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Let k ∈ N and suppose we are given k integers 1 ≤ a 1 , ... , a k ≤ n. If a 1 + ... + a k is not an integer, how close can it be to one? When k = 1 , the distance to the nearest integer is ≳ n − 1 / 2. Angluin-Eisenstat observed the bound ≳ n − 3 / 2 when k = 2. We prove there is a universal c > 0 such that, for all k ≥ 2 , there exists a c k > 0 and k integers in { 1 , 2 , ... , n } with 0 < ‖ a 1 + ... + a k ‖ ≤ c k ⋅ n − c ⋅ k 1 / 3 , where ‖ ⋅ ‖ denotes the distance to the nearest integer. This is a case of the square-root sum problem in numerical analysis where the usual cancellation constructions do not apply: already for k = 3 , the problem appears hard. [ABSTRACT FROM AUTHOR]

This paper develops and verifies a multiscale computational fluid dynamics (CFD) model to investigate the airflow and heat transfer in kiwifruit cold storage under forced-air cooling (FAC). The CFD model incorporates the material properties, geometry, position of kiwifruit and ventilated packaging box, and the detailed structure of the cooling unit. For the multiscale modeling, the material characteristics are described using three interconnected sub-models, focusing each on different spatial scales: the warehouse-scale, packaging-scale, and kiwifruit-scale. In the FAC experiment, the measured airflow and temperature on these three spatial scales were obtained and compared with the simulated results. The data analysis shows that the environmental fluctuations at different scales weaken significantly in a stepwise manner with the cushioning of packaging and fruit flesh, indicating coupling between the spatial scales, which is well reflected in the numerical simulation. The average kiwifruit temperature decreases from 20 to 6 °C in 14.5 h (experimental) and 15.6 h (simulated). Specifically, the average mean absolute error, mean absolute percentage error, and root mean squared error of the predicted airflow and kiwifruit temperature were 0.116 m s−1, 1.26 °C; 26.8%, 14%; and 0.124 m s−1, 1.54 °C, respectively. These results indicate that the multiscale CFD model accurately and efficiently simulates the airflow and spatiotemporal temperature distribution in the given kiwifruit FAC system. Finally, this study provides a reference for accurately simulating large-scale industrial FAC systems and supports optimal decision-making for the design of sustainable kiwifruit cold chains. • Multiscale CFD modeling of warehouse-packaging-kiwifruit under forced-air cooling. • The established model is verified to be accurate through FAC experimental data. • Fine perception of product-scale in large-scale industrial FAC process. • Analysis of spatiotemporal coupling characteristics of multiscale environments. [ABSTRACT FROM AUTHOR]

In Japan, small agricultural tractors without axle suspensions used on bumpy farm roads experience severe vibrations. Excessive vibrations often cause tyres to lose contact with the supporting ground or decrease the vertical tyre force such that the cornering force exceeds the static friction limit. The resulting bouncing and sliding motions induce steering instability, resulting in overturning accidents. This study investigated the effectiveness of axle suspension in alleviating bump disturbance-induced steering instability in small tractors. A step lane change test involving bump disturbances was newly proposed for the steering stability testing of small tractors. The numerical experiments compared four axle suspension structures: no-, front-, rear-, and full-suspensions. The results showed that bump disturbances induce steering instability in the no- and rear-suspension tractors. In contrast, the front- and full-suspension structures significantly improved the steering stability of the tractor by keeping the steering wheel in contact with the ground. The proposed testing method helped evaluate improvements in the steering stability brought about by increasing the ground contact of the steering wheel. Our results can aid in designing and testing suspension systems for small tractors. • Tractor bouncing, sliding, and driver models were newly coupled for simulations. • Step lane change involving bump disturbances was proposed for stability test. • Steering instability was found in the no- and rear-suspension tractors. • Front- and full-suspensions could significantly alleviate steering instability. [ABSTRACT FROM AUTHOR]

Recently, owing to abnormal climate caused by climate change, the frequency of heavy snow has increased, resulting in increased damage to horticultural facilities. Therefore, considering the characteristics of snow distribution, simulating the distribution of snow on the greenhouse is required. Additionally, because it is difficult to artificially design the experimental environment for measuring snow loads in the field experiment, a computer simulation technology approach is necessary as an alternative. In this study, the characteristics and distribution of snow on the greenhouse roof were identified through an artificial snow experiment, and a numerical analysis model was designed using the discrete element method (DEM). The designed model was verified through the results of artificial snow load tests. Using this validated model, the pressure distribution characteristics on the roof surface of the greenhouse for snow cover were analysed. Moreover, computational fluid dynamics (CFD) techniques was integrated to account for the impact of wind. According to the analysis results, the average load was highest at 59.33 Pa in the pitched-roof multi-span, and the maximum load was 193.62 Pa in the arched-roof multi-span greenhouse. CFD–DEM coupled model was developed to simulate the distribution of snow cover based on wind conditions. The simulation results revealed that the snow load on the leeward roof exhibited an increase compared to the windward roof. However, the snow load on the leeward roof tended to decrease as the wind speed increased. These simulation results could be utilised as a reference for greenhouse design standards. • Developed a DEM model simulating greenhouse snow distribution. • Achieved high validation (R2 > 0.96) with small-scale field experiments. • Coupled the DEM with a validated CFD model for commercial greenhouse assessment. • Demonstrated accurate snow load prediction within greenhouses using the CFD–DEM model. [ABSTRACT FROM AUTHOR]

[Display omitted] Nonwetting surfaces, by virtue of their water-repelling trait, offer desirable anti-icing characteristics. Surface roughness, type and wettability are important interfacial characteristics that affect the icing dynamics that can be tailored to achieve desired anti-icing designs. The present study systematically explores the effect of surface roughness on the freezing behaviour of water droplets on surfaces ranging in their wettability. Surfaces with tailored textures and wettability were fabricated using chemical etching and electrodeposition by varying the voltage. The surfaces studied include bare copper, five different dry nonwetting copper surfaces, and five different lubricant-infused copper surfaces that ranged in surface texture fractal dimension from nearly 1.0 to 1.92 and wettability measures of average water contact angle from 91° to 162° and sliding angle from less than 3° to greater than 50°. A computational model is developed to simulate the freezing dynamics on the surfaces studied. With increasing roughness features, the freezing time increased due to the dual effects of increased contact angle and poor interfacial conductance caused by trapped air or infused liquid within the asperity textures. In general, the nonwetting surfaces increased the freezing time by a factor of at least 1.33 and up to about 3.2 compared to freezing on bare copper surfaces. The computational model shows close agreement with experimental measurements on the freeze front progression as well as freeze time. Design guidelines on the suitability of the different nonwetting surfaces for anti-icing purposes are derived from the systematic study, with the overall design recommendation favoring lubricant infused surfaces. [ABSTRACT FROM AUTHOR]

With increasing demand for planting space, a new type of large-span pipe-framed plastic greenhouse has been developed in recent years. However, as the span increases, new problems in structural analysis arise. Compared with small-span plastic greenhouses, large-span pipe-framed plastic greenhouses are more likely to be damaged under wind and snow loads. In this study, the static and dynamic characteristics of a large-span pipe-framed plastic greenhouse were investigated using static analysis and the time history method, respectively. First, a 3-D finite element model of the greenhouse was established using ANSYS software. Second, the static characteristics of the greenhouse under three load cases were investigated along with and the failure mechanisms under the most unfavourable load case. Finally, the dynamic characteristics of the greenhouse were analysed using the time history method. The numerical results showed that the greenhouse was mainly subjected to bending stress, and the axial stress values were small. Compared with uniform snow loads, the pipe-framed plastic greenhouse structure was more sensitive to non-uniform snow loads. The maximum displacement of the greenhouse structure under non-uniform snow loads was approximately 2.2 times that under uniform snow loads. A comparative analysis showed that the maximum displacement and bending stress obtained from the time history method were 1.7 and 1.5 times greater, respectively, than those obtained from the static equivalent method. This study provides a reference for the design and analysis of large-span pipe-framed plastic greenhouse structures. • Large-span pipe-framed plastic greenhouses are sensitive to non-uniform snow loads. • The greenhouse is mainly subjected to bending stress under wind and snow loads. • The response under pulsating wind loads is greater than that under static wind loads. • Load-carrying capacity decreases as the geometric imperfection amplitude increases. • The secondary frame is more susceptible to failure than the primary frame. [ABSTRACT FROM AUTHOR]

