Rigorous Theoretical Derivation Research Articles

Interfacial dynamic impermeable crack analysis in dissimilar piezoelectric materials by a new interaction integral

Dynamic intensity factors (IFs) provide an important parameter for assessing the failure risk of an interfacial crack for piezoelectric composites exposed to electromechanical impact loadings. In the present research, a new dynamic interaction integral (I-integral) is built for computing the dynamic stress IFs (SIFs) and electric displacement IF (EDIF) of an interfacial crack located in dissimilar inhomogeneous piezoelectric media. Through proper selection of auxiliary variables, the domain expression of I-integral for the inhomogeneous piezoelectric bi-materials does not need to take into account any derivative term for any piezoelectric material property. Further, after rigorous theoretical derivation, the resulting I-integral is still valid for complex models where the integration domain contains other multiple interfaces, regardless of whether the extra materials are straight or curved. Incorporating the modified extended finite element approach, the accuracy is confirmed by checking the dynamic IFs extracted from the I-integral with referenced results. The domain-independence is tested by varying ranges of integration domains for inhomogeneous piezoelectric bi-materials and multi-interface piezoelectric composites. Finally, typical examples are employed to discuss the influences of the direction and magnitude of electric impact loading, combination of polarizations, inhomogeneous degree of piezoelectric bi-materials and complex distribution of diverse material properties on the dynamic IFs.

Efficient 2-Distance Coloring Method for Maximum and Average Sparse Graphs in Resource Allocation Optimization of Microgrids

In microgrids management, optimizing resource allocation and enhancing efficiency are critical challenges. This paper introduces the 2-distance coloring technique as a novel approach to address these issues by focusing on the coloring problem of sparse graphs. Through rigorous theoretical derivation, we establish the minimum number of colors required for 2-distance coloring in sparse graph scenarios. Specifically, we demonstrate that for a graph G with an average maximum degree less than 2+17/20 and a maximum degree of 6, it can be list 2-distance colored using no more than 11 colors. This means that, given any set of 11 colors for each vertex, a valid 2-distance coloring can be achieved, ensuring no two adjacent vertices share the same color. This finding is pivotal, as it sets a precedent for the number of resources needed to efficiently manage and allocate resources in microgrids systems through 2-distance coloring. The application of this technique in microgrids promises to revolutionize resource distribution, reducing overlap and maximizing efficiency across the network.

Fixed-time adaptive neural control of electro-hydraulic system with model uncertainties: Theory and experiments

Nonlinearities, uncertainties and unknown external loads decline tracking dynamic performance and steady-state accuracy of electro-hydraulic systems. Most existing electro-hydraulic controllers have well guaranteed both the cylinder position and the load pressure asymptotic stable or uniformly ultimately bounded. However, the corresponding output response is relatively slow and achieves the desired performance in an infinite time, which cannot meet the requirements of fast convergence in some engineering applications. In this study, a fixed-time adaptive neural control (FTANC) is proposed for an electro-hydraulic system to improve the fast convergence performance and steady-state accuracy of the cylinder position in case of hydraulic model uncertainties A rigorous theoretical derivation proves that the electro-hydraulic system obtains practically fixed-time stability, such that all system state errors converge to the zero neighborhood in a fixed time without relation to the initial conditions of electro-hydraulic systems. Finally, both the simulation and experimental results verify the effectiveness of the proposed control method.

Numerical qualification of the GSP3(0) theory using the analytic function expansion nodal method

The simplified P3 (SP3) method is an important way to implement the pin-by-pin neutron transport calculation of the core. This method has the high accuracy but costs twice the computing time of the diffusion method. Recently, the Generalized SPN (GSPN) theory has been developed, and the ad hoc SPN theory is resolved through rigorous theoretical derivation. GSP3(0) theory is the 3rd order and the 0th layer of GSPN theory. Compared with GSP3(0) theory, the SP3 theory with Marshak boundary condition is regarded as the traditional SP3 theory. The equations of the two theories are the same while the interface and the boundary conditions are different. Based on the GSP3(0) theory and the traditional SP3 theory, transport calculation codes have been developed using the analytical function expansion nodal (AFEN) method. The numerical results show that both of the two SP3 theories are more accurate than the diffusion theory, and the GSP3(0) theory can further improve the accuracy of the pin power calculation compared to the traditional SP3 theory.

