Finite Steps Research Articles

Sifat Rantai Naik pada Modul r-Noetherian serta Keterkaitan Modul r-Noetherian dengan Modul Noetherian dan Modul Hampir Noetherian

Modules are algebraic structures formed from Abelian groups and rings as scalars. A module is a Noetherian module if it satisfies the ascending chain condition on its submodules. An R-module M is called an almost Noetherian module if every true submodule in M is finitely generated. There is a new class of r-Noetherian modules. Let\ R be a ring and M an R-module, M is said to be an r-Noetherian module if every r-submodule of M is finitely generated. The symbol r refers to the true ideal of the ring with Ann\ a=0. The properties to be studied are the ascending chain properties of r-Noethetian modules. Furthermore,, the relationship of r-Noetherian module with Noetherian module and almost Noetherian module will be studied. This research uses a literature study approach. The stages carried out in this study begin with completing the proof of the lemma relating to the ascending chain on the r-Noetherian Module. Furthermore, completing the proof of the proposition regarding the relationship of the r-Noetherian module with the Noetherian module and almost Noetherian module. The property of ascending chain on r-Noetherian module is that every ascending chain line of r-submodules on r-Noetherian module will stop at a finite step. Furthermore, the connection of r-Noetherian module with Noetherian module and almost Noetherian module is mutual subset

Numerical and experimental frequency analysis of damaged fiber‐reinforced metal laminated composite

AbstractThis research numerically evaluated the eigenvalue responses of the damaged fiber metal laminate (FML) structure. The current numerical model is delved into including crack‐type damage effect on the structural integrity/ stiffness via frequency response. In this regard, a complete mathematical model of FML has been derived through higher‐order shear deformation kinematics for computational purposes. The mathematical model is converted to computer code in the MATLAB platform to predict the eigenvalue responses of FML components with and without damage. The damage influences are considered via circular meshing of finite element steps associated with the isoparametric element (nine nodes and nine degrees of freedom for each node). The solution consistency is checked via convergence, and the results are compared with data available in the open domain. Further, an experimental test is carried out to improve confidence using an in‐house test rig. The experiment was conducted by varying the length of the FML in 0.1 m increments. The results showed good agreement between the numerical and experimental data, with the lowest deviation being 0.29% and the highest 8.97%. The developed numerical model is extended to analyze the influences of design parameters such as geometry shape, aspect ratio (a/b), thickness ratio (a/h) ratio, curvature ratio, and fiber layup sequence on the natural frequency response.

An iterative method for updating undamped structural systems with connectivity constraints

Model updating is a method of correcting analytical models, such as the finite element models, by improving the correlation between the measured data and the analytical modal data. In this paper, we develop an iterative method to update undamped structural systems by using measured modal parameters. The method allows mass and stiffness matrices to be updated simultaneously. And we can obtain optimal updated matrices within finite iteration steps by choosing a special kind of initial matrix pair. More importantly, the method can preserve the physical connectivity of the original model and the updated model is in good agreement with the experimental modal data. Two real numerical examples show that the proposed method is feasible and efficient.

Nitric oxide-generating metallic wires for enhanced metal implants

Metallic implants are integral in modern medicine, offering excellent biocompatibility and mechanical properties. However, implant-related infections pose a major challenge. Current drug delivery methods, such as surface-coated and drug-eluting implants, are limited by finite drug supplies and complex manufacturing steps. Recent approaches like local drug synthesis, including enzyme-prodrug therapies, present innovative solutions but are hampered by the inherent limitations of enzymes as well as complex procedures. Here, we introduce a simpler alternative: using the intrinsic properties of implant materials to activate prodrugs. Through a simple thermal treatment, metallic implants gain catalytic properties to locally generate nitric oxide, an antibacterial agent. Our findings show this treatment is non-toxic to cells, does not affect cell proliferation rates, and effectively inhibits bacterial biofilm formation. This material-driven approach eliminates the need for external chemical or enzymatic interventions, offering a promising solution to prevent implant-related infections and improve patient outcomes in implant medicine.

