacuum fluctuations, which would predict a current in the opposite direction from that observed. Further, the vacuum fluctuations near the electrode are shown to be approximately independent of the size of the optical cavity, in disagreement with the experimental data which show a dependence on the size. Thus, the proposed mechanism of operation does not appear correct. A more detailed theoretical analysis of these devices is needed, in particular, one that uses real material parameters and computes the vacuum fluctuations for the entire device. Such an analysis would reveal how these devices operate and might suggest design principles for a new genre of electronic devices that make use of vacuum fluctuations.

Eigenbasis for a weighted adjacency matrix associated with the projective geometry Bq(n)

In a recent article Projective geometries, Q-polynomial structures, and quantum groups Terwilliger (arXiv:2407.14964) defined a certain weighted adjacency matrix, depending on a free (positive real) parameter, associated with the projective geometry, and showed (among many other results) that it is diagonalizable, with the eigenvalues and their multiplicities explicitly written down, and that it satisfies the Q-polynomial property (with respect to the zero subspace).In this note we•Write down an explicit eigenbasis for this matrix.•Evaluate the adjacency matrix-eigenvector products, yielding a new proof for the eigenvalues and their multiplicities.•Evaluate the dual adjacency matrix-eigenvector products and directly show that the action of the dual adjacency matrix on the eigenspaces of the adjacency matrix is block-tridiagonal, yielding a new proof of the Q-polynomial property.

Pre-cooling systems in modern hydrogen liquefaction

The research work presents recommendations for choosing a circuit design for low-capacity hydrogen liquefaction plants with a production rate up to 20 kg/h or 0,48 tpd (ton per day). Main design criteria considered are specific energy cost, as well as capital costs and overall characteristics of the system. A review of theoretical and real hydrogen liquefaction cycles is presented. Mathematical models of different circuits are built up considering real parameters of the typical equipment. The advantages and disadvantages of certain solutions are identified, efficiency trends in terms of hydrogen liquefaction plants are analysed. According to the obtained results of the research main of the circuits for low-capacity hydrogen liquefaction plants are selected.

Analytical approach to piezoelectric model synthesis with the use of Cauer’s method for system design

Background Piezoceramic materials have unique property which enables direct and bilateral conversion between mechanical and electrical energy. This ability facilitates significant miniaturisation of technology and opens many opportunities in design of new actuators and energy harvesters. Mathematical modelling of piezoelectric modules is notoriously hard due to complex constitutive equations defining mechanical and electrical energy conversion. Methods The article presents research on a new synthesis method based on the Cauer’s method. Mechanical damping is introduced with the use of Rayleigh’s approximation. A discrete electromechanical model is formed based on the Mason’s piezoelectric model. The proposed approach allows modelling of piezoelectric systems based on a set of characteristic frequencies. The method allows a more general approach to the problem of modelling new systems, as opposed to application-oriented methods seen in literature. A non-standard model analysis method using edge graphs and structural numbers is also verified as a potential alternative for matrix-based method. The authors compare their precision and computation requirements. Results The structural method of mechanical model analysis gave identical results as the reference matrix method. However, the non-classical algorithm took much longer to calculate and was using more memory. The electromechanical model analysis has shown an error of 5% in comparison to resonance frequencies taken from a reference plate specification. The calculated magnitude of displacement was well above the capability of a 3.5mm thick piezoelectric plate. Conclusions The synthesis method presented in this paper allows synthesizing piezoelectric cascade models based on limited information in form of characteristic frequencies. Currently this method allows a coarse approximation of the real piezoelectric parameters with limited number of inputs. The additional method of analysis based on structural numbers offers a promising alternative to matrix calculations but requires a more thorough investigation of the computational power required to determine whether it can compete with existing algorithms.

Evaluating the Crashworthiness of Truck Rear-End Under-Run Bars: A Finite Element Analysis

Rear-end collisions involving trucks can have a direct impact on the safety of vehicle occupants, particularly due to the crashworthiness of the truck's rear-end under-run bar. These types of accidents, which occur between small vehicle and truck, contribute significantly to fatalities and serious injuries, presenting a significant public safety concern. This research paper aims to examine the collision effects on the rear-end under-run bar of a truck and its behaviour when it collides with another vehicle. The study employed the finite element method and simulated the under-run bar and impactor collisions using finite element software. The entire structure of the rear-end under-run bar had been designed, taking into account real parameters. The under-run bar structure was made of steel, and the impactor had a mass of 115kg, which resembled the mass of a motorcycle. A predefined field feature was utilized to apply a velocity of 30km/h to the impactor, which had a cylindrical shape. The element size of the mesh for the under-run bar was determined by using the mesh sensitivity technique. The simulation was tested a few times by using different sizes of elements. It is shown that the force reached a peak value of 28kN at a displacement of 68.25 mm, corresponding to the maximum under-run bar displacement. The data revealed that the energy absorbed increased from time 0.003s to 0.012s, reaching its peak value of 11.08kJ at 0.012s. The results show convincing results and prove the capability of rear-end under-run bar to be simulated and analysed using finite element simulation.

Application of a metric for complex polynomials to bounded modification of planar Pythagorean-hodograph curves

By interpreting planar polynomial curves as complex-valued functions of a real parameter, an inner product, norm, metric function, and the notion of orthogonality may be defined for such curves. This approach is applied to the complex pre-image polynomials that generate planar Pythagorean-hodograph (PH) curves, to facilitate the implementation of bounded modifications of them that preserve their PH nature. The problems of bounded modifications under the constraint of fixed curve end points and end tangent directions, and of increasing the arc length of a PH curve by a prescribed amount, are also addressed.