Refined beam finite element model for thin-walled multi-cell box girders considering distortion and secondary distortional moment deformation effect

In this paper, a novel one-dimensional refined beam finite element model (FEM) accounting for non-uniform distortional warping and secondary distortional moment deformation effect (SDMDE) is formulated for the distortional analysis of thin-walled multi-cell box girders with cantilevered flanges. The extra distortional angle is introduced to incorporate SDMDE, and the validity of which is proved through rigorous theoretical derivation. The in-plane and out-plane deformations at any point around the edge of transverse section built upon the distortional center are unified in the same form and described in detail. The governing differential equations in terms of two generalized displacements, distortional angle χ and primary distortional angle curvature Θ, are derived based on the principle of minimum potential energy (MPE) and solved exactly so as to provide non-polynomial shape functions for the establishment of element stiffness matrix and nodal load vector. A series of multi-cell rectangular hollow section (RHS) girders are analyzed and particular extensions are given to single-cell and multi-cell bridge girders with cantilevered flanges. Comparisons to the results generated from corresponding ones provided by pioneering work or shell FEM analyses not only validate the correctness and reliability of the present beam element formulations but also highlight the significance of the inclusion of SDMDE when the cantilevered flanges are arranged.

Novel Compact Polarized Martian Wind Imaging Interferometer

The Mars Atmospheric Wind Imaging Interferometer offers several advantages, notably its high throughput, enabling the acquisition of precise and high vertical resolution data on the temperature and wind fields in the Martian atmosphere. Considering the current absence of such an Interferometer, this paper introduces a novel Mars wind field imaging interferometer. In analyzing the photochemical model of O2 (a1Δg) 1.27 μm molecular airglow radiation in the Martian atmosphere and considering the impact of instrument signal-to-noise ratio (SNR), we have chosen an optical path difference (OPD) of 8.6 cm for the interferometer. The all-solid-state polarized wind imaging interferometer is miniaturized by incorporating two arm glasses as the compensation medium in its construction, achieving the effects of field-widening and temperature compensation. Additionally, an F-P Etalon is designed to selectively filter the desired three spectral lines of O2 dayglow, and its effect is evaluated through simulations. The accuracy of the proposed compact Mars polarized wind imaging interferometer for detecting Mars’ wind field and temperature field has been validated through rigorous theoretical derivation and comprehensive computer simulations. The interferometer boasts several advantages, including its compact and small size, static stability, minimal stray light, and absence of moving parts. It establishes the theoretical, technological, and instrumental engineering foundations for future simultaneous static measurement of Martian global atmospheric wind fields, temperature fields, and ozone concentrations from spacecraft, thereby significantly contributing to the dataset for investigating Martian atmospheric dynamics.

Ship-Mounted Cranes Hoisting Underwater Payloads: Transportation Control With Guaranteed Constraints on Overshoots and Swing

In recent years, with the rapid development of marine engineering, ship-mounted crane control for transporting payloads in the water has attracted more attention. Compared with the case of transporting payloads above water, ship-mounted cranes with underwater payloads are more difficult to control. On the one hand, the underwater payload is directly affected by the hydrodynamic force, and the dynamics of ship-mounted cranes is much more complex, nonlinear, and coupled; on the other hand, the unactuated underwater payload swing is quite sensitive to external disturbances; thus, the harsh marine environment will bring great challenges to the anti-swing control of underwater payloads. To address the above issues, this article puts forward a coupling characteristic indicator(CCI)-based nonlinear control method to realize accurate positioning and swing suppression for ship-mounted cranes hoisting payloads in the water, which not only simultaneously suppresses actuated boom overshoots and constrains <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">unactuated</i> payload swing, but also indicates whether the coupling terms are beneficial or harmful to make full use of them to improve transient control performance. Rigorous theoretical derivation proves the closed-loop stability. To the best of our knowledge, this is the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">first</i> solution to handle state constraints and utilizing the coupling characteristics of ship-mounted cranes for transferring payloads in the water. Finally, the proposed controller is applied to a self-made hardware platform, and the experimental results show that the designed method achieves satisfactory control performance.

