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In a previous paper (Feng et al., J. Differential Equations (2023)), we studied a seasonally interactive model between closed seasons and open seasons with Michaelis-Menten type harvesting, in which we assumed that the harvesting quantity was relatively large (0 < κ = l G c E < 1) and obtained a length threshold of the closed season T ¯ ⁎ depending on the harvesting parameter and the seasonal fluctuation period. It was shown that the origin is globally asymptotically stable if and only if T ¯ ≤ T ¯ ⁎ , and there exists a unique globally asymptotically stable T -periodic solution if and only if T ¯ > T ¯ ⁎. In this paper, we continue to investigate the periodic dynamics of this model when the harvesting quantity is relatively small (κ = l G c E ≥ 1). By finding another smaller length threshold T ¯ ⁎ ∈ (0 , T ¯ ⁎) , we determine the number of periodic solutions and study their stability, which imply the occurrence of bifurcation of periodic solutions. Our results demonstrate that designing the closed harvesting season properly can prevent the species from extinction. Moreover, by comparing with the continuous harvesting model and combining the results in our previous paper and this article, we provide a complete understanding on the global dynamics for the periodic switching model. Some numerical simulations are also carried out to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is devoted to a bistable system for calcium buffering. We first prove two kinds of stability of diverging traveling fronts of the degenerate system (All buffers do not diffuse): the local C 0 -norm stability and the asymptotic stability. In particular, as for asymptotic stability, we prove a Liouville-type result by the sliding method, and then use the truncation technique to study the long-time behavior of diverging wave like solution. These stabilities imply that, under suitable conditions on the initial data, the solution locally uniformly approaches to the high equilibrium state (1 , b 2). Then, by examining the behavior of solutions with one-parameter family of initial data, we show that the parameter-dependent solutions can be divided into three categories: convergence to the basal equilibrium state (0 , b 0) for small parameter values, convergence to the high equilibrium state (1 , b 2) for large parameter values, whereas neither of these behaviors occurs for intermediate parameter values. We refer to such phenomenon as threshold phenomenon. These intermediate parameter values are called threshold values, and the corresponding solutions are called threshold solutions. At the end of the paper, we present some important properties of the threshold solution and provide some numerical simulations. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of spreading properties and traveling wave solutions for a vector-host disease system, which models the invasion of vectors and hosts to a new habitat. Combining the uniform persistence idea from dynamical systems with the properties of the corresponding entire solutions, we investigate the propagation phenomena in two different cases: (1) fast susceptible vector; (2) slow susceptible vector when the disease spreads. It turns out that in the former case, the susceptible vector may spread faster than the infected vector and host under appropriate conditions, which leads to multi-front spreading with different speeds; while in the latter case, the infected vector and host always catch up with the susceptible vector, and they spread at the same speed. We further obtain the existence and nonexistence of traveling wave solutions connecting zero to the endemic equilibrium. We also conduct numerical simulations to illustrate our analytic results. [ABSTRACT FROM AUTHOR]

This paper demonstrates a theoretical and experimental study on a universal vibro-impact system with bidirectional drift. With a dedicated experimental rig that is able to verify numerical simulations, the system has revealed various bifurcations from a piecewise-smooth dynamical model involving impact and dry friction. This experimental rig with a two-sided constraint is designed with adjustable configurations which can be used for experimental testing of versatile piecewise-smooth dynamical systems, e.g., the impact oscillator, the drifting oscillator and the capsule system. It is able to be customised to alter different system parameters, such as friction, number of constraints, mass ratio, impact gap and constraint stiffness, for developing and testing various control strategies. In this paper we particularly studied several types of bifurcations from our preliminary experimental results and discussed the dynamical responses of the system under different excitation frequencies and amplitudes. It was found that with a higher excitation frequency and amplitude, the vibro-impact dynamics on both ends of the constraints could result in a large amount of uncertainties, thus bi-stable and chaotic motions are likely to be observed. While being unstable, the system runs with a relatively high energy efficiency in this configuration. [Display omitted] • An experimental rig with a two-sided constraint and bidirectional drift is studied. • The rig is designed with adjustable configurations for testing versatile systems. • System parameters are identified and verified by numerical simulations. • Grazing and sliding bifurcations, bi-stability and chaotic motions are studied. • Control parameters that cause instability may lead to high energy efficiency. [ABSTRACT FROM AUTHOR]