Generalization of the Synthetic Aperture Radar Azimuth Multi-Aperture Processing Scheme—MAPS

This paper analyzes the advantages and the drawbacks of using the Synthetic Aperture Radar (SAR) azimuth multichannel technique known as Multi-Aperture Processing Scheme (MAPS), in a set of relevant application cases that are far from the canonical ones. In the scientific literature on this topic, equally distributed azimuth channels with the quasi-monostatic deployment are assumed. With this research, we aim at extending the models from the current literature to (i) a generic bistatic acquisition geometry, (ii) a set of cases where the number of receiving tiles is not the same for each channel, or (iii) the tiles are shared between adjacent channels thus creating an overlapping configuration. The paper introduces the mathematical models for the listed non-conventional MAPS cases. Dealing with the bistatic MAPS, we first solve the problem by interpreting multichannel acquisition as a bank of Linear Time Invariant (LTI) filters. Then, a more physical approach, based on discrimination of the direction of arrivals (DoAs) is pursued. The effectiveness of the two methods and the advantages of the second approach on the first are proved by using a simplified 1D end-to-end simulation. Even limiting to the monostatic configuration, the azimuth antenna tiles have always been supposed equally partitioned among the RX channels. Overcoming this limit has two advantages: (i) more MAPS possible solutions in case few azimuth tiles are available, as in the ROSE-L mission; (ii) the number of channels can be designed independently of the number of tiles, also allowing asymmetric solutions, useful for a phase array antenna with an odd number of tiles such as in the SAOCOM-1 mission. Conversely, sharing one or more receiving tiles in different receiving channels makes the input noise partially correlated. The drawback is an increase in the noise level. A trade-off is determined for the different solutions obtained using simulations with real mission parameters. The theoretical performance and the end-to-end simulations are compared.

Generalized CP symmetries in three-Higgs-doublet models

We study the scalar and Yukawa sectors of three Higgs doublets models with a generalized CP symmetry. Imposing the symmetry on the quadratic and quartic couplings of the scalar potential, we show that there are only four classes of scalar potentials, merely one more than in two-Higgs-doublet models (2HDM). Two 3HDM cases are analogs of two 2HDM cases, while the other 2HDM case splits here into two distinct potentials. In 2HDM with generalized CP symmetries extended to the Yukawa sector, there are only two possible cases: the usual CP, with 18 real Yukawa couplings; and a minimal generalized CP model, with 12 real Yukawa parameters. In contrast, with three Higgs there is a rich variety of allowed models. We classify all possible Yukawa textures, showing that there are 40 possibilities, several of which have only 10 real Yukawa couplings. Published by the American Physical Society 2024

The propagation of inhomogeneous waves in an orthotropic viscoelastic medium

Abstract The present article deals with the propagation of inhomogeneous waves in an orthotropic viscoelastic medium. For chosen directions of propagation and a real finite inhomogeneity parameter, a complex slowness vector is specified to define the propagation of an inhomogeneous incident wave. Then, the reflection and transmission of plane waves at a plane interface between two orthotropic viscoelastic half-spaces are discussed. In this incidence, horizontal slowness determines the slowness vectors for all reflected and transmitted waves. For each reflected and transmitted wave, the corresponding slowness vector is resolved to define its phase direction, phase velocity and attenuation angle. Appropriate boundary conditions on this wave field determine the amplitude ratios for reflected and transmitted waves relative to the incident wave. The numerical examples are provided to show the effect of the inhomogeneity of the incident wave on the propagation characteristic as well as the reflection and transmission coefficients. The existence of homogeneous, inhomogeneous incident waves also is investigated.

Local-to-non-local transition laws for stiffness-tuneable monoatomic chains preserving springs mass.

Recently, non-local configurations have been proposed by adding beyond nearest neighbour couplings among elements in lattices to obtain roton-like dispersion relations and phase and group velocities with opposite signs. Even though the introduction of non-local elastic links in metamaterials has unlocked unprecedented possibilities, literature models and prototypes seem neither to provide criteria to compare local and non-local lattices nor to discuss any related rules governing the transition between the two configurations. A physically reasonable principle that monoatomic one-dimensional chains must obey to pass from single- to multi-connected systems is here proposed through a mass conservation law for elastic springs thereby introducing a suitable real dimensionless parameter [Formula: see text] to tune stiffness distribution. Therefore, the dispersion relations as a function of [Formula: see text] and of the degree of non-locality [Formula: see text] are derived analytically, demonstrating that the proposed principle can be rather interpreted as a general mechanical consistency condition to preserve proper dynamics, involving the spring-to-bead mass ratio. Finally, after discussing qualitative results and deriving some useful inequalities, numerical simulations and two-dimensional FFTs are performed for some paradigmatic examples to highlight key dynamics features exhibited by chains with finite length as the parameters [Formula: see text] and [Formula: see text] vary.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

Explicit Parameterizations of Ortho-Symplectic Matrices in R4

Starting from the very first principles we derive explicit parameterizations of the ortho-symplectic matrices in the real four-dimensional Euclidean space. These matrices depend on a set of four real parameters which splits naturally as a union of the real line and the three-dimensional space. It turns out that each of these sets is associated with a separate Lie algebra which after exponentiations generates Lie groups that commute between themselves. Besides, by making use of the Cayley and Fedorov maps, we have arrived at alternative realizations of the ortho-symplectic matrices in four dimensions. Finally, relying on the fundamental structure results in Lie group theory we have derived one more explicit parameterization of these matrices which suggests that the obtained earlier results can be viewed as a universal method for building the representations of the unitary groups in arbitrary dimension.