An evaluation model for wall heat transfer effects on micro centrifugal compressors and its application in aerodynamic design

In micro gas turbine generators, the significant temperature difference within close proximity of the hot and cold components induces a substantial heat influx into the micro centrifugal compressor. This heat influx profoundly modifies the aerodynamic characteristics of the compressor. Ensuring a precise evaluation of the performance decline attributable to wall heat transfer effects and systematically integrating these impacts into the aerodynamic design process assumes paramount importance. Previous evaluation models, which involved unnecessary simplifications, suffered from limitations in accuracy. This paper presented a novel evaluation model for the diabatic isentropic efficiency through entropy analysis of the diabatic ideal compression process and the actual compression process. The rigorous theoretical derivation without any simplification empowers this model to faithfully mirror the authentic aerodynamic performance of diabatic compressors. The experimental and numerical verification results indicate that the proposed model is more reliable than the previous ‘preheating-adiabatic compression’ model when evaluating performance degradation stemming from wall heat transfer. The new model exhibits an error of approximately 3.7% at the design point and a mean absolute error of about 6% along the characteristic line of the design speed. Both deviations are deemed acceptable within the purview of engineering assessments. Furthermore, this paper illustrated an instance of the novel model’s application in the aerodynamic design process. A prototype compressor, impeccably designed under adiabatic conditions but falling short of performance benchmarks during the performance test, was redesigned using the proposed method. The experimental results show that through the incorporation of wall heat transfer effects, the redesigned compressor aligns perfectly with design requirements, yielding an efficiency enhancement of roughly 1.5%.

Appointed-Time Cooperative Guidance Law With Line-of-Sight Angle Constraint and Time-to-go Control

This study proposes a three-dimensional appointed-time cooperative guidance law for multiple missiles. The maneuvering target can be hit simultaneously by multiple missiles with different expected line-of-sight (LOS) angles. It is worth noting that the actual convergence time of the LOS error or time-to-go can be treated as a tuning parameter along the LOS direction and the normal direction of LOS. Firstly, the simultaneous attack problem of multiple missiles can be regarded as a consensus problem. In the LOS direction, a distributed cooperative guidance law is presented to guarantee the time-to-go of all missiles to be consensus at the appointed time. Subsequently, a guidance law is also presented in the normal direction of LOS to achieve the expected LOS angles at the appointed time. Finally, to improve the robustness of the cooperative guidance system, an appointed-time extended state observer (ATESO) is developed for compensating the guidance commands. The stability of the proposed cooperative guidance law is fully proved by the rigorous theoretical derivation. Numerical simulation results verify the efficacy of this scheme.

A stochastic predator–prey model with Ornstein–Uhlenbeck process: Characterization of stationary distribution, extinction and probability density function

This paper concerns with a stochastic system modeling the population dynamical behavior of one prey and two predators. In this paper, we adopt a special method to simulate the effect of the environmental interference to the system instead of using the linear functions of white noise, i.e., the growth rate of the prey and the death rates of the two predators are all governed by Ornstein–Uhlenbeck processes, which is more practical and interesting. The dynamical behavior among the three species in the model is discussed in detail. The existence and uniqueness, moment boundedness and long time asymptotic behavior of the unique global solution are investigated. Through rigorous proof and theoretical derivation, some sharp sufficient conditions for the persistence and extinction of the three species have been established. Furthermore, we obtain that when one or two predators die out, the remaining species can be stable in time average under same conditions. Moreover, by constructing some suitable Lyapunov functions, the sufficient conditions for the existence of the stationary distribution are explicitly determined. Under the same parametric restrictions, it is worth noting that we obtain the six-dimensional probability density function of the stochastic one-prey two-predator model around the quasi-equilibrium E∗, which can reflect most statistical properties. Finally, several numerical simulations are carried out to illustrate the theoretical results.

