Numerical Results Research Articles

Use of a Semi-Explicit Probabilistic Numerical Model for Concrete Cracking: From Static to Dynamic Loadings

In this paper, concrete cracking is investigated in dynamics through finite element modeling. A probabilistic semi-explicit model, previously developed and validated for static loading, is extended for dynamic loading. The model in statics is based on two material mechanical parameters: the tensile strength and the critical strain-energy release rate in mode I, GIC, of the Linear Elastic Fracture Mechanics (LEFM) theory. Concerning the dynamic aspects of the model, the tensile strength rate effect is modeled by an empirical dynamic-to-static strength ratio (Dynamic Increase Factor—DIF) and a similar formulation is proposed for GIC. The structural rate effect is naturally captured when mass and damping are included in the equation of motion. For static and dynamic loading, only macroscopic crack propagation is considered. Some numerical simulations in statics and dynamics are presented in the present paper. The main results related to this work can be summarized as follows: the dispersion of the numerical results related to the load–displacement curves decreases with the loading rate. The crack pattern considerably changes with loading rate (numerically and experimentally); the agreement between the experimental and numerical results (load–displacement curves and crack pattern) indicates the model is promising for engineering applications.

Mathematical model and the solution of the capillary vibration in a nanoscale deformable

The capillary effect acts a key role in our daily life, and its vibration can significantly affect its mass transmission. Here, we aim to study the vibration of the capillary in a nanoscale deformable tube. First, we present the mathematical model, and then we give a detailed study on its vibration characteristics by means of the Hamiltonian‐based method, which is based on the variational principle and Hamiltonian. In the view of the energy conservation, the residual equations are introduced to determine the frequency‐amplitude formulation. We finally verify the effectiveness and reliability of the proposed method by comparing with existing method through the numerical results. The finding in this work is expected to be helpful for the study of the nonlinear vibration.

Adaptive Factored Incomplete Inverse Matrices

ABSTRACTThe solution of large sparse linear systems is an essential part in many scientific fields. Numerical solution of such systems is usually performed using iterative methods in conjunction with effective preconditioning schemes. A new class of factored approximate inverses is proposed, namely adaptive factored incomplete inverse matrices, which are computed using a recursive Schur complement‐based approach. This class of approximate inverses does not require the knowledge of a sparsity pattern, which is formed adaptively during computation. For this to be possible, a flexible sparse storage scheme was designed. Several numerical dropping strategies are showcased and discussed, along with the effects of reordering to the preconditioner density and the corresponding convergence behavior. Dropping based on monitoring the growth of elements in the incomplete LU factorization is also presented and discussed along with improvements during computation of the successive Schur complements. A static sparsity pattern variant is also provided and discussed. Implementation details and analysis, for computing the proposed scheme, are given along with the computational complexity and memory requirements. Numerical results depicting the effectiveness and applicability of the proposed scheme are also presented.

How to Effectively Cool Blade Batteries in Extreme High-Temperature Environments?

The market share of blade batteries is rising rapidly due to their high energy density, efficient space utilization, and low cost. Nevertheless, effective cooling solutions for blade batteries are crucial to ensure the safe operation of electric vehicles, especially in extreme high-temperature environments. This paper numerically investigates the effects of a cooling plate and the blade battery parameters on maximum battery temperature, maximum temperature difference, and cooling water pressure drop. Additionally, the energy efficiency of these solutions under various cooling demands is analyzed. The numerical results show that increasing the channel number and changing the flow direction does not significantly improve the cooling performance of the cooling plate. Moreover, the effect of cooling water temperature on the maximum temperature difference in blade batteries is negligible. Furthermore, increasing the cooling water mass flow rate and the rotational speed of the cooling fan is preferred when Tmax − Ta > 6 K, while reducing the cooling water temperature is more energy-efficient when Tmax − Ta < 6 K. These results are expected to offer theoretical guidance and data support for designing cooling systems for blade batteries in extreme high-temperature environments.