[Display omitted] • Spreading dynamic of a deposited drop on a solid substrate is studied. • Viscous timescale mainly governs the spreading at a certain Bond number and static contact angle. • Droplet spreading master curves to capture the dynamic shape of the droplet are developed. • A correlation to predict the equilibrium shape of droplet is developed. There exists a generalized solution for the spontaneous spreading dynamics of droplets taking into account the influence of interfacial tension and gravity. This work presents a generalized scaling theory for the problem of spontaneous dynamic spreading of Newtonian fluids on a flat substrate using experimental analysis and numerical simulations. More specifically, we first validate and modify a dynamic contact angle model to accurately describe the dependency of contact angle on the contact line velocity, which is generalized by the capillary number. The dynamic contact model is implemented into a two-phase moving mesh computational fluid dynamics (CFD) model, which is validated using experimental results. We show that the spreading process is governed by three important parameters: the Bo number, viscous timescale τ viscous , and static advancing contact angle, θ s . More specifically, there exists a master spreading curve for a specific Bo and θ s by scaling the spreading time with the τ viscous . Moreover, we developed a correlation for prediction of the equilibrium shape of the droplets as a function of both Bo and θ s . The results of this study can be used in a wide range of applications to predict both dynamic and equilibrium shape of droplets, such as in droplet-based additive manufacturing. [ABSTRACT FROM AUTHOR]

We develop a new framework for error analysis on stochastic numerical schemes, with the rough path theory and stochastic backward error analysis. Based on our approach, we prove that the almost sure convergence rate of the modified Milstein scheme for stochastic differential equations driven by multiplicative multidimensional fractional Brownian motion with Hurst parameter H ∈ (1 4 , 1 2) is (2 H − 1 2) − for sufficiently smooth coefficients, which is optimal in the sense that it is consistent with the best probable convergence rate of implementable approximations of the Lévy area of fractional Brownian motion. Our result gives a positive answer to the conjecture proposed in [12] for the case H ∈ (1 3 , 1 2) , and reveals for the first time that numerical schemes constructed by a second-order Taylor expansion converge for the case H ∈ (1 4 , 1 3 ]. [ABSTRACT FROM AUTHOR]

Initially on an elliptical orbit, C/2021 A1 experimented significant changes in its orbital configuration due to planetary perturbations upon entering the planetary region. Images of the comet C/2021 A1 (Leonard) obtained in March 2022 allow to estimate that its disintegration occurred in December 2021. The aim of this paper is to analyze the comet's dust behavior during the period when its disintegration is presumed to have commenced, so a series of images of this comet on the broadband B, V, and R filters were taken on December 21 and 23, 2021 with the 0.6 m Helen Sawyer Hogg (HSH) telescope at the Complejo Astronómico El Leoncito (CASLEO) to do a morphological, photometric, and numerical analysis of this comet. Analysis of the magnitudes and dust production rate suggests a significant increase in activity on December 21 compared to two days later, indicating a potential outburst. Digital filters were applied to enhance contrast in the cometary images, revealing two active regions on opposite sides of the nucleus. Additionally, the A (0 °) f ρ parameter was obtained for this comet. Finally, to gain deeper insights into Leonard's dust behavior, observations were fitted to a newly developed theoretical model for studying dust comas. Combined with photometric data and gas production information from the literature, the analysis suggests that the comet's activity on December 21, 2021, may mark the beginning of its disintegration. • Comet C/2021 A1 (Leonard) dust behavior study. • Images taken on December 21 and 23, 2021 with HSH telescope at CASLEO. • Morphological, photometric, and numerical analysis. • Leonard's dust activity on 2021/12/21, may mark the beginning of its disintegration. [ABSTRACT FROM AUTHOR]

A new definition of entropy fluctuation is provided in this paper, that allows properly separating entropy and mixture composition fluctuations. This decomposition into linearly independent variables prevents from overestimating compositional noise in indirect noise prediction. When considering quasi one-dimensional flow in nozzles, a new resulting system of linearized Euler equations is obtained. Two analytical solutions of this system of equations are investigated in this study, one dedicated to low-frequency perturbations and another one for all frequency perturbations. This new theory is then validated by comparing the model predictions with direct numerical simulation of nozzle flows in which composition fluctuations are pulsed. To do so, new Navier–Stokes characteristics boundary conditions to account for the new properly defined entropy wave are provided. Furthermore, non-reflecting inlet boundary conditions have been newly derived, relaxing on the axial mass-flow rate, static temperature and species mass fractions. Finally, a parametric study based on an air-kerosene (equivalent C 10 H 20 ) mixture and an ideal framework shows that composition noise can reach a maximum of 10% of entropy noise for lean combustion and choked nozzle while for rich combustion, composition noise and entropy noise show comparable levels. [Display omitted] • New entropy noise decomposition that prevents overestimation of the compositional part of indirect combustion noise. • New system of linearized equations that characterize indirect combustion noise. • New non-reflecting Navier–Stokes boundary conditions for pulsing species mass factions fluctuations. [ABSTRACT FROM AUTHOR]

In this study, we propose a bidirectional high-speed inchworm actuator driven by two PZT stacks by employing innovative flexible symmetric clamp feet with a multilayer structure design, where the switching of the clamp feet is performed by a single PZT. In addition, the symmetric clamp foot design synchronizes the clamping forces and improves the efficiency of the driving mechanism. The drive principle is analyzed, and a model on the clamping performance with respect to the single-step length is developed based on the compliance matrix method. A numerical analysis is conducted to verify the proposed model and optimize driving performance. The experimental results demonstrate that the proposed actuator achieves high-speed and stable bidirectional motion with a maximum speed of 43.8 mm/s and a maximum driving force of 3 N at a driving frequency of 150 Hz, which significantly outperforms existing results. The experiments also demonstrate that the motion resolution of the proposed actuator is 1.57 nm with a large travel range (25 mm in this particular design). The innovative design of the PZT inchworm actuator promises various applications in precision engineering with high-speed and large range nanomanipulatons. [ABSTRACT FROM AUTHOR]