Sensitivity Analysis in Coupled Monte Carlo Radiation Transport Simulations

Sensitivity analysis methods have found extensive use in nuclear criticality safety applications for understanding the impact of uncertain nuclear data on eigenvalue estimates. Significant uncertainty exists in nuclear data and nuclear physics models for photon and electron transport applications, and the goal of this work is to explore whether recently developed adjoint-based, first-order generalized perturbation theory reaction rate sensitivity methods can be extended to coupled Monte Carlo radiation transport simulations. This paper presents a rigorous theoretical derivation for this extended sensitivity analysis method, which is then implemented in a one-dimensional test Monte Carlo code. The adjoint-based sensitivity coefficients are found to agree well with reference direct perturbation and deterministic SENSMG sensitivity coefficients for a simple test problem.

Analysis of Price Effect and Employment Effect of Government Tax Reduction

Under the influence of today's pandemic, it has led to the stagnation of production and business operations in various industries and the shutdown of enterprises, bringing serious disasters to the global economy. In order to mitigate the loss, governments are adopting policies to ensure the economic development of their countries, such as reducing taxes and fees, issuing national bonds, etc. In this paper, we will assume a closed economy and use Keynesian model to study the effect of government tax cuts on price level and labor employment. Through the rigorous logical analysis and theoretical derivation of this paper, it is found that in a closed economy, if the government reduces taxes, the employment of a country will be increased accordingly, and the price level will have a restraining effect to curb inflation. At the same time, this study can allow the government to formulate and improve policies more scientifically, bring reference and reference to the market, and help enterprises adapt to the market, understand the information and make the proper decisions.

Predefined-time control of chaotic finance/economic system based on event-triggered mechanism

&lt;abstract&gt;&lt;p&gt;Aiming at the problem that the convergence time of the chaotic finance/economic system cannot be set independently and the continuous macro-control is required, this paper investigates the predefined-time control of the chaotic finance/economic system based on event-triggered mechanism. The predefined-time control approach ensures the chaotic finance system quickly converge to the stable state within a pre-determined time. Moreover, in order to avoid continuous macro-control, an event-trigger mechanism is added into the above predefined-time control approach, which guarantees that the control input is updated only when some predefined event occurs. Rigorous theoretical derivation is presented and concrete simulation experiments are carried out to validate the feasibility and applicability of the proposed control strategy.&lt;/p&gt;&lt;/abstract&gt;

A Transaction Cardinality Estimation Approach for QoS-Adjustable Intelligent Blockchain Systems

The rapid development of the blockchain leads to a blowout of on-chain transactions, contracts, and currencies, which will further accelerate the increase of data. The existing blockchain systems typically support exact transaction queries, which, however, cannot satisfy the QoS requirements with intelligent adjustment in the blockchain systems. To this end, this paper takes the first step to define and address the practically important problem of transaction cardinality estimation for QoS-adjustable intelligent blockchain systems. We first establish a mathematical relationship between the bit string and transaction cardinality. Thus, we can leverage the number of leading 1s of the obtained bit string to estimate the transaction cardinality. We then improve the block header and body with a corresponding search algorithm to access bit strings in blocks. We also propose an estimation protocol with intelligent adjustable QoS to support accuracy-guaranteed and efficiency-optimized estimation. Finally, we design an authentication scheme and guarantee the reliability of our protocol through rigorous theoretical derivation. When achieving the transaction cardinality estimation in blockchain, two technical challenges need to be addressed. (i) To ensure efficient, verifiable, and overhead-saving bit string accessing mechanism in blockchain, we propose the Merkle Cardinality Tree (MCT) and target block filtering mechanism based on Bloom Filter (BF) in off-chain and improve on-chain block header by joining the abstract of MCT and BF. (ii) To improve estimation efficiency while guaranteeing accuracy requirements in hybrid blockchain scheme, we propose a Dynamic One-round Sampling-based cardinality Estimation (DOSE) protocol and integrate BF-DOSE to intelligently accelerate estimation. We build MCT in Ethereum and store the MCT Root in the block header for estimation authentication. Extensive experiments reveal that our BF-DOSE protocol can well satisfy various accuracy and efficiency requirements of QoS-adjustable intelligent blockchain systems, and is one to two orders of magnitude faster compared with benchmark schemes.