Fast event-driven simulations for soft spheres: from dynamics to Laves phase nucleation.

Conventional molecular dynamics (MD) simulations struggle when simulating particles with steeply varying interaction potentials due to the need to use a very short time step. Here, we demonstrate that an event-driven Monte Carlo (EDMC) approach was first introduced by Peters and de With [Phys. Rev. E 85, 026703 (2012)] and represents an excellent substitute for MD in the canonical ensemble. In addition to correctly reproducing the static thermodynamic properties of the system, the EDMC method closely mimics the dynamics of systems of particles interacting via the steeply repulsive Weeks-Chandler-Andersen (WCA) potential. In comparison to time-driven MD simulations, EDMC runs faster by over an order of magnitude at sufficiently low temperatures. Moreover, the lack of a finite time step in EDMC circumvents the need to trade accuracy against the simulation speed associated with the choice of time step in MD. We showcase the usefulness of this model to explore the phase behavior of the WCA model at extremely low temperatures and to demonstrate that spontaneous nucleation and growth of the Laves phases are possible at temperatures significantly lower than previously reported.

Lorentzian Quantum Cosmology from Effective Spin Foams

Effective spin foams provide the most computationally efficient spin foam models yet and are therefore ideally suited for applications, e.g., to quantum cosmology. Here, we provide the first effective spin foam computations of a finite time evolution step in a Lorentzian quantum de Sitter universe. We will consider a setup that computes the no-boundary wave function and a setup describing the transition between two finite scale factors. A key property of spin foams is that they implement discrete spectra for the areas. We therefore study the effects that are induced by the discrete spectra. To perform these computations, we had to identify a technique to deal with highly oscillating and slowly converging or even diverging sums. Here, we illustrate that high-order Shanks transformation works very well and is a promising tool for the evaluation of Lorentzian (gravitational) path integrals and spin foam sums.

Robust design optimization using a non-intrusive second-order approximation of stochastic moments

This paper presents a new formulation of the second-order fourth-moment method (sometimes referred to as second-order perturbation method or second-order method of moments). The method allows to efficiently predict the stochastic moments of a response function and is therefore often used within robust design optimization. The new approach allows a non-intrusive implementation at the same cost as existing, highly intrusive formulations. Therefore, the new approach can be applied to any objective function without significant implementation effort. It is based on a few finite difference steps into special directions and hence is dependent on the corresponding step sizes. An automatic step size procedure is supplied beside a detailed convergence analysis. The advantages of the new formulation are demonstrated by robust design optimizations of a 2D and a 3D example using the geometrically nonlinear finite element method.

A random active set method for strictly convex quadratic problem with simple bounds

The active set method aims at finding the correct active set of the optimal solution and it is a powerful method for solving strictly convex quadratic problems with bound constraints. To guarantee the finite step convergence, existing active set methods all need strict conditions or some additional strategies, which can significantly impact the efficiency of the algorithm. In this paper, we propose a random active set method that introduces randomness in the active set’s update process. We prove that the algorithm can converge in a finite number of iterations with probability one, without any extra conditions on the problem or any supplementary strategies. At last, numerical experiments show that the algorithm can obtain the correct active set within a few iterations, and it has better efficiency and robustness than the existing methods.