Optimal investment strategies under the relative performance in jump-diffusion markets

AbstractWe work on a portfolio management problem for one agent and a large group of agents under relative performance concerns in jump-diffusion markets with the CRRA utility function. Herein, we define two wealth dynamics: the agent’s and the group’s wealth. We measure the performances of both the agent and the group with preferences linked to the group performance. Therefore, we have stochastic optimal control problems for both the representative agent and the group to determine what the group does and the agent’s optimal proportion in the portfolio relative to the group’s performance. Further, our framework assumes that the agent’s performance does not affect the group, while the group affects the agent’s utility. Moreover, we investigate special cases where all agents in the market are homogeneous in their risk aversion and relative performances. We explore the qualitative behavior of the agent and show some numerical results depending on her relative performance consideration and risk tolerance degree.

On buckling of compact I-section beams subjected to biaxial bending

This paper aims at providing a new insight into the lateral-torsional buckling behavior of compact I-section steel beams subjected to biaxial bending, without axial force, a subject seldom treated in the literature. This investigation is based on both analytical and numerical results, the latter obtained using a two-node geometrically exact beam finite element developed by one of the authors (Gonçalves, 2019), which has all the required features. Several geometrically non-linear analysis (GNA) types are used to characterize the buckling behavior, namely with geometric imperfections (GNIA), with material non-linearity (GMNA) and combining material non-linearity and imperfections (GMNIA). Different boundary conditions along the two principal planes are allowed and particular attention is paid to cases which involve the same first-order bending moment diagrams but different support schemes. As a consequence, it is shown that the buckling behavior depends not only on the slenderness and the first-order moment diagrams, but also on the supports. On the basis of results obtained concerning the application of the Eurocode 3 provisions for different support conditions, it is shown that unsafe results can be obtained but may be resolved using the recommendations presented in the paper.

Dynamic response analysis of concrete filled steel tube tied arch bridge on a slab foundation under moving train load

The analysis of bridge vibration response under train loads is crucial for the operational safety of railway bridge structures. In this study, a three-dimensional coupled dynamic model of train-track-truss arch bridge is established. Based on the numerical simulation results, the effects of different train axle loads and speeds on the vibration response of the truss arch bridge are analyzed, and the time-history changes of the displacement and stress at critical sections of the bridge are revealed. The results show that: during the train operation, the maximum vertical dynamic stress and maximum vertical displacement are linearly related to the train axle load and speed. The greater the train axle load and speed, the larger the maximum vertical dynamic stress and maximum vertical displacement. The maximum vertical acceleration generated during train operation increases linearly with train speed and exponentially with train axle load. The most unfavorable section occurs at the mid-span of the bridge, where the maximum vertical displacement, maximum vertical dynamic stress, and maximum vertical acceleration are all at their peak. This research has significant implications for engineering safety and operation.

Towards p-11B medium configurations with high Pfus/PBrems ratios

Aneutronic p-11B nuclear fusion is promising for clean energy production, as it produces three (3) alpha particles with 8.7 MeV total energy. However, the main difficulty for p-11B fusion ignition (Q = Pfus/PBrems≥ 1) concerns the nuclear cross section and thus, reactivity efficiency at higher than 200 keV medium temperatures. To overcome this difficulty, the present work emphasizes on the numerical investigation of medium schemes (configurations) with enhanced reactivity. The configurations refer to the addition of energetic protons in a low-density 11boron or proton–11boron medium (n = 1020 m−3), with (np/nB) > 1 for Bremsstrahlung losses optimization and initial temperature in the range of 1 keV ≤ Tin≤ 400 keV. A self-consistent multi-fluid global particle and energy balance code, including collisions between all medium species (p, 11B, e, α), is used for the description of the temporal evolution of all fusion medium physical parameters and the evaluation of the optimum initial conditions for the obtainment of Q ≥ 1. The numerical simulation results show that the coupling between the 200 keV < Ep,0≤ 750 keV energetic protons and the 1 keV ≤ Tin≤ 400 keV initial fusion medium leads to ignition, 1 ≤ Q < 1.4, below Tin= 100 keV. In all the presented initial medium temperature cases, and especially, the lower (<) than 100 keV, the ignition condition (Pfus/PBrems) > 1 arises, as a consequence of the chain reactions and the related avalanche alpha heating effect.