A Leakage Rate Model for Metal-to-Metal Seals Based on the Fractal Theory of Porous Medium

Due to the complexity of sealing surface topography, it is difficult to take the surface topography into consideration when building a leakage rate model theoretically. Therefore, a theoretical model for estimating the leakage rate of metal-to-metal seals based on the fractal theory of porous medium, which can objectively reflect the influence of sealing surface topography from a microscopic perspective, is proposed in the present work. In the approach, fractal parameters are adopted to characterize the sealing surface. The sealing interface is supposed to be a porous medium space and the intrinsic parameters are obtained through rigorous theoretical derivation. The results show that the topography parameters of the sealing surface have a significant effect on the intrinsic parameters of the pore space and lead to a significant influence on the leakage rate of metal-to-metal seals. Specifically, the smoother the sealing surface, the lower the leakage rate of the metal-to-metal seal. Moreover, the leakage rate decreases with an increase in the contact pressure, and, if the fluid pressure difference is too large, the sealing performance will be seriously reduced. The proposed model provides a novel way to calculate the leakage rate of metal-to-metal seals.

Vertical dynamic response of pipe pile embedded in unsaturated soil based on fractional‐order standard linear solid model and Rayleigh‐Love rod model

AbstractConsidering the flow‐independent viscosity of soil skeleton and the lateral inertia effect of pipe pile, the vertical dynamic behavior of a pipe pile embedded in unsaturated soil is investigated in this work when the pipe pile is subjected to the vertical dynamic loading. In order to model this problem, the fractional‐order standard linear solid (FSLS) model is introduced to characterize the flow‐independent viscosity of the soil skeleton, the Rayleigh‐Love rod model is employed to specify the lateral inertia effect of pipe pile, while both vertical and radial soil displacement are entirely considered. The analytical solution of the pipe pile complex impedance is obtained through the rigorous theoretical derivation. Numerical results with known analytical solution are finally presented to discuss the influence of the model parameters for the FSLS model, lateral inertia effect and geometrical characteristic for the pipe pile, and saturation degree and intrinsic permeability for the unsaturated soil on the vertical complex impedance of the pipe pile. The main results indicate that enlarging the fractional‐order index, raising the strain relaxation time, or shortening the stress relaxation time will reduce the oscillation amplitude and natural frequency for the dynamic stiffness and damping of the pipe pile but will improve their mean value. The lateral inertia effect of pipe pile has effect on its complex impedance only in the high‐frequency region. The outer and inner radii of pipe pile, pile length, soil saturation degree, and soil intrinsic permeability are highly correlated with the pipe pile complex impedance.

