Hybrid Strategy of Partitioned and Monolithic Methods for Solving Strongly Coupled Analysis of Inverse and Direct Piezoelectric and Circuit Coupling

The inverse and direct piezoelectric and circuit coupling are widely observed in advanced electro-mechanical systems such as piezoelectric energy harvesters.Existing strongly coupled analysis methods based on direct numerical modeling for this phenomenon can be classified into partitioned or monolithic formulations.Each formulation has its advantages and disadvantages,and the choice depends on the characteristics of each coupled problem.This study proposes a new option:a coupled analysis strategy that combines the best features of the existing formulations,namely,the hybrid partitioned-monolithic method.The analysis of inverse piezoelectricity and the monolithic analysis of direct piezoelectric and circuit interaction are strongly coupled using a partitioned iterative hierarchical algorithm.In a typical benchmark problem of a piezoelectric energy harvester,this research compares the results from the proposed method to those from the conventional strongly coupled partitioned iterative method,discussing the accuracy,stability,and computational cost.The proposed hybrid concept is effective for coupled multi-physics problems,including various coupling conditions.

Research on the Generation Mechanism and Suppression Method of Aerodynamic Noise in Expansion Cavity Based on Hybrid Method

The expansion chamber serves as the primary silencing structure within the exhaust pipeline.However,it can also act as a sound-emitting structure when subjected to airflow.This article presents a hybrid method for numerically simulating and analyzing the unsteady flow and aerodynamic noise in an expansion chamber under the influence of airflow.A fluid simulation model is established,utilizing the Large Eddy Simulation(LES)method to calculate the unsteady flow within the expansion chamber.The simulation results effectively capture the development and changes of the unsteady flow and vorticity inside the cavity,exhibiting a high level of consistency with experimental observations.To calculate the aerodynamic noise sources within the cavity,the flow field results are integrated using the method of integral interpolation and inserted into the acoustic grid.The acoustic analogy method is then employed to determine the aerodynamic noise sources.An acoustic simulation model is established,and the flow noise source is imported into the sound field grid to calculate the sound pressure at the far-field response point.The calculated sound pressure levels and resonance frequencies show good agreement with the experimental results.To address the issue of airflow regeneration noise within the cavity,perforated tubes are selected as a means of noise suppression.An experimental platformfor airflow regeneration noise is constructed,and experimental samples are processed to analyze and verify the noise suppression effect of perforated tube expansion cavities under different airflow velocities.The research findings indicate that the perforated tube expansion cavity can effectively suppress low-frequency aerodynamic noise within the cavity by impeding the formation of strong shear layers.Moreover,the semi-perforated tube expansion cavity demonstrates the most effective suppression of aerodynamic noise.

A Hybrid Level Set Optimization Design Method of Functionally Graded Cellular Structures Considering Connectivity

With the continuous advancement in topology optimization and additive manufacturing(AM)technology,the capability to fabricate functionally graded materials and intricate cellular structures with spatially varying microstructures has grown significantly.However,a critical challenge is encountered in the design of these structures–the absence of robust interface connections between adjacent microstructures,potentially resulting in diminished efficiency or macroscopic failure.A Hybrid Level Set Method(HLSM)is proposed,specifically designed to enhance connectivity among non-uniform microstructures,contributing to the design of functionally graded cellular structures.The HLSM introduces a pioneering algorithm for effectively blending heterogeneous microstructure interfaces.Initially,an interpolation algorithm is presented to construct transition microstructures seamlessly connected on both sides.Subsequently,the algorithm enables the morphing of non-uniform unit cells to seamlessly adapt to interconnected adjacent microstructures.The method,seamlessly integrated into a multi-scale topology optimization framework using the level set method,exhibits its efficacy through numerical examples,showcasing its prowess in optimizing 2D and 3D functionally graded materials(FGM)and multi-scale topology optimization.In essence,the pressing issue of interface connections in complex structure design is not only addressed but also a robust methodology is introduced,substantiated by numerical evidence,advancing optimization capabilities in the realm of functionally graded materials and cellular structures.