As we have known that it is impossible to attenuate the vibration displacement of the floating-slab depending on a strong stiffness and to improve the low-frequency vibration isolation performance of the floating-slab track (FST) depending on a soft stiffness simultaneously in engineering. In this paper, we propose a novel method to solve the paradox by introducing a "Hardening-First-Then-Softening" (HFTS) design based upon the energy distribution of wheel-rail loads to formulate a model of nonlinear floating-slab isolator. The average procedure is employed to analyze the vibration isolation ability of the isolator with parameters taken from a metro line load excitation. A simulation model of train-FST-tunnel with HFTS isolator is constructed to study the dynamic behaviors of the system. The numerical simulations show the significant suppression of displacement response of floating-slab and Z weighted acceleration vibration level of the tunnel. The results presented herein this paper provide a scheme to solve the strict requirements of displacement suppression and the vibration isolation which is of beneficial to steady and silent urban rail transit. [ABSTRACT FROM AUTHOR]

Refuge provides an important mechanism for preserving many ecosystems. Prey refuges directly benefit prey but also indirectly benefit predators in the long term. In this paper, we consider the complex dynamics and bifurcations in Holling-Tanner model with generalist predator and prey refuge. It is shown that the model admits a nilpotent cusp or focus of codimension 3, a nilpotent elliptic singularity of codimension at least 4, and a weak focus with order at least 3 for different parameter values. As the parameters vary, the model can undergo three types degenerate Bogdanov-Takens bifurcations of codimension 3 (cusp, focus and elliptic cases), and degenerate Hopf bifurcation of codimension 3. The system can exhibit complex dynamics, such as multiple coexistent periodic orbits and homoclinic loops. Moreover, our results indicate that the constant prey refuge prevents prey extinction and causes global coexistence. A preeminent finding is that refuge can induce a stable, large-amplitude limit cycle enclosing one or three positive steady states. Numerical simulations are provided to illustrate and complement our theoretical results. [ABSTRACT FROM AUTHOR]

Existence, uniqueness and stability of forced pulsating waves as well as gap formation of reaction diffusion models in a shifting habitat are challenging problems in the field of propagation dynamics. In this paper, we design to tackle these problems for a time periodic Lotka-Volterra competition system. By using alternatively-coupling upper-lower solution method, we establish the existence of forced pulsating traveling wave, as long as the shifting speed falls in a finite interval where the end points are obtained from KPP-Fisher speeds. The asymptotic behaviors of the forced pulsating traveling wave are derived and this helps us show that this wave is unique. Moreover in the Lyapunov sense, the stability of the forced pulsating wave is also studied. Finally, when the forced speed is beyond the finite interval, gap formation is investigated theoretically and illustrated further by numerical simulations. [ABSTRACT FROM AUTHOR]

[Display omitted] The paper proposes to identify the parameters of linear dynamic models based on the original implementation of least absolute deviation estimators. It is known that the object estimation procedures synthesized in the sense of the least sum of absolute prediction errors are particularly resistant to occasional outliers and gaps in the analyzed system data series, while the classical least squares procedure unfortunately becomes of little use for reliably identifying systems in the presence of destructive measurement errors. Bearing in mind that the classic task of minimizing the quality functional of absolute deviations encounters fundamental analytical problems, it is proposed to use a dedicated iterative estimator for off-line evaluation of the parameters of the analyzed process. In addition, a simplified recursive version of the absolute deviation estimation procedure was developed, which allows for practical on-line tracking of the evolution of variable parameters of non-stationary systems. Importantly, a novel refinement of the discussed absolute deviation estimators was proposed to effectively overcome some inconvenient numerical effects. We also present an interesting comparison of the improved (by non-linear modification) iterative absolute-deviation estimator with the classical Gauss-Newton gradient algorithm, which leads to constructive conclusions. Finally, using computer simulations, the operation of the developed iterative and recursive estimators minimizing the absolute deviation is illustrated. The work ends with an indication of directions for further research. [ABSTRACT FROM AUTHOR]