• The whirl orbit with inner loop pattern in a cracked rotor system is found to be not necessarily associated with subcritical rotational speed. • The appearance of inner loop pattern within the whirl orbit is mainly depending on the magnitude of the unbalance force rather than the subcritical rotational speed. • The whirl orbit with inner loop is found to exist before and after the resonance zone. • The numerical simulation findings are validated via robust experimental analysis. • The findings provide a breakthrough in the fundamental understanding to the whirl orbit with inner loop. Cracks in rotor systems are generated because of internal as well as external heavy loading conditions. The external loading conditions could be attributed to thermal gradients (such as in turbomachinery) or other environmental conditions that result in cracks developments. The internal loading conditions can be attributed to cyclic fatigue loading during continuous and recurrent shaft's running which is the most common cause for cracks propagation. The presence of cracks in rotor systems induces nonlinearities into the system which affects its whirl response. Many published literature on cracked rotors have indicated that when the rotational speed is at sub-critical resonance of order 1/n (1/2, 1/3,1/4, etc....) of the critical rotational speed, the fundamental whirl orbit takes patterns including inner loop/loops of order (n-1) or outer loop/loops of order (n +1) depending on the critical whirling direction. The present study investigates the strong impact of the magnitude of unbalance force on whirling pattern with inner loop in a cracked rotor. Numerical analysis is carried out on the mathematical model of the considered cracked rotor. The unbalance force magnitude is observed to be the main factor affecting the inner loop pattern in the whirl orbit rather than the ½ of the critical resonance speed. Accordingly, the appearance of inner loop in shaft's whirl orbit due to crack propagation in the rotor system is found here to be present before and after passing through resonance speed. This inner loop whirl orbit pattern is not restricted to be associated with ½ of the critical rotational speed as believed in plenty of literature. This kind of whirling is observed to be strongly depending on the unbalance force magnitude rather than the subcritical resonance speed. The experimental results also validate the numerical simulation findings. Therefore, the whirl orbits of the cracked rotor can be categorized into pre-resonance whirl orbit (Pr-WO), resonance whirl orbit (R-WO) and post-resonance whirl orbit (Po-WO) based on the magnitude of the unbalance force. The resultant numerical and experimental findings on the whirl orbit with inner loop can provide a robust insight into the cracked rotor whirl behavior. [ABSTRACT FROM AUTHOR]

When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also known as embedded or immersed) finite element methods offer a significant advantage in dealing with complex geometries, eliminating the need for generating unstructured body-fitted meshes. However, current unfitted finite elements on nonlinear geometries are restricted to implicit (possibly high-order) level set geometries. In this work, we introduce a novel automatic computational pipeline to approximate solutions of partial differential equations on domains defined by explicit nonlinear boundary representations. For the geometrical discretization, we propose a novel algorithm to generate quadratures for the bulk and surface integration on nonlinear polytopes required to compute all the terms in unfitted finite element methods. The algorithm relies on a nonlinear triangulation of the boundary, a kd-tree refinement of the surface cells that simplify the nonlinear intersections of surface and background cells to simple cases that are diffeomorphically equivalent to linear intersections, robust polynomial root-finding algorithms and surface parameterization techniques. We prove the correctness of the proposed algorithm. We have successfully applied this algorithm to simulate partial differential equations with unfitted finite elements on nonlinear domains described by computer-aided design models, demonstrating the robustness of the geometric algorithm and showing high-order accuracy of the overall method. • Robust and accurate intersection algorithm for background cells and Bézier patches of arbitrary order. • Mathematical analysis of the correctness of the algorithm. • Numerical analysis of the accuracy and robustness of the intersection algorithm. • Experimentation of a high-order unfitted finite element method for high-order boundary representations. • Application of the methods to problems defined in computer-aided design geometries. [ABSTRACT FROM AUTHOR]

First-order energy dissipative schemes in time are available in literature for the Poisson–Nernst–Planck (PNP) equations, but second-order ones are still in lack. This work proposes novel second-order discretization in time and finite volume discretization in space for modified PNP equations that incorporate effects arising from ionic steric interactions and dielectric inhomogeneity. A multislope method on unstructured meshes is proposed to reconstruct positive, accurate approximations of mobilities on faces of control volumes. Numerical analysis proves that the proposed numerical schemes are able to unconditionally ensure the existence of positive numerical solutions, original energy dissipation, mass conservation, and preservation of steady states at discrete level. Extensive numerical simulations are conducted to demonstrate numerical accuracy and performance in preserving properties of physical significance. Applications in ion permeation through a 3D nanopore show that the modified PNP model, equipped with the proposed schemes, has promising applications in the investigation of ion selectivity and rectification. The proposed second-order discretization can be extended to design temporal second-order schemes with original energy dissipation for a type of gradient flow problems with entropy. • Novel second-order numerical schemes for Poisson-Nernst-Planck equations. • Unconditional preservation of positivity. • Unconditional preservation of original energy dissipation. • Second-order discretization applies to a large type of gradient flow problems with entropy. [ABSTRACT FROM AUTHOR]

In this work, an energy stable BDF2 scheme with general nonuniform time steps is developed for the nonlocal Cahn-Hilliard model to capture the multi-scale behavior of evolution efficiently and accurately. The fully discrete numerical scheme is demonstrated to inherit main physical properties of the continuous model, namely, mass conservation and energy dissipation. Recently, various variants of the Cahn-Hilliard model with nonlocal operators and fractional Laplacian have attracted great attention in terms of theoretical analysis and numerical approximation, while there is less emphasis on the comparisons among the different variant models. By comparing the impact of various parameters and coarsening behaviors, numerical results suggest that the nonlocal Cahn-Hilliard model bears a strong resemblance to the space fractional Cahn-Hilliard model derived from H − 1 gradient flow of the nonlocal energy. Nevertheless, the order of the fractional Laplacian appears to affect only the rate of energy decay, without altering the profile of the solution for the fractional model relating to the H − β (0 < β < 1) gradient flow of the classical Ginzburg-Landau energy functional in one dimensional case. [ABSTRACT FROM AUTHOR]

HPL-AI, also known as HPL-MxP, is a new benchmark program used to evaluate the upper-bound performance of AI-related tasks on a specific computing cluster. It solves a large linear equation system in FP64, preconditioned by complete LU factorization in lower precision. In this paper, we propose a new HPL-AI approach that relies on the factorization of the coefficient matrix in mixed precision: FP32 diagonals and FP16 off-diagonals. Without compromising the quality of the resultant LU preconditioner, the proposed approach only utilizes the primitive of dense matrix multiplication in FP16 on the accelerator, maximizing the FP16 throughput. Numerical analysis and experiments validate our approach, ensuring avoidance of numerical underflow or overflow during factorization. We implement the proposed approach on Kunpeng+Ascend clusters, a novel AI-specific platform with exceedingly high FP16 peak performance. By applying various optimization techniques, including 2D lookahead, HCCL-based communication pipeline, and SYCL-based tasks overlapping, we achieve 975 TFlops on a single node and nearly 100 PFlops on a cluster of 128 nodes, with a weak scalability of 79.8%. • First-time adaptation and optimization of HPL-AI on the Kunpeng+Ascend platform. • A novel approach for mixed-precision LU: FP32 diagonals and FP16 off-diagonals. • Over/underflow avoidance: error analysis and magnitude estimation of HPL-AI LU. • On a single node, 8 Ascend 910A Pro AI accelerators achieve 42.3% HPL-AI efficiency. • On a 128-node cluster: 98.9 PFlops HPL-AI performance and 79.8% weak scalability. [ABSTRACT FROM AUTHOR]

[Display omitted] Due to high sensitivity to the changes in external excitation intensity, the implementation of nonlinear energy sinks (NESs) have been greatly limited in practical applications. This study presents a stable state adjustable NES (SA-NES) structure. By adjusting the structural geometric relationship, the SA-NES structure can easily switch its stable state among monostable, bistable, and tristable. The governing equation of the coupled system is obtained by Hamilton's principle. The approximate analytical solution is obtained by the harmonic balance method, and the slow invariant manifold is obtained complexification-averaging method, which are validated through numerical analysis. Through theoretical analysis and experimental validation, the dynamic response of the SA-NES and vibration reduction performance are studied under different levels of excitations. The obtained results show that the designed SA-NES can effectively suppress the vibration under different level excitation intensities. It is also shown that the SA-NES structure can be adjusted to the monostable state, and the vibration of the linear oscillator can be effectively suppressed by the strong modulation response under a certain excitation intensity. When the excitation intensity is weak or strong, the SA-NES can be adjusted to the bistable state and the tristable state, respectively, thus effectively suppressing the vibration through chaotic inter-well oscillation. This study reveals the vibration suppression mechanism of the SA-NES, and introduces a new NES configuration to suppress different levels of engineering excitations. [ABSTRACT FROM AUTHOR]

