Inertia Terms Research Articles

A novel hybrid information-based PF-WOA algorithm for gas source localization in 3D space

Abstract In recent years, dangerous gas leakage events occur frequently. Rapid and accurate location of gas leakage sources by mobile robots is the key to avoid the expansion of disasters. In order to solve the problem of discontinuous gas concentration gradient and sparse gas environment in three-dimensional space, particle filter, and whale swarm optimization algorithm are integrated to locate gas source. Firstly, the Z-shape search and comb search are used to locate the plume, and then, the particle filter algorithm is combined with the whale optimization method to guide the particle movement, and the random inertial disturbance term is designed to improve the convergence speed and search accuracy of the algorithm. Experimental results in three-dimensional environment show that the proposed information-driven particle filter whale optimization hybrid algorithm effectively guides the robot in localizing gas source within a certain range, significantly enhancing both the efficiency and accuracy of localization compared to other algorithms.

Multidimensional and Nonlinear Fractional Langevin Equations: Advancing the Theory in of Anomalous Diffusion

This paper presents a comprehensive theoretical analysis of fractional Langevin equations (FLEs) and their applications in modeling anomalous diffusion processes. We extend the classical FLE framework in several significant directions to address the complexities observed in various physical, biological, and social systems. First, we derive a multidimensional extension of the FLE, providing a robust tool for studying anomalous diffusion in higher-dimensional spaces. Second, we incorporate non-Gaussian Lévy α-stable noise into the FLE, enabling the description of systems characterized by heavy-tailed distributions and extreme events. Third, we develop a nonlinear variant of the FLE to model more intricate restoring forces and potential landscapes. Finally, we analyze a generalized FLE with different orders of fractional derivatives for the inertial and friction terms, offering a flexible framework capable of capturing a wider range of anomalous diffusion phenomena. For each extension, we prove the existence and uniqueness of solutions, derive the corresponding probability distributions, and analyze the scaling behavior of the mean squared displacement in the long-time limit. Our results demonstrate how these generalized FLEs can describe various regimes of anomalous diffusion, from subdiffusive to superdiffusive behavior. This work provides a unified theoretical foundation for understanding and modeling complex diffusive processes across diverse disciplines, paving the way for more accurate descriptions of systems exhibiting memory effects, non-Gaussian statistics, and multiscale dynamics.

Strong Energy Conversion by a Ribbon‐Like Magnetic Structure in Tailward High‐Speed Flow

AbstractThe tailward high‐speed flows, in which various kinetic processes and magnetic structures can be embedded, are usually produced by the magnetic reconnection in the Earth's magnetotail. Here, using high‐resolution measurements from the Magnetospheric Multiscale (MMS) mission, we report an intense current in the tailward high‐speed flow. The current density can reach ∼180 nA/m2 and is primarily carried by electrons. Taking advantage of the First‐Order Taylor Expansion (FOTE) method, we reveal that such an intense current is associated with a ribbon‐like magnetic structure. A large electric field, reaching ∼90 mV/m, is also observed at the magnetic structure. The Hall term dominates the electric field, however, the contribution from the pressure gradient term and the electron inertial term is nonnegligible and can lead to strong energy conversion (E ⋅ J > 2 nW/m3) through the synergistic action with the intense current. This study improves the understanding of the current behaviors and energy conversion associated with magnetic structures in the Earth's magnetotail.

Particle Focusing and Separation in the Low Aspect Ratio Serpentine‐Hook Shape Microarray

ABSTRACTIn recent years, researchers have been heavily focused on developing effective techniques for isolating and counting particles. Particle separation methods are enhancing disease point of care and treatment applications. Separation techniques not only increase the chance of early detection of illness but also greatly improve the success rate of treatment. This article introduces a passive microarray separator with a low aspect ratio (<20%). By incorporating a low aspect ratio design, the flow inertial term is effectively diminished, leading to a creeping flow at the channel. This strategy results in negligible lift force and mixing effect on particles. Terminating the mentioned factors provides a channel with sensitive focusing properties. In the proposed research we enhanced a hook‐shaped geometry to increase regional centrifugal force. This configuration results in size‐base particle separation. An expansion was also added to improve the performance of the channel. To validate the functionality and limitations of the designed channel numerical simulation and experimental tests were conducted. To provide better insights into the low aspect ratio separator a numerical simulation using COMSOL Multiphysics has been established. The experiments indicated 91% purity at an input flow of 720 µL/min.