Dynamical behavior of a hepatitis B epidemic model and its NSFD scheme

Hepatitis is inflammation of the liver, and one of its types, hepatitis B, is a contagious infection. Using mathematical models, the nature of the spread of the Hepatitis B virus can be predicted. In the present paper, a hepatitis B epidemic model with a Beddington–DeAngelis type incidence rate and a constant vaccination rate is considered. Some dynamical properties of this model, such as non-negativity, boundedness character, the basic reproduction number R0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {R}_0$$\\end{document}, stability nature, and the bifurcation phenomenon, are investigated. By the Bendixson theorem, it is demonstrated that the disease-free equilibrium is globally asymptotically stable. It is shown that a transcritical bifurcation phenomenon occurs when R0=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {R}_0=1$$\\end{document}. It is concluded that the endemic equilibrium is globally asymptotically stable when R0>1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {R}_0>1$$\\end{document}, by utilizing Dulac’s criteria. Also, a discrete system of difference equations is obtained by constructing a non-standard finite difference (NSFD) scheme for the continuous model. It is shown that the solutions of this discrete system are dynamically consistent for all finite step sizes. The theoretical results obtained are also supported and visualized by numerical simulations. These simulations also demonstrate that the NSFD scheme produces much more efficient results than the Euler or RK4 schemes, as shown in the theoretical results obtained.

Research on Expansion Coefficient Based on Water Temperature Density Regression Function

Based on the regression function of water temperature and water density, two expressions of the thermal expansion coefficient function of water are obtained by integrating and differentiating the function. Compared with the measured data, the theoretical formula of the integral method is in good agreement with the measured accumulated thermal expansion coefficient of water obtained by the cumulative step size. The theoretical formula of the differential method is in good agreement with the measured cumulative thermal expansion coefficient of water obtained by equal step size and variable step size. Therefore, no matter the theoretical formula of the integral method or differential method, it can be used for the thermal expansion coefficient of water with cumulative step size or with finite equal step size or finite variable step size. The theoretical formula of the thermal expansion coefficient of water with integral method and differential method is of high precision and easy to use.

Intrinsic rotation modulation by diffusive neutral particles in tokamaks

The modulated transport model, a model kinetic ion transport equation for the pedestal and scrape-off layer (SOL), is generalized to self-consistently include effects of a single neutral particle species. The neutrals contribute additional transport terms, modifying the v∥ -dependent orbit-averaged ion diffusivities of the original work and the resulting predicted intrinsic rotation of the ions. After making simplifying assumptions of the neutral transport, in particular taking the continuous transport limit via a short charge-exchange step expansion, we derive relatively simple analytic expressions that capture the diffusive neutral physics. Within the scope of the model’s validity, the neutral-driven intrinsic rotation can compete with the turbulence-driven intrinsic rotation. However, for physically motivated parameters, the neutral-driven intrinsic rotation appears negligible, either on a term-by-term basis or due to a strong cancellation between the neutral-driven momentum diffusion and pinch terms. It appears that a treatment containing finite charge-exchange steps is necessary to capture neutral transport of strong flow momentum into the confined region from the SOL.

Privacy-preserving finite-time average consensus and its application to power allocation of battery energy storage systems

In this paper, the privacy-preserving problem of finite-time discrete-time average consensus is studied by adding random numbers. The privacy leakage conditions are given for systems with curious but not malicious nodes and eavesdroppers, respectively. By introducing the random numbers and node decomposition mechanism, the privacy information of the nodes cannot be estimated by the adversaries. The proposed algorithm is applied to the power allocation problem of distributed battery energy storage systems. Based on the previous proposed multi-rate sampling method, the privacy-preserving finite-time discrete-time average consensus is utilized to estimate the accurate average value within finite steps. The accurate power allocation based on the same relative SoC variation rate can be achieved with the privacy preservation of the transmission information. Finally, based on a networked battery energy storage system, simulation studies are presented to verify the effectiveness of the proposed method.

Common Fixed-Point Theorem and Projection Method on a Hadamard Space

In this paper, we obtain an equivalent condition to the existence of a common fixed point of a given family of nonexpansive mappings defined on a Hadamard space. Moreover, if the space is bounded, we show that the generating process of the approximate sequence by a specific projection method will stop in finite steps if there is no common fixed point. It is a significant advantage to reveal the nonexistence of a common fixed point in a finite time.