[Display omitted] • Simplify and derive the formulae based on TRL theory and computer programs to demonstrate the relation between parameters. • Derived from the relation of ε' and ε'', a criterion is established to decide what parameters have the possibility of absorbing performance. • A new fitting method is utilized to construct the relation between permittivity and content of absorber. Non-magnetic materials show a great potentiality in microwave absorption with the advantages of low-density, wideband, and thin thickness. Even so, it is still difficult to accurately analyze the connection between performance and parameters. To reveal what electromagnetic parameters could lead to excellent absorbing performance, we simplify and derive the formulae based on Transmission-Reflection-Line theory (TRL) and computer programs. Based on the relation of ε' and ε'', a criterion is established to decide what parameters have the possibility of absorbing performance. Using a new fitting method, the relationship between dielectric constant and absorber content is established. Further, an instruction derived from the relation between ε' and p is used to screen thicknesses. The optimum permittivity of ultra-low reflectivity and ultra-wide band is obtained by combining the numerical analysis results. To verify the accuracy and reliability of results and deductions, the permittivity of four prepared materials and fifty published papers are investigated. [ABSTRACT FROM AUTHOR]

Managed aquifer recharge (MAR) has emerged as a potential solution to resolve water insecurity, globally. However, integrated studies quantifying the surplus source water, suitable recharge sites and safe recharge capacity is limited. In this study, a novel methodology is presented to quantify transient injection rates in unconfined aquifers and generate MAR suitability maps based on estimated surplus water and permissible aquifer recharge capacity (PARC). Subbasin scale monthly surplus surface runoff was estimated at 75% dependability using a SWAT model. A linear regression model based on numerical solution was used to capture the aquifer response to injection and to calculate PARC values at subbasin level. The available surplus runoff and PARC values was then used to determine the suitable site and recharge rate during MAR operation. The developed methodology was applied in the semi-arid region of Lower Betwa River Basin (LBRB), India. The estimated surplus runoff was generally confined to the monsoon months of June to September and exhibited spatial heterogeneity with an average runoff rate of 5000 m3/d in 85% of the LBRB. Analysis of the PARC results revealed that thick alluvial aquifers had large permissible storage capacity and about 50% of the LBRB was capable of storing over 3500 m3/d of water. This study revealed that sufficient surplus runoff was generated in the LBRB, but it lacked the adequate safe aquifer storage capacity to conserve it. A total 65 subbasins was identified as the best suited sites for MAR which had enough surplus water and storage capacity to suffice 20% of the total water demand in the LBRB. The developed methodology was computationally efficient, could augment the field problem of determining scheduled recharge rates and could be used as a decision-making tool in artificial recharge projects. • Surplus runoff at 75% dependability give 5000 m3/d of source water in 85% of LBRB. • PARC calculation using presented methodology is computationally efficient. • 27 subbasins in LBRB can store adequate surplus runoff to meet 20% of water demand. • The average change in head was 1.46 m in 17-year injection period. [ABSTRACT FROM AUTHOR]

This study uses a hybrid finite element method to predict dynamic behavior of truncated conical shells with ring stiffeners under fluid loading. The proposed approach combines classical shell theory and the finite element method, making use of displacement functions derived from exact solutions of Sanders' shell equilibrium equations for conical shells. The analysis of the shell-fluid interface involves leveraging the velocity potential, Bernoulli's equation, and impermeability conditions to determine an explicit expression for fluid pressure. To the best of our knowledge, this paper is the first to compare the methods applied to ring-stiffened shells against other numerical and experimental findings. Our results on conical shells in various conditions, with and without ring stiffeners, are largely consistent with previous findings. This study also explores the influence of geometric parameters, stiffener quantity, cone angle, and applied boundary conditions on the natural frequency of fluid-loaded ring-stiffened conical shells. The paper concludes with a discussion of several useful implications for further research. • Vibration analysis of fluid-filled ring-stiffened conical shells. • Finite element method for hydroelastic stability of conical shell. • The solid model based on Sanders' shell theory. • Fluid pressure is expressed using velocity potential and Bernoulli's equation. • Natural frequency is determined for different boundary conditions and geometries. [ABSTRACT FROM AUTHOR]

• The relation between residual pump power and effect of thermal expansion of long distance side pumping fiber was investigated. • Experiment of different cooling water temperature of coupling part was adapted to verify the thermal expansion of assumption. With the same fiber preform, two long distance side pumping fibers were fabricated and measured based on a master oscillator power structure. The residual pump power tendency of the two fibers were obtained in experiment. It was found the residual pump power would arise rapidly when the power reached turning point, which was defined by derivative value of residual pump power to pump power equal to 2.5%. Numerical analysis reveals that the thermal expansion of low refractive polymer between signal and pump fibers, will increase the distance between fibers, deteriorate the coupling efficiency, and lead to an exponential increasing of the residual pump power. [ABSTRACT FROM AUTHOR]

Bistable systems have been of great research interest due to their rich dynamics arising from a variety of excitations. This study presents an investigation into the nonlinear dynamics of a continuous bistable beam subjected to a form of vibro-impact forcing. A fixed–fixed Euler–Bernoulli beam, precompressed to achieve bistability, is considered, while a shaker with sinusoidally-prescribed velocity applies transverse impact forcing. By varying excitation parameters such as frequency and amplitude, the system response can be tuned. The study begins by employing a Galerkin expansion to the continuous equation of motion, using the buckling modes to remove buckling level dependence and ensure equilibrium symmetry. A Hertzian contact law is chosen to model the collision between the shaker and the buckled beam. The rich dynamics of this system are then explored through numerical and experimental analyses. The focus lies on investigating the emergence of intrawell and interwell dynamics that arise with varying excitation frequency, amplitude, and location. Moreover, we evaluate the significance of including higher-order modes in the modeling of bistable beam dynamics, particularly near snapthrough. This research provides valuable insights into the behavior of continuous bistable structures under vibro-impact forcing, contributing to the understanding and control of such systems in engineering applications. • Novel multi-mode model studies nonlinear dynamics of a buckled beam with impact. • Experiment and computational results reveal rich excitation-dependent dynamics. • More modes are required to model high frequencies and off-center excitation. • Shaker frequency, amplitude, and location strongly influence buckled beam response. [ABSTRACT FROM AUTHOR]

This work is devoted to the analysis of a numerical approximation to a general multi-dimensional kinetic Fokker–Planck (FP) equation with reaction and source terms and subject to specular reflection boundary conditions. This numerical approximation is based on splitting the kinetic FP model into a transport equation in space and a FP diffusive model in the velocity coordinates. The former is discretized by a Kurganov-Tadmor finite-volume scheme, while the latter is approximated by a generalized Chang & Cooper finite-volume method. Time integration is performed by a strong stability-preserving Runge-Kutta method where the reaction and source terms are accommodated with a Strang splitting technique and the use of a Magnus integrator. It is proved that the resulting numerical solution method is conservative and positive preserving, in the case where the continuous model has these properties, and it is second-order accurate in time and in phase space in the L 1 -norm, subject to a CFL condition. Results of numerical experiments are reported that validate these theoretical results. • A rigorous analysis of a class of numerical approximations to a generalized kinetic Fokker-Planck (FP) equation is presented. • The generalized FP equation includes reaction and source terms and is subject to specular reflection boundary equations. • A new numerical splitting scheme is developed that is proven to be positive, conservative, and second order accurate. • Numerical experiments with different scenarios are presented to validate the theoretical findings on the proposed method. [ABSTRACT FROM AUTHOR]