New correlations for evaluating the equivalent bare charge mass for a cased charge

Munitions contain casings that consume explosive energy. The blast load (e.g., peak overpressure and maximum impulse) intensity generated by ammunition explosion will be lower than that generated by a bare charge with equal mass. To evaluate the blast load of a cased charge under different conditions, the equivalent bare mass needs to be calculated. However, the accuracy of existing correlations strongly depends on the empirical determination of relevant controlling parameters and lacks theoretical clarification. In this paper, new correlations are proposed based on a more rigorous theoretical derivation, considering both the mechanical behaviors of the casing’s material and the change of the polytropic exponent during the expansion process of the explosion products. The controlling parameters are attributed to the rupture radius ratio and the polytropic exponent of detonation products expansion to casing rupture state. The reasonability is validated by both comprehensive numerical simulations with dynamic mechanical constitutive model and theoretical derivations. The results calculated by the new correlation show better agreement with the experimental results than those calculated by previous correlations, and the results difference is explained in more consistency with the thermos-physical properties of the charge and mechanical behaviors of casing material. Furthermore, the correlation of the cased-to-bare impulse ratio is also theoretically improved, providing a more accurate theoretical basis for both the equivalent bare mass and impulse evaluation for a cased charge.

Enforcing detailed balance in the Borgnakke–Larsen redistribution method with temperature dependent relaxation models

For decades, it has been observed that the commonly used Borgnakke–Larsen method for energy redistribution in Direct Simulation Monte Carlo codes fails to satisfy the principle of detailed balance when coupled to a wide variety of temperature dependent relaxation models, while seemingly satisfying detailed balance when coupled to others. Many attempts have been made to remedy the issue, yet much ambiguity remains, and no consensus appears in the literature regarding the root cause of the intermittent compatibility of the Borgnakke–Larsen method with temperature dependent relaxation models. This paper alleviates that ambiguity by presenting a rigorous theoretical derivation of the Borgnakke–Larsen method's requirement for satisfying detailed balance. Specifically, it is shown that the Borgnakke–Larsen method maintains detailed balance if and only if the probability of internal-energy exchange during a collision depends only on collision invariants (e.g., total energy). The consequences of this result are explored in the context of several published definitions of relaxation temperature, including translational, total, and cell-averaged temperatures. Of particular note, it is shown that cell-averaged temperatures, which have been widely discussed in the literature as a way to ensure equilibrium is reached, also fail in a similar, although less dramatic, fashion when the aforementioned relationship is not enforced. The developed theory can be used when implementing existing or new relaxation models and will ensure that detailed balance is satisfied.

Optimal control of TB transmission based on an age structured HIV-TB co-infection model

The World Health Organization’s 2021 global tuberculosis report points out that people living with human immunodeficiency virus are more likely than others to become sick with tuberculosis. Therefore, it is necessary to consider the factor of human immunodeficiency virus infection when studying how to control the tuberculosis epidemic. In this paper, we establish an age structured human immunodeficiency virus and tuberculosis co-infection model and prove well-posedness of the model. Then we study the least cost-deviation problem. In this problem, detection and treatment of latent tuberculosis cases and public education campaigns are use as the control variables. Through rigorous theoretical derivation and detailed mathematical calculation, we obtain the necessary condition of optimal control. We also perform numerical simulation based on the forward-backward sweep method. Finally, combining the theoretical analysis with numerical simulation of the model, we present optimal strategies that may help China achieve the End Tuberculosis Strategy of the World Health Organization as much as possible (the new tuberculosis cases reduce by 90% by 2035 compared to 2015). In addition, in the process of numerical simulation, we also study the effect of available funds on control effectiveness and find that the control effect is better in the case of sufficiency of available funds, which shows that available funds are crucial to tuberculosis control.

Stabilizing regions of PID controller for a class of unknown nonlinear non‐affine discrete‐time systems

AbstractBased on the technology of dynamic linearization, the stability regions of PID, PI, PD, and P type controllers are investigated for a class of unknown nonlinear non‐affine discrete‐time systems. An equivalent data model to the unknown nonlinear system is established first through the dynamic linearization technique. Then based on the established data model, the determination of the structure of PID/PI controller has been given by rigorous theoretical derivation. The closed‐loop system is shown to be asymptotically stable for the PID, PI controllers, and the output/input signals of the closed loop system are bounded for the PD and P type controllers with the method of contraction mapping principle. An example of nonlinear non‐affine discrete‐time systems is used to demonstrate its correspondingly stability regions.