Subsampling Algorithms for Irregularly Spaced Autoregressive Models

With the exponential growth of data across diverse fields, applying conventional statistical methods directly to large-scale datasets has become computationally infeasible. To overcome this challenge, subsampling algorithms are widely used to perform statistical analyses on smaller, more manageable subsets of the data. The effectiveness of these methods depends on their ability to identify and select data points that improve the estimation efficiency according to some optimality criteria. While much of the existing research has focused on subsampling techniques for independent data, there is considerable potential for developing methods tailored to dependent data, particularly in time-dependent contexts. In this study, we extend subsampling techniques to irregularly spaced time series data which are modeled by irregularly spaced autoregressive models. We present frameworks for various subsampling approaches, including optimal subsampling under A-optimality, information-based optimal subdata selection, and sequential thinning on streaming data. These methods use A-optimality or D-optimality criteria to assess the usefulness of each data point and prioritize the inclusion of the most informative ones. We then assess the performance of these subsampling methods using numerical simulations, providing insights into their suitability and effectiveness for handling irregularly spaced long time series. Numerical results show that our algorithms have promising performance. Their estimation efficiency can be ten times as high as that of the uniform sampling estimator. They also significantly reduce the computational time and can be up to forty times faster than the full-data estimator.

Decays Z → eaeb in a 3-3-1 model with neutral leptons

Abstract We investigate the 3-3-1 model with neutral leptons, a specific extension of the 3-3-1 models that includes heavy neutral leptons, which are sufficient to accommodate the neutrino oscillation data via the inverse seesaw mechanism. We will point out that this model can simultaneously explain the lepton flavor violating decays of the Z and Standard Model-like Higgs bosons into different charged leptons Z, h → e a e b , as well as the charged lepton decays e b → e a γ, in agreement with the recent experimental data. In addition, the numerical results show strong correlations among the decay rates of the Z and h bosons predicted by this model. Specifically, some of these rates are nearly linearly dependent on each other. Consequently, the decay channels can be theoretically determined if one of them is detected in experiments.

Analysis of impact of limb segment length variations during reinforcement learning in four-legged robot.

Crawling robots are becoming increasingly prevalent in both industrial and private applications. Despite their many advantages over other robot types, they have complex movement mechanics. Artificial intelligence can simplify this by reinforcement learning. This process requires configuring the training environment and defining input parameters, including a robot model for movement training. To translate the virtual results into real-world scenarios, a 3D model with appropriate mechanical parameters must be developed.These parameters can vary significantly between multiple mechanical configurations, which will further impact the reinforcement learning process of such a robot. For this reason, it was decided to test which limb configurations would work best in this process. Initially, various kinematic types of walking robots were analysed, drawing on the anatomy of mammals, reptiles, and insects for the biological model. The reptilian model was chosen for its balance of stability, dynamics, and energy efficiency. The article reviews the preparation of robot models and the configuration of the Unity3D development environment using the ML-Agents toolkit. The experiment examined how different limb lengths affect training, resulting in movement algorithms for various quadruped robot configurations using artificial neural networks. Based on the numerical results, the best configuration was the default, with the same length of the tibia as the thigh, achieving a reward function value of 883.9 and an episode length of 245.5. Taking into account the same criteria, the least efficient configuration was definitely the one characterised by the shortest thigh and the longest tibia among those considered. In its case, the reward function reached a value of only 526.2 with an episode lasting 999.0, which means that it never achieved the intended goal.

A model for scheduling the resource deployment in a multi-stage ramp-up production system

Rapid and continuous changes in customer product requirements affect demand, requiring the supply chain to be more responsive. A new product ramp-up is integral to responsiveness, where it is paramount to implement it successfully and manage it effectively. A smooth ramp-up process minimises problems and delays, leading to lower costs and higher profitability. This study develops and analyses a model that describes a multi-stage ramp-up production system to identify the most cost-effective policy for controlling multiple ramp-ups. We propose a search-based optimisation approach to solve the problem. Through numerical analyses, we develop a decision framework to classify the patterns of resource deployment and planning, aiming to make the ramp-up process efficient and responsive to increasing demand. Additionally, we conduct sensitivity analyses to examine how variations in input parameters affect system behaviour. Our findings offer managerial implications and insights based on the numerical results.

Sieve Maximum Likelihood Estimation of Partially Linear Transformation Models With Interval-Censored Data.