A recent fixed point method based on two inertial terms

A recent fixed point method based on two inertial terms

Double Tseng’s Algorithm with Inertial Terms for Inclusion Problems and Applications in Image Deblurring

In this research paper, we present a novel theoretical technique, referred to as the double Tseng’s algorithm with inertial terms, for finding a common solution to two monotone inclusion problems. Developing the double Tseng’s algorithm in this manner not only comprehensively expands theoretical knowledge in this field but also provides advantages in terms of step-size parameters, which are beneficial for tuning applications and positively impact the numerical results. This new technique can be effectively applied to solve the problem of image deblurring and offers numerical advantages compared to some previously related results. By utilizing certain properties of a Lipschitz monotone operator and a maximally monotone operator, along with the identity associated with the convexity of the quadratic norm in the framework of Hilbert spaces, and by imposing some constraints on the scalar control conditions, we can achieve weak convergence to a common zero point of the sum of two monotone operators. To demonstrate the benefits and advantages of this newly proposed algorithm, we performed numerical experiments to measure the improvement in the signal–to–noise ratio (ISNR) and the structural similarity index measure (SSIM). The results of both numerical experiments (ISNR and SSIM) demonstrate that our new algorithm is more efficient and has a significant advantage over the relevant preceding algorithms.

Enhanced high-frequency continualization scheme for inertial beam-lattice metamaterials

A multifield continualization technique is introduced that offers a thermodynamically consistent description of the constitutive and dispersive properties of beam-lattice inertial metamaterials with periodic microstructures. The balance equations governing the mechanics of the discrete Lagrangian system are appropriately handled using an innovative continualization scheme to derive an equivalent integral-type continuum model. Based on formal Taylor series expansion of the integral kernels or the corresponding pseudo-differential functions incorporating shift operators and appropriate pseudo-differential downscaling laws, the proposed multifield enhanced continualization scheme allows the derivation of a gradient-type continuum model of given rank and equivalent to lattices. Two different resolution techniques are proposed. Firstly, the corresponding infinite-order average differential equations are tackled using a perturbative approach to describe the forced Bloch wave propagation in the metamaterial. Secondly, higher-order continuum models are employed through proper differential equation truncation to characterize the dispersive properties of the metamaterial in both high- and low-frequency regimes. Moreover, an energetically consistent generalized equivalent Micropolar continua, with non-local inertial terms, are here identified. The multifield continualization procedure is applied to two-dimensional periodic microstructures with tetrachiral, hexachiral, and hexa-tetrachiral topologies. Illustrative examples highlight the ability of the equivalent continuum model to accurately describe the effective constitutive properties of inertial metamaterials with periodic microstructures and to define a dynamic response consistent with the discrete Lagrangian model, validated and tested through virtual experimental verification under free and forced wave conditions.

From Darcy to turbulent flow: Investigating flow characteristics and regime transitions in porous media

This research addresses the flow characteristics within a porous medium composed of a monolayer of closely packed spheres, spanning from viscous-dominated to turbulent flow regimes. In the first part of this paper, the turbulent flow characteristics at a 30 MPa pressure drop within the domain are presented. The results are averaged across different cross sections between the inlet and outlet. In the second part of the study, simulations are conducted with pressure drops, ranging from nearly 0 to 100 MPa. The analysis finds distinct flow patterns within the domain and provides estimations for the permeability and the inertial term coefficient. Moreover, the transition from Darcy to non-Darcy and turbulent flow is achieved through the use of different criteria. The specified geometry is suitable for validating and calibrating simplified discrete element method models coupled with computational fluid dynamics. The main goal of this research is to produce a reliable benchmark to figure out the challenge of limited experimental data concerning fluid flow characteristics in densely packed granules specially subjected to high pressure conditions. To do this, representative specimens are designed, accurate simulations are conducted, and precise assessments of the results are carried out.

Strong convergence of Bregman projection algorithms for solving split feasibility problems

Bregman distance methods play a key role in solving problems in nonlinear analysis and optimization theory, since the Bregman distance is a useful substitute for the metric. The main purpose of this paper is to investigate two new iterative algorithms based on the Bregman distance and the Bregman projection for solving split feasibility problems in real Hilbert spaces. The algorithms are constructed around these methods: Byrne’s CQ method, Polyak’s gradient method, Halpern method, and hybrid projection method. The proposed methods involve inertial extrapolation terms and self-adaptive step sizes. We prove that the proposed iterations converge strongly to the Bregman projection of the initial point onto the solution set. Some numerical examples are provided to illustrate the computational effectiveness of our algorithms. The main results extend and improve the recent results related to the split feasibility problem.

A modified inertial proximal minimization algorithm for structured nonconvex and nonsmooth problem

We introduce an enhanced inertial proximal minimization algorithm tailored for a category of structured nonconvex and nonsmooth optimization problems. The objective function in question is an aggregation of a smooth function with an associated linear operator, a nonsmooth function dependent on an independent variable, and a mixed function involving two variables. Throughout the iterative procedure, parameters are selected employing a straightforward approach, and weak inertial terms are incorporated into two subproblems within the update sequence. Under a set of lenient conditions, we demonstrate that the sequence engendered by our algorithm is bounded. Furthermore, we establish the global and strong convergence of the algorithmic sequence, contingent upon the assumption that the principal function adheres to the Kurdyka–Łojasiewicz (KL) property. Ultimately, the numerical outcomes corroborate the algorithm’s feasibility and efficacy.