Behavioral Decision-Making of Key Stakeholders in Public-Private Partnerships:A Hybrid Method and Benefit Distribution Study

Public-private partnerships(PPPs)have been used by governments around the world to procure and construct infrastructural amenities.It relies on private sector expertise and funding to achieve this lofty objective.However,given the uncertainties of project management,transparency,accountability,and expropriation,this phenomenon has gained tremendous attention in recent years due to the important role it plays in curbing infrastructural deficits globally.Interestingly,the reasonable benefit distribution scheme in a PPP project is related to the behavior decisionmaking of the government and social capital,aswell as the performance of the project.In this paper,the government and social capital which are the key stakeholders of PPP projects were selected as the research objects.Based on the fuzzy expected value model and game theory,a hybrid method was adopted in this research taking into account the different risk preferences of both public entities and private parties under the fuzzy demand environment.To alleviate the problem of insufficient utilization of social capital in a PPP project,this paper seeks to grasp the relationship that exists between the benefit distribution of stakeholders,their behavioral decision-making,and project performance,given that they impact the performance of both public entities and private parties,as well as assist in maximizing the overall utility of the project.Furthermore,four game models were constructed in this study,while the expected value and opportunity-constrained programming model for optimal decision-making were derived using alternate perspectives of both centralized decision-making and decentralized decision-making.Afterward,the optimal behavioral decision-making of public entities and private parties in four scenarios was discussed and thereafter compared,which led to an ensuing discussion on the benefit distribution system under centralized decision-making.Lastly,based on an example case,the influence of different confidence levels,price,and fuzzy uncertainties of PPP projects on the equilibrium strategy results of both parties were discussed,giving credence to the effectiveness of the hybrid method.The results indicate that adjusting different confidence levels yields different equilibriumpoints,and therefore signposts that social capital has a fair perception of opportunities,as well as identifies reciprocal preferences.Nevertheless,we find that an increase in the cost coefficient of the government and social capital does not inhibit the effort of both parties.Our results also indicate that a reasonable benefit distribution of PPP projects can assist them in realizing optimum Pareto improvements over time.The results provide us with very useful strategies and recommendations to improve the overall performance of PPP projects in China.

Numerical Treatments for Crossover Cancer Model of Hybrid Variable-Order Fractional Derivatives

In this paper,two crossover hybrid variable-order derivatives of the cancer model are developed.Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators.The existence,uniqueness,and stability of the proposed model are discussed.Adams Bashfourth’s fifth-step method with a hybrid variable-order fractional operator is developed to study the proposed models.Comparative studies with generalized fifth-order Runge-Kutta method are given.Numerical examples and comparative studies to verify the applicability of the used methods and to demonstrate the simplicity of these approximations are presented.We have showcased the efficiency of the proposed method and garnered robust empirical support for our theoretical findings.

The Hybrid Power Mean Involving the Character Sum of Polynomials and a Sum Analogous to Kloosterman Sum

The main purpose of this paper is using the properties of the classical Gauss sum and the analytic methods to study the computational problem of one kind of hybrid power mean involving the character sum of polynomials and a sum analogous to Kloosterman sum mod p,an odd prime,and give two sharp asymptotic formulae for them.

High-Order Solitons and Hybrid Behavior of (3 + 1)-Dimensional Potential Yu-Toda-Sasa-Fukuyama Equation with Variable Coefficients

In this paper, some exact solutions of the (3 + 1)-dimensional variable-coefficient Yu-Toda-Sasa-Fukuyama equation are investigated. By using Hirota’s direct method and symbolic computation, we obtained N-soliton solution. By using the long wave limit method, the N-order rational solution can be obtained from N-order soliton solution. Then, through the paired complexification of parameters, the lump solution is obtained from N-order rational solution. Meanwhile, we obtained a hybrid solution between 1-lump solution and N-soliton (N=1,2) by using the long wave limit method and parameter complex. Furthermore, four different sets of three-dimensional graphs of solitons, lump solutions and hybrid solutions are drawn by selecting four different sets of coefficient functions which include one set of constant coefficient function and three sets of variable coefficient functions.

Influence of Temperature-Dependent Thermophysical Properties of TiO2-SiO2-ZnO-Fe2O3/PAO Tetra-Hybrid Nanofluid along a Vertical Porous Surface with Suction