Partially linear models provide a valuable tool for modeling failure time data with nonlinear covariate effects. Their applicability and importance in survival analysis have been widely acknowledged. To date, numerous inference methods for such models have been developed under traditional right censoring. However, the existing studies seldom target interval-censored data, which provide more coarse information and frequently occur in many scientific studies involving periodical follow-up. In this work, we propose a flexible class of partially linear transformation models to examine parametric and nonparametric covariate effects for interval-censored outcomes. We consider the sieve maximum likelihood estimation approach that approximates the cumulative baseline hazard function and nonparametric covariate effect with the monotone splines and -splines, respectively. We develop an easy-to-implement expectation-maximization algorithm coupled with three-stage data augmentation to facilitate maximization. We establish the consistency of the proposed estimators and the asymptotic distribution of parametric components based on the empirical process techniques. Numerical results from extensive simulation studies indicate that our proposed method performs satisfactorily in finite samples. An application to a study on hypobaric decompression sickness suggests that the variable TR360 exhibits a significant dynamic and nonlinear effect on the risk of developing hypobaric decompression sickness.

Mixed Finite Element Formulation in Nonlinear Geometrical Analysis of Space Trusses and Application to Trusses With Member Length Imperfection

Abstract Space trusses usually have a significant number of elements. As a result, it is inevitable that some elements have imperfections. In this study, the authors proposed a mixed finite element method for nonlinear geometrical analysis of space trusses. The post-buckling behavior of space trusses with length imperfections was predicted using a code list written in the programming software. The numerical results indicate that when the length imperfection approaches zero, the results converge to those obtained in studies on standard trusses. A second approach based on the displacement model is also proposed, in which the Lagrange multiplier method is used to deal with the member length imperfection. The results show that the two approaches proposed by the authors are effective, in which the mix formulation based on the finite element model is superior to that based on the displacement model. These results verify the accuracy of the method. Based on the proposed method, the effects of imperfections in the element layers on the truss were studied. The results show that the imperfections in the top two element layers have the maximum influence on the limit load value, whereas the remaining layers have a negligible influence. The combination of the imperfect lengths of these two layers of elements can produce results in which the limit load value is much larger than in the case of a perfect system. Based on the obtained results, it is possible to provide a solution for improving the overall stability of truss structures by creating reasonable imperfections.

A numerical comparison of Gd, Pr0.65Sr0.35MnO3 and single LaFeCoSi, for use in room temperature magnetic cooling applications

Abstract One of the most significant scientific difficulties to achieving excellent performance for room-temperature magnetic cooling devices is finding suitable magnetocaloric refrigerants. To contribute to this research field, three kinds of magnetocaloric materials (Gd, Pr0.65Sr0.35MnO3 and single LaFeCoSi) in the same conditions (Curie temperature, applied magnetic field) have been considered to evaluate their potential in the magnetic refrigeration application using a 1D-AMRR (Active-Magnetic-Refrigeration-Regenerator) cycle with a parallel plate regenerator. In this way, four cooling performance parameters were investigated, namely the temperature span, the cooling power, the exergy, and the coefficient of performance. The temperature span was found to be 11.79K for Gd , 8K for LaFeCoSi and 4.47 K for Pr0.65Sr0.35MnO3. The obtained numerical results reveal that the Gd-based AMR system displays a higher efficiency, while the Pr0.65Sr0.35MnO3-based AMR system exhibits a smaller one. The magnetocaloric effect (MCE) in the magnetic refrigerants was considered to explain the result obtained and can be considered as one of the main factors to enhance the magnetic refrigeration performance.

An Online Dual Consensus Algorithm for Distributed Resource Allocation over Networks

We address the problem of online resource allocation in a distributed environment where requests arrive dynamically over time at different agents in the network. As each request arrives, the receiving agent must make an immediate decision that incurs a cost and consumes a certain amount of resources. The requests are drawn independently from unknown distributions that are different for each agent. First, we present an online consensus alternating direction method of multipliers (OC-ADMM) algorithm for the dual counterpart of the online distributed resource allocation problem, focusing on the dual variables. Then, we propose an online dual consensus ADMM (ODC-ADMM) algorithm for the primal problem to derive the primal variables from the dual update process in the OC-ADMM algorithm. The ODC-ADMM algorithm exhibits sublinear growth in both regret and expected constraint violation with respect to the time horizon. Furthermore, extensive numerical results on both synthetic and real-world data confirm its effectiveness.