An intelligent schedule maintenance method for hydrogen fuel cell vehicles based on deep reinforcement learning considering dynamic reliability

Schedule maintenance activities for hydrogen fuel cell vehicles are aimed to keep them in better condition in long-term operation. In this paper, we develop a reinforcement learning based schedule maintenance strategy, which is used to comprehensively consider the balance between safety and maintenance cost, so as to find the optimal maintenance strategy. A multi-level framework is established with remaining useful life of key components, fault tree analysis, and logistics cost model to generate an exploration environment that can express the operational stability, the failure rate of components, and the cost of repair and storage. The trained agent combines a deep neural network to explore the optimal strategy under the dynamic reliability of key components. Finite steps are the constraints. Safety rates, maintenance cost, and episode of operation are incorporated into a multi-objective reward function. The hydrogen supply circuit of fuel cell vehicle is simulated via Python. The trained agent is compared with traditional time-based schedule maintenance strategy and corrective maintenance strategy. The results show that the reinforcement learning based schedule maintenance agent has optimized the total reward, cost control and accident rate by 77%, 59% and 5%, respectively, compared with the traditional time-based schedule maintenance strategy. In the safe operation management of fuel cell vehicles, efficient and stable decision-making ability has been achieved.

Controller design of coordinated control problems over finite fields via fully actuated approach

This paper discusses coordinated control problems for systems over finite fields via fully actuated approach. Novel types of consensus and synchronization, which are irrelevant to initial states, are proposed. For different coordinated control problems, suitable controllers are designed, which are able to drive the system to the corresponding trajectory in finite steps. Besides, the conclusions are applied to stabilization, and the convergence time is analyzed. As an application, a camera network example is given to illustrate the results.

Limitations of probabilistic error cancellation for open dynamics beyond sampling overhead

Quantum simulation of dynamics is an important goal in the noisy intermediate-scale quantum era, within which quantum error mitigation may be a viable path towards modifying or eliminating the effects of noise. Most studies on quantum error mitigation have focused on the resource cost due to its exponential scaling in the circuit depth. Methods such as probabilistic error cancellation rely on discretizing the evolution into finite time steps and applying the mitigation layer after each time step, modifying only the noise part without any Hamiltonian dependence. This may lead to Trotter-like errors in the simulation results even if the error mitigation is implemented ideally, which means that the number of samples is taken as infinite. Here we analyze the aforementioned errors which have been largely neglected before. We show that they are determined by the commutating relations between the superoperators of the unitary part, the device noise part, and the noise part of the open dynamics to be simulated. We include both digital quantum simulation and analog quantum simulation setups and consider defining the ideal error mitigation map both by exactly inverting the noise channel and by approximating it to first order in the time step. We use single-qubit toy models to numerically demonstrate our findings. Our results illustrate fundamental limitations of applying probabilistic error cancellation in a stepwise manner to continuous dynamics, thus motivating the investigations of truly time-continuous error cancellation methods. Published by the American Physical Society 2024

The first application of a numerically exact, higher-order sensitivity analysis approach for atmospheric modelling: implementation of the hyperdual-step method in the Community Multiscale Air Quality Model (CMAQ) version 5.3.2