The significance of the thermophysical properties of Tetra hybrid nanofluid in enhancing heat transmission in various applications like heat exchangers, automobiles, and solar storage cannot be overstated. These features can be tampered with when nanoparticles are been introduced into the base fluid to produce an improved heat carrier fluid for the system. This study investigates the impact of temperature-dependent properties on the movement of TiO2-SiO2-ZnO-Fe2O3/PAO Tetra hybrid nanofluid along a vertical porous surface with suction. The system of governing Partial Differential Equations (PDEs) was formulated and transformed into the system of coupled nonlinear third-order Ordinary Differential Equations (ODEs) by similarity techniques. The resulting ODEs were solved numerically using the shooting method and fourth order Runge-Kutta method with the aid of Maple 18.0 software. Using numerical and statistical methods, the study analyzes velocity, temperature profiles, skin friction coefficient, and Nusselt number. It was found that as the variable thermal conductivity parameter upsurges both the skin friction coefficient and Nusselt number intensify at the rate of 0.011697519 and 8.043581616 respectively. This study underscores the vital role of Tetra hybrid nanofluid’s thermophysical properties in improving heat transmission for diverse appli cations. By manipulating nanoparticles within the base fluid, the heat carrier fluid’s efficiency can be enhanced, critical for industries like automotive and enewable energy. These insights inform the design of more efficient heat exchange systems, advancing sustainability and performance in real-world scenarios.

Hybrid Nanofluid Flow over a Stretching Curved Surface with Induced Magnetic Field and Homogeneous-Heterogeneous Reactions

This study explores the 2D stretching flow of a hybrid nanofluid over a curved surface influenced by a magnetic field and reactions. A steady laminar flow model is created with curvilinear coordinates, considering thermal radiation, suction, and magnetic boundary conditions. The nanofluid is made of water with copper and MWCNTs as nanoparticles. The equations are transformed into nonlinear ODEs and solved numerically. The model’s accuracy is confirmed by comparing it with published data. Results show that fluid velocity increases, temperature decreases, and concentration increases with the curvature radius parameter. The hybrid nanofluid is more sensitive to magnetic field changes in velocity, while the nanofluid is more sensitive to magnetic boundary coefficient changes. These insights can optimize heat and mass transfer in industrial processes like chemical reactors and wastewater treatment.

High-Order Soliton Solutions and Hybrid Behavior for the (2 + 1)-Dimensional Konopelchenko-Dubrovsky Equations

In this paper, the evolutionary behavior of N-solitons for a (2 + 1)-dimensional Konopelchenko-Dubrovsky equations is studied by using the Hirota bilinear method and the long wave limit method. Based on the N-soliton solution, we first study the evolution from N-soliton to T-order (T=1,2) breather wave solutions via the paired-complexification of parameters, and then we get the N-order rational solutions, M-order (M=1,2) lump solutions, and the hybrid behavior between a variety of different types of solitons combined with the parameter limit technique and the paired-complexification of parameters. Meanwhile, we also provide a large number of three-dimensional figures in order to better show the degeneration of the N-soliton and the interaction behavior between different N-solitons.

Tracking a Tip Vortex with Adaptive Vorticity Confinement and Hybrid RANS-LES

The prediction of coherent vortices with standard RANS solvers suffers especially from discretisation and modelling errors which both introduce numerical diffusion. The adaptive Vorticity Confinement (VC) method targets to counteract one part of the discretisation error: the one due to the discretisation of the convection term. This method is applied in conjunction with a hybrid RANS-LES turbulence model to overcome the overprediction of turbulence intensity inside vortex cores which is a typical deficiency of common RANS solvers. The third main source for numerical diffusion originates from the spatial discretisation of the solution domain in the vicinity of the vortex core. The corresponding error is analysed within a grid convergence study. A modification of the adaptive VC method used in conjunction with a high-order discretisation of the convection term is presented and proves to be superior. The simulations of a wing tip vortex flow are validated in terms of vortex velocity profiles using the results of a wind tunnel experiment performed by Devenport and colleagues (1996). Besides, the results are compared with another numerical study by Wells (2009) who uses a Reynolds Stress turbulence model. It turns out that the application of the modified adaptive VC method on the one hand reinforces the tip vortex, and on the other hand accelerates the axial flow which leads to a slight degradation compared to the experimental results. The result of Wells is more accurate close to the wing, but the result obtained here is superior further downstream as no excessive diffusion of the tip vortex occurs.

2D multi-scale hybrid optimization method for geophysical inversion and its application

Local and global optimization methods are widely used in geophysical inversion but each has its own advantages and disadvantages. The combination of the two methods will make it possible to overcome their weaknesses. Based on the simulated annealing genetic algorithm （SAGA） and the simplex algorithm, an efficient and robust 2-D nonlinear method for seismic travel-time inversion is presented in this paper. First we do a global search over a large range by SAGA and then do a rapid local search using the simplex method. A multi-scale tomography method is adopted in order to reduce non-uniqueness. The velocity field is divided into different spatial scales and velocities at the grid nodes are taken as unknown parameters. The model is parameterized by a bi-cubic spline function. The finite-difference method is used to solve the forward problem while the hybrid method combining multi-scale SAGA and simplex algorithms is applied to the inverse problem. The algorithm has been applied to a numerical test and a travel-time perturbation test using an anomalous low-velocity body. For a practical example, it is used in the study of upper crustal velocity structure of the A＇nyemaqen suture zone at the north-east edge of the Qinghai-Tibet Plateau. The model test and practical application both prove that the method is effective and robust.