• A MNES for torsional vibration suppression of a spline-rotor system is proposed. • The optimal parameters of the MNES are determined using the response surface. • The effectiveness of the MNES under various spline clearances is demonstrated. • The experimental implementation of the MNES validates the numerical findings. To tackle the prominent issue of torsional vibrations in the spline-rotor system, a multi-stable nonlinear energy sink (MNES) is presented. A nonlinear torque expression for the spline is presented by emphasizing backlash nonlinearities. The nonlinear characteristics of the MNES are created by merging the positive stiffness of the ball-inner cone structures with the negative stiffness of the permanent magnet pairs. Consequently, a torsional dynamic model for the spline-rotor system incorporating the MNES is established. By analyzing the vibration response surfaces, the optimal parameters for the MNES are determined when subjected to both transient and steady-state excitations. Numerical analysis is conducted to evaluate the suppression performance of the MNES under various clearances. The findings are subsequently validated by establishing a spline-rotor system experimental platform. The results indicate that backlash nonlinearities have a certain impact on the vibration responses of the system. When the external excitation is appropriately applied, the MNES demonstrates effectiveness in mitigating torsional vibrations across varying clearances. In terms of transient response, the displacement attenuation rate of the primary system increased by 83.78 % after implementing the MNES. Regarding steady-state response, the simulation demonstrates a 77.84 % improvement in vibration suppression percentage, while the experiment exhibits a 63.05% enhancement. [ABSTRACT FROM AUTHOR]

• A vibrating system with four reverse internal-driving degrees of freedom is proposed. • Self-balancing characteristics and stability are studied. • Stable states and the motion types in the different resonant regions are analyzed. • Test bench is designed to verify the correctness of the theory and analysis results. For self-synchronous vibrating systems, the large dynamic loads are usually transmitted by the system to the foundation, resulting in the problems of noise pollution, damaging the foundation, and exacerbating components and parts wear and tear, etc. In the current study, from the perspectives of mechanics and mechanism, we have discovered the principle of self-balancing based on self-synchronization theory, which can effectively solve these problems. First, a dynamical model with four internal degrees of freedom driven by four reverse-rotating exciters is proposed to study its synchronization, stability, and self-balancing characteristics. Then, in theory, the equations of motion, the criteria of synchronization and stability of the system are deduced using Lagrange's methods, the average method, and Routh–Hurwitz stability criterion, respectively. Based on the principle that the dynamic load transmitted to the foundation when the system realizes self-balancing is theoretically zero, the self-balancing conditions of the system are further provided. Based on these conditions, the stability and self-balancing characteristics of the system in different resonant regions are qualitatively analyzed numerically, including the stable phase differences among exciters, stability ability of the system, amplitudes of rigid frames, and motion characteristics. Finally, the simulations and experiments are further carried out to examine the correctness of the theoretical results and numerical analysis results. It's shown that the reasonable working point in engineering should be selected in the first sub-resonant region of the vibrating system. The present work can provide theoretical guidance for designing some new types of vibrating systems with the function of self-balancing. [ABSTRACT FROM AUTHOR]

Cultural macroevolution concerns a long-term evolutionary process involving transmission of non-genetic or cultural traits between populations as well as birth and death of populations. To understand the spatial dynamics of cultural macroevolution, we present a one-locus model of cultural diffusion in which a cultural trait is transmitted on a network of populations. Borrowing the method of ancestral backward process from population genetics, our model explores the lineage of a trait variant sampled in the present generation to quantify when and where the variant was invented. Mathematical analysis of the model enables us to predict the distribution of cultural age in each population of the network, estimate the frequencies of trait variants originating from given populations, and discuss the time it takes for a trait variant to diffuse between a given pair of populations. We also perform numerical analysis on random scale-free network of populations to investigate the effect of network topology and innovation rate on the age and origin of variants in each population. The result suggests that trait variants are more likely to derive from a population with higher innovation rate. Our numerical analysis also shows that trait variants invented in populations with higher network-centrality values are likely to be maintained at a higher frequency and transmitted to other populations in a shorter time period. [ABSTRACT FROM AUTHOR]

In 1912, Edmund Taylor Whittaker (1873–1956) was appointed to the Chair of Mathematics at the University of Edinburgh. The following year he opened the Edinburgh Mathematical Laboratory. The purpose of the Laboratory was practical instruction in topics which are now classed together as numerical analysis. In this article I explore the inspiration, purpose, and impact of the Laboratory in the context of early 20th century British applied mathematics. [ABSTRACT FROM AUTHOR]

• Acoustic superscatterer concept that is tunable through externally applied stimuli is proposed. • Analysis and numerical simulation results demonstrating the concept are reported. • Potential applications of this superscatterer in water are discussed. Metamaterials have been widely studied in recent years, setting out their various exotic properties, but typically passive configurations are discussed, with limitations in frequency or loading performance. Here, we present a novel tunable acoustic superscatterer, a type of metamaterial, whose scattering cross-section in water can be varied with externally applied stimuli. The core of the superscatterer is filled with a magnetorheological fluid and the envelope is made of an extremely anisotropic acoustic metasurface in the form of a maze-like annular sleeve which can be additively manufactured. When an external magnetic field is applied in a direction perpendicular to the direction of the incoming acoustic field, the scattering boundary of the core is modulated, resulting in switchable total scattering cross-section of the superscatterer. Here we report analytical studies demonstrating this concept, as well as numerical simulation results that support the analytical results. [ABSTRACT FROM AUTHOR]

[Display omitted] • New type auxetic beams are designed for energy harvesting applications. • All of beam types examined numerically and experimentally. • The vibration new types of beam are experimentally investigated. • Experimental Harmonic analysis and experimental flow induced vibration test conducted and compared. In this study, different types of auxetic beams were designed and their vibration characteristics were investigated experimentally and numerically for to improve output electrical power in energy harvesting applications. In order to analyze the energy harvesting performance of all designed beams, different frequency conditions were investigated. To see the vibration-based energy harvesting potential of all auxetic beams, the displacement responses under vibration were analyzed using different methods. Firstly experimental modal analysis of non-traditional beams were made and compare with the FEM methods numerically. The displacement of beam were obtained under forced vibration by numerical harmonic analysis to evaluate beams in terms of energy harvesting performance. Then, sinusoidal vibration experiments in the electro-mechanical shaker were carried out in order to verify numerical modal analyses results for non-classical beams. Finally, galloping geometry was attached to the ends of all auxetic samples produced and exposed to wind load. The effect of air flow on beam vibrations and energy harvesting performance was investigated experimentally. [ABSTRACT FROM AUTHOR]

• Frequency responses of cracked piezoelectric beam under moving load are examined. • Distributed piezoelectric sensor is reliable to measure beam deflection response. • A new damage index gained from the measured response is highly sensitive to crack. • A novel criterion is proposed for crack detection by measured frequency response. • Controlled moving load and distributed sensor are useful for crack identification. The present study addresses the problem of crack identification in beam-like structures using a distributed piezoelectric sensor and controlled moving load. First, governing equations for the vibration of a cracked Timoshenko beam integrated with a piezoelectric layer and subjected to a moving load are established and their solution in the frequency domain is derived and acknowledged as electro-mechanical response of the beam. Then, variation of the electro-mechanical frequency response is examined versus crack and moving load parameters with the aim to propose a novel indicator, called herein spectral assurance criterion, for crack detection in beam-like structures. Finally, a procedure is developed for crack identification from moving load-induced frequency response measured by the distributed piezoelectric sensor based on the proposed spectral assurance criterion. The numerical analysis demonstrates that (a) the piezoelectric layer can be used as a distributed sensor for reliably measuring the mechanical response of beam subjected to moving load; (b) the speed-controlled moving harmonic force is a useful tool for exciting a beam-like structure for its health monitoring purpose and (c) the proposed spectral assurance criterion is actually a novel and efficient indicator for crack identification in beam-like structures. [ABSTRACT FROM AUTHOR]

We construct explicit easily implementable polynomial approximations of sufficiently high accuracy for locally constant functions on the union of disjoint segments (see (1)). This problem has important applications in several areas of numerical analysis, complexity theory, quantum algorithms, etc. The one, most relevant for us, is the amplification of approximation method: it allows to construct approximations of higher degree M and better accuracy from the approximations of degree m. [ABSTRACT FROM AUTHOR]