Abstract. Sensitivity analysis in chemical transport models quantifies the response of output variables to changes in input parameters. This information is valuable for researchers engaged in data assimilation and model development. Additionally, environmental decision-makers depend upon these expected responses of concentrations to emissions when designing and justifying air pollution control strategies. Existing sensitivity analysis methods include the finite-difference method, the direct decoupled method (DDM), the complex variable method, and the adjoint method. These methods are either prone to significant numerical errors when applied to nonlinear models with complex components (e.g. finite difference and complex step methods) or difficult to maintain when the original model is updated (e.g. direct decoupled and adjoint methods). Here, we present the implementation of the hyperdual-step method in the Community Multiscale Air Quality Model (CMAQ) version 5.3.2 as CMAQ-hyd. CMAQ-hyd can be applied to compute numerically exact first- and second-order sensitivities of species concentrations with respect to emissions or concentrations. Compared to CMAQ-DDM and CMAQ-adjoint, CMAQ-hyd is more straightforward to update and maintain, while it remains free of subtractive cancellation and truncation errors, just as those augmented models do. To evaluate the accuracy of the implementation, the sensitivities computed by CMAQ-hyd are compared with those calculated with other traditional methods or a hybrid of the traditional and advanced methods. We demonstrate the capability of CMAQ-hyd with the newly implemented gas-phase chemistry and biogenic aerosol formation mechanism in CMAQ. We also explore the cross-sensitivity of monoterpene nitrate aerosol formation to its anthropogenic and biogenic precursors to show the additional sensitivity information computed by CMAQ-hyd. Compared with the traditional finite difference method, CMAQ-hyd consumes fewer computational resources when the same sensitivity coefficients are calculated. This novel method implemented in CMAQ is also computationally competitive with other existing methods and could be further optimized to reduce memory and computational time overheads.

An iterative method for updating finite element models with connectivity constraints

It is well known that the analytical matrices arising from the discretization of distributed parameter systems using the finite element technique are usually symmetric and banded. How to preserve the coefficient matrices of the updated model being of the same band structure is an important yet difficult challenge for model updating in structural dynamics. In this paper, an iterative method for updating mass, damping and stiffness matrices simultaneously based on partial modal measured data is provided. By the method, the optimal updated matrices can be obtained within finite iteration steps by choosing a special kind of initial matrix triplet. The proposed approach not only preserves the physical connectivity of the original model, but also the updated model reproduces the measured modal data, which can be utilized for various finite element model updating problems. Numerical examples confirm the effectiveness of the introduced method.

Finite-Time Robust Distributed Estimate for Nonlinear Systems With Heterogeneous Sensors.

This article proposes a finite-time distributed state estimation (DSE) algorithm for discrete-time stochastic nonlinear systems with heterogeneous sensors. Considering the network with heterogeneous sensors, the distributed estimate framework is designed by three phases, namely, priori prediction, measurement update, and consensus fusion. To obtain the accurate priori prediction results, the interactive multiple model (IMM) method is adopted to calculate the priori state value in the priori prediction phase. By introducing the measurement probability matrix, a novel heterogeneous measurement information fusion algorithm is designed. Then the measurement information of each sensor is used to update the priori prediction estimates to calculate the estimate results in the measurement update phase. Based on the consensus method, the estimate results of each sensor are fused with consensus weight to calculate the distributed state estimates of nonlinear systems in the consensus fusion phase. Besides, with finite consensus fusion steps, the bounds of the proposed distributed estimate algorithm are proved to be existed. Finally, distributed state estimate simulation example for nonlinear system is set to validate the performance.

Periodic Event-Triggered Model Predictive Control for Networked Nonlinear Uncertain Systems With Disturbances.

This article investigates the event-triggered model predictive control (MPC) problem for a class of networked nonlinear uncertain systems subject to time-varying disturbances. Different from the traditional MPC, the proposed periodic event-triggered MPC (PETMPC) method does not generate new control sequence unless a predesigned periodic event-triggering mechanism (PETM) is violated. First, a generalized proportional-integral observer (GPIO) is developed to estimate the unknown state and disturbance information by using the sampled-data output of controlled system. Then, the disturbance predictions for future finite steps are obtained based on forward Euler method. After that, with the help of prediction model, the optimal control sequence, including the future finite step predicted control inputs, is generated and dexterously exploited during the interevent interval by storing it in a buffer installed between the control sequence generator and actuator, thereby leading to the further reduction of signal transmission number and the frequency of control sequence computations. Through a rigorous stability analysis, it can be proved that the closed-loop hybrid control system is globally bounded stable under the nominal PETMPC law. Finally, numerical simulations are conducted to substantiate the feasibility and superiority of the proposed PETMPC method.