宽速域RANS-LES混合方法的发展及应用

传统的雷诺平均方法(RANS)已经不能满足大范围分离、激波振荡、压力脉动、动载荷等极端工况下的流动预测需求;大涡模拟(LES)、直接数值模拟(DNS)等方法资源耗费多、效率低,离工程湍流问题仍较为遥远。RANSLES混合方法结合了RANS高效率和LES高精度的特点,近期有望大规模应用到工程湍流问题中。首先对现有的RANS-LES混合方法进行了归类,对各自的构造思想、特点进行了分析。然后报告了脱体涡模拟(DES)类方法的发展历程和现状,讨论了使用DES类方法计算分离流动时,对流项离散格式对分离特性、小尺度结构及频谱特性等的影响,并构造了自适应耗散函数。最后介绍了近年来国内外RANS-LES混合方法在宽马赫数范围(马赫数从0.1到20)内的机理研究和工程应用。现有的以DES类方法为代表的RANS-LES混合方法能够较为精细地模拟非定常大分离流动中的复杂现象,但在计算效率等方面还有较大的改进空间;植入式DES方法在模拟全机带部件流动上具有较高的效率和模拟精度,是重要的发展方向。RANS-LES混合方法在动态失速、燃烧、气动弹性、气动噪声、气动光学等与非定常流动密切相关的方面也有广阔的应用前景。

Hybrid method for investigation of electromagnetic scattering from conducting target above the randomly rough surface

A current based hybrid method （HM） is proposed which combines the method of moment （MOM） with the Kirchhoff approximation （KA） for the analysis of scattering interaction between a two-dimensional （2D） infinitely long conducting target with arbitrary cross section and a one-dimensional （1D） Gaussian rough surface. The electromagnetic scattering region in the HM is split into KA region and MOM region. The electric field integral equation （EFIE） in MOM region （target） is derived, the computational time of the HM depends mainly on the number of unknowns of the target. The bistatic scattering coefficient for the infinitely long cylinder above the rough surface with Gaussian roughness spectrum is calculated, and the numerical results are compared and verified with those obtained by the conventional MOM, which shows the high efficiency of the HM. Finally, the influence of the size, location of the target, the rms height and correlation length of the rough surface on the bistatic scattering coefficient with different polarizations is discussed in detail.

Yield and tillering response of super hybrid rice Liangyoupeijiu to tillage and establishment methods

Tillering is an important agronomic trait for rice grain production. To evaluate yield and tillering response, Liangyoupeijiu(super hybrid rice) was grown in Hunan, China during 2011–2012 under different methods of tillage(conventional and no-tillage system) and crop establishment methods(transplanting at a spacing of 20 cm × 20 cm with one seedling per hill and direct seeding at a seeding rate of 22.5 kg ha-1). Our results revealed that, at maximum tillering(Max.) and at maturity(MA) stages, direct seeding(DS) resulted in 22% more tillers than transplanting(TP) irrespective of tillage system. Tiller mortality reached a peak between panicle initiation(PI) and booting(BT) stages, and was 16% higher under conventional tillage(CT) than under no-tillage(NT). Transplanting required 29% more time for the completion of tillering and less for DS. Tillering rate was 43% higher in DS than TP under either CT or NT. There was a positive correlation between panicle number per m2and maximum tiller number per m2, but not panicle-bearing tiller rate. The panicle bearing tiller rate was higher under DS than TP and higher under NT than CT. Tiller dry weight gradually increased up to heading(HD) stage, and was 14% higher under TP than DS. Leaf area(cm2tiller-1) gradually increased from Max. to HD stage and then decreased by 34% in conventional tillage transplanting(CTTP) and 45% in no-tillage transplanting(NTTP) from 12DAH–24DAH(days after heading), but was similar(35%) under DS under either CT or NT. Grain yield was higher under CTTP owing to the larger sink size(heavier panicle, more spikelets in per cm length of panicle) than under DS.