[Display omitted] • We have developed a novel workflow to clean up the cryo-electron microscopy datasets directly at the 3D level. • We introduce a modular framework that emphasizes various facets of encoder design for the amortized inference of hidden variables in cryo-electron microscopy image processing. • Our introduced uncertainty measure offers a method to quantify the confidence level of our estimations. • Utilizing contrastive learning significantly bolsters the robustness of orientation estimation. • Incorporating preprocessing layers and employing curriculum learning bolster neural network performance in orientation estimation. In single-particle cryo-electron microscopy (cryo-EM), efficient determination of orientation parameters for particle images poses a significant challenge yet is crucial for reconstructing 3D structures. This task is complicated by the high noise levels in the datasets, which often include outliers, necessitating several time-consuming 2D clean-up processes. Recently, solutions based on deep learning have emerged, offering a more streamlined approach to the traditionally laborious task of orientation estimation. These solutions employ amortized inference, eliminating the need to estimate parameters individually for each image. However, these methods frequently overlook the presence of outliers and may not adequately concentrate on the components used within the network. This paper introduces a novel method using a 10-dimensional feature vector for orientation representation, extracting orientations as unit quaternions with an accompanying uncertainty metric. Furthermore, we propose a unique loss function that considers the pairwise distances between orientations, thereby enhancing the accuracy of our method. Finally, we also comprehensively evaluate the design choices in constructing the encoder network, a topic that has not received sufficient attention in the literature. Our numerical analysis demonstrates that our methodology effectively recovers orientations from 2D cryo-EM images in an end-to-end manner. Notably, the inclusion of uncertainty quantification allows for direct clean-up of the dataset at the 3D level. Lastly, we package our proposed methods into a user-friendly software suite named cryo-forum , designed for easy access by developers. [ABSTRACT FROM AUTHOR]

• Existence and propagation of soliton solutions are investigated in double-well potentials with cubic nonlinearity. • Soliton solutions are obtained including single and multiple peaks. • Significant discussion is devoted to fundamental, tripole, and quadrupole solitons. • Effect of potential well separation on the formation and stability of solitons is studied. The existence, stability and propagation of spatial solitons in double-well potentials with cubic nonlinearity are investigated. The symmetric, tripole and quadrupole solitons show stability at lower power, while the symmetry-broken and antisymmetric solitons can remain stable throughout their existence curves. In comparison, the centered fundamental solitons are less stable than their symmetry-broken bound states and bifurcate from symmetric solitons. In this article, we study the effect of the separation between the two wells of the potential on the formation and stability of solitons. The threshold power of stable solitons tends to decrease with increasing separation for fundamental and symmetric solitons, while it is more complicated for tripole and quadrupole solitons. In general, there is a specific separation between two potential wells at which there are hardly any stable tripole and quadrupole solitons. Linear stability analysis and direct numerical simulations have provided evidence for the stability and propagation of solitons. [ABSTRACT FROM AUTHOR]

Toroidal involute worm (TI worm) meshing with plastic gear can serve as an efficient reducer for applications in smart home and automatic driving, owing to its stable transmission and high carrying capacity. This necessitates an in-depth analysis of the vibration and noise associated with TI worm drive to enhance the comfort in these scenarios. Utilizing the meshing characteristics of TI worm drive, a dynamic model including nonlinear factors such as time-varying meshing stiffness and meshing damping is established. The dynamic characteristics of TI worm meshing with different plastic helical gears are compared and analyzed. The TI worm drive experiments are carried out, and vibration signals are collected though accelerometers. The numerical analysis results align with the experimental findings. The results reveal that TI worm meshing with different plastics exhibits the maximum vibration amplitude in the axial direction of the worm. Specifically, PEEK demonstrates the highest amplitude, followed by POM, while Nylon has the smallest vibration amplitude. These findings serve as a valuable reference for mitigating vibration and noise of TI worm drives. [ABSTRACT FROM AUTHOR]

• Consideration of a coupled dynamic analysis of cylindrical shells with an external and an internal fluid. • Analysis of free surface motion of internal fluid. • Use of Chebyshev polynomials to describe the displacement fields of the clamped cylindrical shell. • Free vibration analysis of a large shell geometry compatible with large offshore structures. Cylindrical shells filled with fluid are structures widely used in different engineering installations, such as oil platforms, nuclear power plants and storage tanks. In offshore structures, the action of ocean waves must be carefully evaluated, because the influence of the external fluid to the external walls of this structure can modify its dynamic behavior. This article presents an analytical-numerical approach to analyze the linear vibrations of a clamped cylindrical shell, considering the presence of external and internal fluid with the inclusion of the effects of the free surface motion of the internal fluid. The strain fields and curvature changes of the middle surface of the cylindrical shell are described by the Sanders–Koiter linear theory. The modal expansions, that describe the displacement fields of the clamped cylindrical shell, are obtained from the Chebyshev polynomials. Finally, the Rayleigh–Ritz method is used to derive the linear equations of motion of the system which, in their turn, are solved to obtain the natural frequencies and vibration modes of the clamped cylindrical shell with external and internal fluid interaction. The obtained results are compared, when it is possible, with others works found in the literature. Also, a finite element analysis in a commercial software is conducted to evaluate the reliability and the convergence of the obtained analytical-numerical results. They indicate that the fluid level alters the free vibrations of the cylindrical shell. The consideration of the external and internal fluid for free vibration analysis with application of a hydrodynamic pressures is important, since it incorporates additional mass and reduces the values of natural frequencies. The influence of the free surface also alters the free vibrations of the cylindrical shell, and for large structures, a considerable effect is observed that cannot be disregarded. [ABSTRACT FROM AUTHOR]

• Use the relationship between the modal damping and shapes to identify bridge damping ratio. • Derive novel formula for determining the bridge damping ratio from the correlation of the front and rear contact points. • Use wavelet transform to obtain the component response of the bridge in time–frequency domain. • Use RANdom SAmple Consensus to downplay the deviated data points in curve-fitting for the damping ratio. • Suggest using the first-span data as representative ones in calculating the damping ratio of multi-span bridges. A novel formula is derived for determining the bridge damping ratio from the correlation of the front and rear wheels of a test vehicle using the modal components extracted by the wavelet transform (WT). Firstly, closed-form solutions are derived for the dynamic responses of the bridge under a moving two-axle vehicle. Next, to remove the masking effect by vehicle's frequencies, the wheel-bridge contact responses back-calculated from the vehicle responses are used in analysis. Then, the WT is employed to obtain the instantaneous amplitudes of the component responses of the two contact points. Finally, using the correlation between the two contact points, a novel formula is derived for the bridge damping ratio. The above derivations are validated by numerical simulations. Through the theoretical analysis and numerical simulations, the following conclusions are made: (1) the spatial correlation of the front and rear contact points is utilized to derive the bridge damping formula using the WT; (2) for multi-span bridges, the RANdom SAmple Consensus (RANSAC) can beneficially downplay the data points with large deviations near the internal supports in fitting the bridge damping ratio; (3) the first span can be reliably used to calculate the damping ratio of multi-span bridges, especially in the presence of pavement roughness; and (4) the formula has been attested to be robust against various levels of vehicle and bridge damping. [ABSTRACT FROM AUTHOR]