Quantum Fisher information of a $\Diamond$-type four level atom interacting with a single-mode quantized field in an optomechanical cavity

Abstract In science and technology, precision measurement of physical quantities is crucial, and the quantum Fisher information (QFI) plays a significant role in the study of quantum systems. In this work, we explore the dynamics of QFI for a hybrid optomechanical system, which consists of a $\Diamond$-type four level atom interacting with a single-mode quantized field through multi-photon process. We account for various sources of dissipation, including the decay rates of the atom, the cavity, and the mechanical modes. Using an effective Hamiltonian, we analytically derive the explicit form of the state vector of the entire system via the time-dependent Schr"{o}dinger equation. We then investigate the atomic QFI for the estimation precision of the decay rate of the mechanical oscillator. Furthermore, we examine how optomechanical and atom-field coupling strengths, dissipation parameters, and multi-photon transition influence the dynamics of atomic QFI. Our numerical results suggest that the estimation precision of the decay rate of the mechanical oscillator can be controlled by these parameters.

Optimal maintenance and pricing strategy for a periodic review production system with fixed maintenance costs and limited maintenance capacity

In recent times, the escalating complexity of advanced production systems has led to increased exposure to various uncertainties, which impact systems' reliability. To maintain the reliability of systems, reduce maintenance costs and increase revenues, we establish an effective joint optimal maintenance and pricing strategy for a periodic review production system, which is of practical importance. Compared with the existing literature, we make a contribution to considering limited maintenance capacity and fixed maintenance costs simultaneously, and developing joint optimal maintenance and pricing strategies. We initially construct a dynamic programming model for this problem, and prove the objective function is strong CK-concave. We then show that the optimal maintenance strategy is partially characterized by two thresholds, and the optimal pricing strategy depends on the optimal number of operational machines after repairs. Numerical results show that the optimal maintenance and pricing strategy is quite robust, and is not much affected by various parameters.

Long-Range Electrostatic Adhesive Contact Between an Elastic Half-Space and a Rigid Indenter With Power-Law Profile

Abstract In this study, the electrostatic adhesive contact between a smooth indenter with a power-law geometry and an elastic half-space is studied using both a theoretical and numerical approach. Both the indenter and substrate are coated with an electrically insulating layer. The Maxwell stress and hard-wall constraint are applied to describe the interaction between the indenter and elastic counter face. By assuming electrostatic adhesion as a long-range interaction, we derived a theoretical relation between external load and contact radius. We show that the theoretical and numerical results are plausible when the Tabor parameter is small. However, when the Tabor parameter is large, the numerical results get closer to the Johnson–Kendall–Roberts (JKR) limit. The generalized Tabor parameter, which depends on the applied voltage and indenter shape, has been derived by following the technique of dimensional analysis.

Experimental and numerical study on double wedge shock/shock interaction controlled by a single-pulse plasma synthetic jet

Abstract The phenomenon of shock/shock interaction (SSI) is widely observed in high-speed flow, and the double wedge SSI represents one of the typical problems encountered. The control effect of plasma synthetic jet (PSJ) on double wedge type-VI and type-V SSI was experimentally and numerically investigated, and the influence of discharge energy was also explored. The findings indicate that the interaction between PSJ and the high-speed freestream results in the formation of a plasma layer and a jet shock, which collectively governs the control of SSI. The control mechanism of single-pulse PSJ on SSI lies in its ability to attenuate shock and SSI. For type-VI SSI, under the control of PSJ, the original second-wedge oblique shock is eliminated, resulting in a new type-VI SSI formed by the jet shock and the first-wedge oblique shock. For type-V SSI, under the control of PSJ, Mach stem, supersonic jet and the reflected shocks are significantly attenuated, resulting in a transformation of type-V SSI into type-VI SSI. The numerical results indicate that the maximum reduction of peak pressure is approximately 32.26%. The development of PSJ also extends in the Z direction. The pressure decreases in the area affected by both PSJ and jet shock due to the attenuation of the SSI zone. The control effect of PSJ on SSI is gradually enhanced with increasing discharge energy.