Analytical prediction of temperature effects on Lamb wave response in smart plates and its experimental verification

Abstract This article examines the effectiveness of a recently developed theoretical model for the generation and sensing of Lamb waves in thin plates with surface-bonded piezoelectric transducers in predicting temperature effects on Lamb waves and their time reversibility. In particular, the analytical model provides a closed-form solution, which incorporates both the shear-lag effect of the bonding layer and the system inertia in transducer-plate interaction modeling. Temperature-dependent material properties and thermal expansion of the system constituents are considered to predict the Lamb wave signal under a thermal environment. The accuracy of the theoretical prediction is assessed in comparison with experimental results obtained using an aluminum plate with adhesively bonded lead zirconate titanate transducers to its surface at different system temperatures ranging from 20°C to 75°C. Comparison is also made with experimental data and analytical solutions presented earlier without considering the inertia effect. The study reveals that the current solution accurately predicts the change in Lamb wave signal due to temperature variation, including the frequency dependency of the peak amplitude change with temperature rise. However, the theoretical model fails to predict the experimental trends when the inertia terms are neglected. The current model is also used to study the contributions of individual system parameters to the overall temperature effect on the time reversibility of Lamb waves and its dependence on the excitation frequency.

The topology-conditioned turbulence kinetic energy budget

The paper reports on the conditionally averaged turbulence kinetic energy (TKE) budget, where the conditioning is based on the invariants of the velocity gradient tensor. Three different datasets are utilized for this analysis. The particular terms of the budget are presented in the (R, Q) plane, showcasing a striking similarity (both quantitative and qualitative) among the results from each dataset. The importance of conditional averages for the overall variance of the specific terms of the TKE budget is also evaluated. Subsequently, the budgets are presented along conditional mean trajectories (CMTs), revealing the dynamics of the TKE budget associated with the evolution of local flow topology. Results obtained for different CMTs approximately collapse when suitably normalized (at least for certain parts of the trajectories). The conditional budget is clearly dominated by inertial and pressure transport terms, indicative of a “sweeping” effect.

Aperiodically intermittent quantized control-based exponential synchronization of quaternion-valued inertial neural networks

Inertial neural networks are proposed via introducing an inertia term into the Hopfield models, which make their dynamic behavior more complex compared to the traditional first-order models. Besides, the aperiodically intermittent quantized control over conventional feedback control has its potential advantages on reducing communication blocking and saving control cost. Based on these facts, we are mainly devoted to exploring of exponential synchronization of quaternion-valued inertial neural networks under aperiodically intermittent quantized control. Firstly, a compact quaternion-valued aperiodically intermittent quantized control protocol is developed, which can mitigate significantly the complexity of theoretical derivation. Subsequently, several concise criteria involving matrix inequalities are formulated through constructing a type of Lyapunov functional and employing a direct analysis approach. The correctness of the obtained results eventually is verified by a typical example.

Dynamic analysis of cracked thick composite shells by the Boundary Element Method

This article presents a numerical formulation based on the Boundary Element Method for the transient dynamic analysis of cracked thick symmetrical composite shells. The integral formulation uses the static fundamental solutions for thick orthotropic symmetric plates and the anisotropic plain elasticity fundamental solution. Domain integrals associated to distributed loads, curvature and inertial terms are evaluated employing the Radial Integration Method. The crack was modeled using the sub-region method. The developed formulation is implemented computationally and validated through the analysis of several proposed examples. The obtained results demonstrate the validity and robustness of the developed formulation.

Generalized Fejér monotone sequences and their finitary content

We provide quantitative and abstract strong convergence results for sequences from a compact metric space satisfying a certain form of generalized Fejér monotonicity where (1) the metric can be replaced by a much more general type of function measuring distances (including, in particular, certain Bregman distances), (2) full Fejér monotonicity is relaxed to a partial variant and (3) the distance functions are allowed to vary along the iteration. For such sequences, the paper provides explicit and effective rates of metastability and even rates of convergence, the latter under a regularity assumption that generalizes the notion of metric regularity introduced by Kohlenbach, López-Acedo and Nicolae, itself an abstract generalization of many regularity notions from the literature. In the second part of the paper, we apply the abstract quantitative results established in the first part to two algorithms: one algorithm for approximating zeros of maximally monotone and maximally ρ-comonotone operators in Hilbert spaces (in the sense of Combettes and Pennanen as well as Bauschke, Moursi and Wang) that incorporates inertia terms every other term and another algorithm for approximating zeros of monotone operators in Banach spaces (in the sense of Browder) that is only Fejér monotone w.r.t. a certain Bregman distance.