This study rigorously addresses the Neumann–Robin problem of sound radiation from a vibrating flexible disk embedded into a hemispherical enclosure. The enclosure is acoustically soft on its inside surface and hard on its outside surface. The method of superimposed solutions, expressed in terms of Dini series and spherical harmonics, has been applied for this purpose. The presented solution is applicable to any vibration velocity profile on the radiator, with an elastically supported thin plate excited asymmetrically used as an example. The results presented here can be valuable for modeling vibroacoustic responses of various speakers, sensors, and microphones with edges either clamped to the enclosure or nearly free. Achieving this involves modifying the values of the boundary stiffness for resisting transverse displacement and the rotation of the plate's edge. Additionally, when applying these results to model the responses of alarm or signaling transducers, high-amplitude responses are expected for selected resonant frequencies. In such cases, the boundary stiffness values can be set to ensure multiple strong and wide resonant maxima in the frequency characteristics. In addition, the results presented in this study include solving the dynamic equation of motion for the plate or rigid piston with external excitation. This equation is coupled with the wave equation inside and outside the hemispherical enclosure, allowing the inclusion of the enclosure's effect on the plate-enclosure system's responses. This approach can be useful for modeling and improving the acoustic responses of spherical speakers. In such cases, the boundary stiffness values should be relatively small to emulate a soft suspension of the plate. The impedance of the enclosure's internal surface can be arbitrarily selected, ranging from acoustically hard to acoustically soft. In this study, the impedance of mineral wool has been applied. Numerical analysis is presented for frequencies below 4 kHz, with errors smaller than 0.2%. The results have been validated using the finite element method. • Asymmetric vibrations of an elastically supported circular plate and a rigid circular piston. • Including the effect of fluid loading on the excited vibrations of plate and piston. • Solving the problem using the Dini expansion series and the spherical harmonics. • Improving analytical and numerical results using rigorous methods within the low frequency range. [ABSTRACT FROM AUTHOR]

The presence of magnetized anomalies in the shell of the Earth interrupts its geomagnetic field. We consider the inverse problem of identifying the anomalies by monitoring the variation of the geomagnetic field. Motivated by the theoretical unique identifiability result in [7] , we develop a novel numerical scheme of locating multiple magnetized anomalies. In our study, we do not assume the source that generates the geomagnetic field, and the medium configurations of the Earth's core and the magnetized anomalies are a-priori known. The core of the reconstruction scheme is a novel imaging functional whose quantitative behaviours can be used to identify the anomalies. Both rigorous analysis and extensive numerical experiments are provided to verify the effectiveness and promising features of the proposed reconstruction scheme. • Magnetic anomalies detection from geomagnetic monitoring is practically important and challenging. • Based on a sophisticated geomagnetic model, a novel reconstruction scheme is proposed and developed. • In our method, the geomagnetic source and the medium configuration of the Earth's core are both not a-priori known. • The core is a novel imaging functional whose promising features are both theoretically and computationally verified. [ABSTRACT FROM AUTHOR]

• A piezoelectric combined cantilever-asymmetric-pendulum structure is proposed. • Can efficiently harvest vibratory energy from any arbitrary direction. • Numerical analysis presented as well as simulation conducted to validate theory and proposed model. • The improvement of the voltage amplitude and operational bandwidth are 128.5 % and 229.8 % over variable excitation amplitudes, respectively. This paper introduces a novel approach to address the challenges faced by traditional unidirectional cantilever-based energy harvesters in adapting to multi-directional vibration environments. The proposed solution combines a flexible cantilever with an asymmetric-conical-pendulum structure which consists of two different concentrated end masses and a rigid thin rod By investigation of energy interchange relationship between the kinetic feature of the asymmetric pendulum and beam bending vibration under horizontal and vertical excitations respectively from base movements, utilizing the Lagrange's theorem and multiple-scale method, 1:2 internal resonance can be induced for enabling the delivery of multi-directional motion of pendulums to the unidirectional bending of cantilever. On this basis, the advantages of the proposed system are revealed by comparing with traditional piezoelectric cantilever and piezoelectric cantilever-single-pendulum systems. Furthermore, the performance of the voltage amplitude and operational bandwidth was potentially improved up to 128.5 % and 229.8 % under x -direction. In addition, it is confirmed that its maximum voltage RMS value is 57.9 % and 11.4 % higher than that of the piezoelectric cantilever-single-pendulum in the x - and z -directions, owing to its multi-peak energy harvesting over variable excitation amplitudes. Therefore, the feasibility and superiorities of the proposed configuration are demonstrated theoretically and numerically in this paper. [ABSTRACT FROM AUTHOR]

In this work we extend the shifted Laplacian approach to the elastic Helmholtz equation. The shifted Laplacian multigrid method is a common preconditioning approach for the discretized acoustic Helmholtz equation. In some cases, like geophysical seismic imaging, one needs to consider the elastic Helmholtz equation, which is harder to solve: it is three times larger and contains a nullity-rich grad-div term. These properties make the solution of the equation more difficult for multigrid solvers. The key idea in this work is combining the shifted Laplacian with approaches for linear elasticity. We provide local Fourier analysis and numerical evidence that the convergence rate of our method is independent of the Poisson's ratio. Moreover, to better handle the problem size, we complement our multigrid method with the domain decomposition approach, which works in synergy with the local nature of the shifted Laplacian, so we enjoy the advantages of both methods without sacrificing performance. We demonstrate the efficiency of our solver on 2D and 3D problems in heterogeneous media. • A scalable Shifted Laplacian multigrid method for the Elastic Helmholtz equation. • The elastic Helmholtz equation is solved at the same efficiency as the acoustic. • We provide detailed local Fourier analysis to validate our numerical results. • Domain decomposition is combined to enhance parallelism and reduce memory costs. • The two parts of the hybrid method work in synergy due to their local nature. [ABSTRACT FROM AUTHOR]

We present a general kernel-based framework for learning operators between Banach spaces along with a priori error analysis and comprehensive numerical comparisons with popular neural net (NN) approaches such as Deep Operator Networks (DeepONet) [46] and Fourier Neural Operator (FNO) [45]. We consider the setting where the input/output spaces of target operator G † : U → V are reproducing kernel Hilbert spaces (RKHS), the data comes in the form of partial observations ϕ (u i) , φ (v i) of input/output functions v i = G † (u i) (i = 1 , ... , N), and the measurement operators ϕ : U → R n and φ : V → R m are linear. Writing ψ : R n → U and χ : R m → V for the optimal recovery maps associated with ϕ and φ , we approximate G † with G ¯ = χ ∘ f ¯ ∘ ϕ where f ¯ is an optimal recovery approximation of f † : = φ ∘ G † ∘ ψ : R n → R m. We show that, even when using vanilla kernels (e.g., linear or Matérn), our approach is competitive in terms of cost-accuracy trade-off and either matches or beats the performance of NN methods on a majority of benchmarks. Additionally, our framework offers several advantages inherited from kernel methods: simplicity, interpretability, convergence guarantees, a priori error estimates, and Bayesian uncertainty quantification. As such, it can serve as a natural benchmark for operator learning. • A general kernel-based framework for learning operators between Banach spaces. • A priori error analysis and convergence guarantees for this method. • Comprehensive numerical comparisons with popular neural net approaches. • Our approach matches or beats the cost-accuracy performance of NN methods. • Bayesian uncertainty and interpretability inherited from kernel methods. [ABSTRACT FROM AUTHOR]

Wrinkling and creasing of an elastic membrane are post-buckling processes induced by in-plane compression. When a hyperelastic capsule is suspended in a simple shear flow, its membrane forms several wavy patterns. To elucidate the post-buckling behavior of a capsule in a Stokes shear flow, we investigated the effects of the shear rate and membrane thickness on capsule deformation by performing numerical analysis to capture the wrinkling and creasing of the capsule membrane. The deformation of the capsule was formulated based on the Kirchhoff–Love shell theory and the Stokes flow was calculated using the boundary integral equation. The capsule shape was represented by a T-spline surface. The isogeometric boundary element analysis showed that the capsule in the shear flow formed wrinkles and creases. Whereas wrinkling occurred at low shear rates, both wrinkling and creasing occurred at high shear rates depending on the membrane thickness. Based on the geometrical consistency of the capsule surface, we suggest that the deformation type can be determined by mechanical and geometrical effects of the membrane thickness, that is, the bending rigidity and ease of self-contact, respectively. This approach will be useful for investigating the geometrical consistency for further understanding the post-buckling behavior of capsules in Stokes flows. • The post-buckling process of a capsule in a Stokes shear flow is investigated. • Isogeometric BEM with Kirchhoff–Love shell theory enables capturing creasing. • Creasing of the capsule membrane occurs at high shear rates. • The deformation type depends on the mechanical and geometrical effects of thickness. [ABSTRACT FROM AUTHOR]