NEW HYBRID CONJUGATE GRADIENT METHOD AS A CONVEX COMBINATION OF LS AND FR METHODS

In this paper, we present a new hybrid conjugate gradient algorithm for unconstrained optimization. This method is a convex combination of Liu-Storey conjugate gradient method and Fletcher-Reeves conjugate gradient method. We also prove that the search direction of any hybrid conjugate gradient method, which is a convex combination of two conjugate gradient methods, satisfies the famous D-L conjugacy condition and in the same time accords with the Newton direction with the suitable condition. Furthermore, this property doesn't depend on any line search. Next, we also prove that, moduling the value of the parameter t,the Newton direction condition is equivalent to Dai-Liao conjugacy condition.The strong Wolfe line search conditions are used.The global convergence of this new method is proved.Numerical comparisons show that the present hybrid conjugate gradient algorithm is the efficient one.

Simulation of bluff body stabilized flows with hybrid RANS and PDF method

The motivation of this study is to investigate the turbulence-chemistry interactions by using probability density function （PDF） method. A consistent hybrid Reynolds Averaged Navier-Stokes （RANS）/PDF method is used to simulate the turbulent non-reacting and reacting flows. The joint fluctuating velocity-frequency-composition PDF equation coupled with the Reynolds averaged density, momentum and energy equations are solved on unstructured meshes by the Lagrangian Monte Carlo （MC） method combined with the finite volume （FV） method. The simulation of the axisymmetric bluff body stabilized non-reacting flow fields is presented in this paper. The calculated length of the recirculation zone is in good agreement with the experimental data. Moreover, the significant change of the flow pattern with the increase of the jet-to-coflow momentum flux ratio is well predicted. In addition, comparisons are made between the joint PDF model and two different Reynolds stress models.

Evaluation of integration methods for hybrid simulation of complex structural systems through collapse

This study examines the performance of integration methods for hybrid simulation of large and complex structural systems in the context of structural collapse due to seismic excitations. The target application is not necessarily for real-time testing, but rather for models that involve large-scale physical sub-structures and highly nonlinear numerical models. Four case studies are presented and discussed. In the first case study, the accuracy of integration schemes including two widely used methods, namely, modified version of the implicit Newmark with fixed-number of iteration （iterative） and the operator-splitting （non-iterative） is examined through pure numerical simulations. The second case study presents the results of 10 hybrid simulations repeated with the two aforementioned integration methods considering various time steps and fixed-number of iterations for the iterative integration method. The physical sub-structure in these tests consists of a single-degree-of-freedom （SDOF） cantilever column with replaceable steel coupons that provides repeatable highly- nonlinear behavior including fracture-type strength and stiffness degradations. In case study three, the implicit Newmark with fixed-number of iterations is applied for hybrid simulations of a 1：2 scale steel moment frame that includes a relatively complex nonlinear numerical substructure. Lastly, a more complex numerical substructure is considered by constructing a nonlinear computational model of a moment frame coupled to a hybrid model ofa 1：2 scale steel gravity frame. The last two case studies are conducted on the same porotype structure and the selection of time steps and fixed number of iterations are closely examined in pre-test simulations. The generated unbalance forces is used as an index to track the equilibrium error and predict the accuracy and stability of the simulations.

AN IMPROVED HYBRID BOUNDARY NODE METHOD IN TWO-DIMENSIONAL SOLIDS

The hybrid boundary node method （HBNM） is a promising method for solving boundary value problems with the hybrid displacement variational formulation and shape functions from the moving least squares（MLS） approximation. The main idea is to reduce the dimensionality of the former and keep the meshless advantage of the latter. Following its application in solving potential problems, it is further developed and numerically implemented for 2D solids in this paper. The rigid movement method is employed to solve the hyper-singular integrations. Numerical examples for some 2D solids have been given to show the characteristics. The computation results obtained by the present method are in excellent agreement with the analytical solution. The parameters that influence the performance of this method are studied through numerical examples.

DUAL RECIPROCITY HYBRID BOUNDARY NODE METHOD FOR THREE-DIMENSIONAL ELASTICITY WITH BODY FORCE

Combining Dual Reciprocity Method （DRM） with Hybrid Boundary Node Method （HBNM）, the Dual Reciprocity Hybrid Boundary Node Method （DRHBNM） is developed for three-dimensional linear elasticity problems with body force. This method can be used to solve the elasticity problems with body force without domain integral, which is inevitable by HBNM. To demonstrate the versatility and the fast convergence of this method, some numerical examples of 3-D elasticity problems with body forces are examined. The computational results show that the present method is effective and can be widely applied in solving practical engineering problems.