Role of inertial nonlinearity and coupling stiffness on a series of coupled harvesters

This study investigates the effect of coupling configuration on a state-of-the-art harvesting system consisting of a series of spring-coupled piezoelectric nonlinear monostable tip-loaded cantilever-based vibration energy harvesters (VEHs). The investigation finds favorable coupling configurations that exploit complex nonlinear interaction for improving system performance. The system model incorporates the beam's geometric nonlinearities in the governing equation using inertial and stiffness nonlinear terms. The study first analytically investigates the effect of grounding stiffness on a single harvester's performance. Then, it numerically investigates the effect of increasing array size and changing stiffness distribution. The study discovers a novel hardening/softening transition phenomenon at a critical grounding stiffness value induced by the inertial nonlinear effect. This critical event also maximizes peak output power near the largest eigenfrequency at an optimum grounding stiffness value. At larger arrays, the peak power shows a complex bifurcation behavior, hinting at the presence of multiple attractors. The numerical study of different stiffness configurations and linearized eigenanalysis reveals the necessity of a multilevel optimization strategy focused on both the stiffness ratio between the coupling springs' and their overall stiffness level. This study bridges the gap between previous studies on spring-coupled linear and bistable arrays, offering new insights into coupled nonlinear interactions and proposing novel optimization strategies.

Double Inertial Krasnosel'skii-Mann-Type Method for Approximating Fixed Point of Nonexpansive Mappings

In this paper, we investigate a new method motivated by current advancements in general inertial algorithms. Specifically, we incorporate double inertial extrapolation terms into an iterative sequence, derived from Krasnosel'skii-Mann techniques. The weak convergence theorem for fixed points of nonexpansive mappings in real Hilbert spaces is established. The theoretical developments are rigorously proven, extending existing methods in literature. We also utilize our convergence analysis to solve real-world problems, such as convex minimization problems and zero finding for sums of monotone operators.

LUCMT: Learnable under-sampling and reconstructed network with cross multi-head attention transformer for accelerating MR image reconstruction

Background and ObjectiveAs a widely used technique for Magnetic Resonance Image (MRI) acceleration, compressed sensing MRI involves two main issues: designing an effective sampling strategy and reconstructing the image from significantly under-sampled K-space data. In this paper, an innovative approach is proposed to address these two challenges simultaneously. MethodsA novel MRI reconstruction method, termed as LUCMT, is implemented by integrating a learnable under-sampling strategy with a reconstruction network based on the Cross Multi-head Attention Transformer. In contrast to conventional static sampling methods, the proposed adaptive sampling scheme is processed optimally by learning the optimal sampling technique, which involves binarizing the sampling pattern by a sigmoid function and computing gradients by backpropagation. And the reconstruction network is designed by using CS-MRI depth unfolding network that incorporates a Cross Multi-head Attention (CMA) module with inertial and gradient descent terms. ResultsT1 brain MR images from the FastMRI dataset are used to validate the performance of the proposed method. A series of experiments are conducted to validate the superior performance of our proposed network in terms of quantitative metrics and visual quality. Compared with other state-of-the-art reconstruction methods, LUCMT achieves better reconstruction performances with more accurate details. Specifically, LUCMT achieves PSNR and SSIM results of 41.87/0.9749, 46.64/0.9868, 50.41/0.9924, and 53.51/0.9955 at sampling rates of 10 %, 20 %, 30 %, and 40 %, respectively. ConclusionsThe proposed LUCMT method can provide a promising way for generating optimal under-sampling mask and accelerating MRI reconstruction accurately.

Enhancing convergence speed in sparse signal denoising: the APFISTA algorithm

Among numerous first-order algorithms, the Fast Iterative Shrinkage-Thresholding Algorithm, known as FISTA, is renowned for its convergence speed of O ( 1 k 2 ) in terms of the objective function value, where k denotes the number of iterations. Additionally, various improvements to FISTA have been proposed in the literature. Among them, the convergence rate of a parameterized FISTA (PFISTA) proposed by Liang, Luo and Schonlieb [SIAM J Sci Comput. 2022:44(3):A1069–A1091] is obviously faster than that of the original FISTA, which can reach o ( 1 k 2 ) convergence rate. Building upon the idea of parameterization, we introduce the fully parameterized APFISTA for complete parameterization of the inertia term, aiming to enhance the current situation of partially parameterized inertia terms. We establish the convergence speed of its objective function value and the sequence generated by the algorithm. Finally, we apply the proposed method to solve the least squares problem and linear inverse problems. The obtained numerical results illustrate the practical behavior and theoretical analysis of the proposed approach.

Nonlocal to Local Convergence of Phase Field Systems with Inertial Term

Nonlocal to Local Convergence of Phase Field Systems with Inertial Term