For many algorithms, parameter tuning remains a challenging task, which becomes tedious in a multi-parameter setting. Multi-penalty regularization, successfully used for solving undetermined sparse regression problems of unmixing type, is one of such examples. We propose a novel algorithmic framework for an adaptive parameter choice in multi-penalty regularization with focus on correct support recovery. By extending ideas on regularization paths, we provide an efficient procedure for the construction of regions containing structurally similar solutions, i.e., solutions with the same sparsity and sign pattern, over the range of parameters. Combined with a model selection criterion, regularization parameters are chosen in a data-adaptive manner. Another advantage of our algorithm is that it provides an overview on the solution stability over the parameter range. We provide a numerical analysis of our method and compare it to the state-of-the-art algorithms for compressed sensing problems to demonstrate the robustness and power of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Tractor overturning is a leading cause of fatalities for farmers. In Japan, small tractors are used for farming on harsh terrain, such as slippery fields and steep passage slopes. On such potentially dangerous terrain, steering instability induced by bouncing and sliding can cause tractor overturning accidents. Steering instability can also deteriorate the precision of trajectory tracking in autonomous driving tractors. The present study numerically investigated tractor steering instability due to bouncing and sliding. A bouncing model and bicycle model were coupled based on Coulomb's classical theory of friction, and numerical experiments were conducted using the developed model. In the simulations, the tractor's travel velocity, the static friction coefficient, the bump length, and the turning radius were considered as control parameters. A turning test was conducted to investigate the basic steering performance of the developed model. The numerical results revealed that the bouncing and sliding caused by the disturbance exciter reduced the cornering force to zero, which led to a deviation of the turning trajectory from the desired trajectory. The tractor was then operated on a steep passage slope similar to those reported in accidents in Japan. In the simulation, bouncing and sliding occurred because of the steep slope. The results obtained in this study strongly suggest that bouncing and sliding occurring on specific terrain result in steering instability and are a major cause of overturning accidents. • A dynamic tractor model coupling a bouncing model and bicycle model was developed. • Steering instability induced by bouncing and sliding was investigated. • Intensive numerical experiments were conducted for various parameter combinations. • Bouncing and sliding reduced steering stability in numerical experiments. [ABSTRACT FROM AUTHOR]

Immediate changes in vascular mechanics during aortic cross-clamping remain widely unknown. By using a numerical model of the arterial network, vascular compliance and resistance can be estimated and the time constant of pressure waves can be calculated and compared with results from the classic arterial waveform analysis. Experimental data were registered from continuous invasive radial artery pressure measurements from 11 patients undergoing vascular surgery. A stable set of beats were chosen immediately before and after each clamping event. Through the arterial waveform analysis, the time constant was calculated for each individual beat and for a mean beat of each condition as to compare with numerical simulations. Overall proportional changes in resistance and compliance during clamping and unclamping were calculated using the numerical model. Arterial waveform analysis of individual beats indicated a significant 10% median reduction in the time constant after clamping, and a significant 17% median increase in the time constant after unclamping. There was a positive correlation between waveform analysis and numerical values of the time constant, which was moderate (ρ = 0.51; P = 0.01486) during clamping and strong (ρ = 0.77; P ≤ 0.0001) during unclamping. After clamping, there was a significant 16% increase in the mean resistance and a significant 23% decrease in the mean compliance. After unclamping, there was a significant 19% decrease in the mean resistance and a significant 56% increase in the mean compliance. There are significant hemodynamic changes in vascular compliance and resistance during aortic clamping and unclamping. Numerical computer models can add information on the mechanisms of injury due to aortic clamping. [ABSTRACT FROM AUTHOR]

In this paper, we consider an approximation method, and a novel general analysis, for second-order elliptic differential equations with heterogeneous multiscale coefficients. We obtain convergence of the Generalized Multi-scale Finite Element Method (GMsFEM) method that uses local eigenvectors in its construction. The analysis presented here can be extended, without great difficulty, to more sophisticated GMsFEMs. For concreteness, the obtained error estimates generalize and simplify the convergence analysis of Y. Efendiev et al. (2011) [22]. The GMsFEM method construct basis functions that are obtained by multiplication of (approximation of) local eigenvectors by partition of unity functions. Only important eigenvectors are used in the construction. The error estimates are general and are written in terms of the eigenvalues of the eigenvectors not used in the construction. The error analysis involve local and global norms that measure the decay of the expansion of the solution in terms of local eigenvectors. Numerical experiments are carried out to verify the feasibility of the approach with respect to the convergence and stability properties of the analysis. • We clarify and simplify the numerical analysis previously presented in [J. Comput. Phys. 230 (2011), 937-955]. • We design and analyze GMsFEM spaces constructed using local Neumann and Dirichlet eigenvalues problems. • We present an example with no optimal GMsFEM convergence rate when only Neumann eigenvalues are used. • A novel and general regularity numerical analysis tool for the high-contrast multiscale elliptic problems is presented. • We present numerical results with realistic high-contrast multiscale coefficients. [ABSTRACT FROM AUTHOR]

Stochastic resonance (SR) has been proven effective for weak signal detection under low signal-to-noise ratio (SNR) conditions. In this paper, a parameter matched stochastic resonance (PMSR) method is proposed to enhance the detection and extraction ability to weak signatures of moving vessels. Theoretical matched framework is established with a damped bistable SR model by optimizing the input-output signal-to-noise ratio improvement (SNRI) to nonlinear system parameters. By selecting a proper damping factor within a determinate constraint range, a weak periodic signal, background noise, and nonlinear system can be matched in generating a desired optimal output in the regime of matched parameter relationship. Then, we propose a PMSR based energy detection (ED) algorithm by taking the fully advantage of the Lorentzian characteristics. Numerical simulation analyses and application verifications are carried out to validate the effectiveness and efficiency of the proposed method, which reflects an excellent enhancement performance especially for low-frequency ship signatures. [ABSTRACT FROM AUTHOR]

In our recent article [1] published in this journal we provide quantitative evidence to show that there are warnings and caveats in the way Gu and collaborators [2] define controllability of brain networks and measure the contribution of each of its nodes. The comment by Pasqualetti et al. [3] confirms the need to go beyond the methodology and approach presented in Gu et al.'s original work. In fact, they recognize that "the source of confusion is due to the fact that assessing controllability via numerical analysis typically leads to ill-conditioned problems, and thus often generates results that are difficult to interpret". This is indeed the first warning we discussed in [1]: our work was not meant to prove that brain networks are not controllable from one node, rather we wished to highlight that the one node controllability framework and all consequent results were not properly justified based on the methodology presented in Gu et al. [2]. We used in our work the same method of Gu et al. not because we believe it is the best methodology, but because we extensively investigated it with the aim of replicating, testing, and extending their results. The warning and caveats we have proposed are the results of this investigation. Indeed, on the basis of our controllability analyses of multiple human brain networks datasets, we concluded: " The λ min (W K) are statistically compatible with zero and thus the associated controllability Gramian cannot be inverted 1 . These results show that it is not possible to infer one node controllability of the brain numerically ". Hence both groups agree that one node controllability cannot be inferred numerically. [ABSTRACT FROM AUTHOR]