In this paper, we present a computational framework based on fully Eulerian models for fluid–structure interaction for the numerical simulation of biological capsules. The flexibility of such models, given by the Eulerian treatment of the interface and deformations, allows us to easily deal with the large deformations experienced by the capsule. The modeling of the membrane is based on a full membrane elasticity Eulerian model that is capable of capturing both area and shear variations thanks to the so-called backward characteristics. In the validation section several test cases are presented with the goal of comparing our results to others present in the literature. In this part, the comparisons are done with different well-known configurations (capsule in shear flow and square-section channel), and by deepening the effect of the elastic constitutive law and capillary number on the membrane dynamics. Finally, to show the potential of this framework we introduce a new test case that describes the relaxation of a capsule in an opening channel. In order to increase the challenges of this test we study the influence of an internal nucleus, modeled as a hyperelastic solid, on the membrane evolution. Several numerical simulations of a 3D relaxation phenomenon are presented to provide characteristic shapes and curves related to the capsule deformations, while also modifying size and stiffness parameter of the nucleus. [ABSTRACT FROM AUTHOR]

Mesh-based Eulerian and particle-based Lagrangian models are common computational fluid dynamics (CFD) tools for simulating wave-structure interactions. While Eulerian models are efficient in terms of computational time, they are limited in their ability to handle large interface discontinuities between two flows and complex structure motion responses. Conversely, Lagrangian models are suitable for such discontinuities and motion responses but can be computationally expensive. However, there is a lack of comprehensive discussion on the (dis)advantages of hybrid Eulerian-Lagrangian models, which have the potential to achieve both numerical efficiency and flexibility through a combined use of mesh and particles. This paper presents a comparative study of a hybrid Eulerian-Lagrangian Particle-In-Cell (PIC) model and the widely-used OpenFOAM model, applied to a variety of complex wave interactions with floating offshore renewable energy structures in both 2D and fully 3D domains. We found that both models demonstrate good performance in simulating complex floating structures. Additionally, it is the first time that the two models have been compared in parallel on the same computing facility, allowing us to directly show their computational efficiency. The PIC model has the advantage of using staggered grids, which enables it to achieve computational efficiency comparable to the pure mesh-based OpenFOAM. The findings of this study provide researchers and practitioners in the field of computational fluid dynamics with a clear understanding of the performance of the hybrid Eulerian-Lagrangian PIC model and OpenFOAM for simulating complex fluid-structure interaction problems. [ABSTRACT FROM AUTHOR]

Observation missions of meteoroids entering the Earth's atmosphere are conducted regularly. Meanwhile a method to replicate the flight in a ground test facilities has been established. However, numerical simulations with subsequent comparison of the spectroscopic data, on the other hand, are not yet widely used in this field. This is mainly due to the complex flow environment, which includes not only non-equilibrium radiation, but also the outgassing of species from the meteoroid that do not enter the shock since they have only the thermal velocity of the wall without macroscopic flow and therefore cannot heat up as much as the other species. This paper presents a numerical approach to replicate experimental measurements. The Direct Simulation Monte Carlo (DSMC) method is used and bi-directionally coupled with a radiation solver to simulate the atmospheric entry in 80 km of an iron meteorite with a diameter of 38 mm. The paper provides information and references on the numerical models used, the challenges encountered, and the simulation results. The study shows that the simulation models are well-suited to handle the non-equilibrium effects of meteorite entry and show good agreement with the experimental measurements. • Complete non-equilibrium simulation of a meteoroid with a gas kinetic solver. • First coupled radiative flow simulation of a meteoroid. • First successful numerical reproduction of a measured meteor spectrum by simulation. [ABSTRACT FROM AUTHOR]

• A large-scale benchmark dataset with airfoil mesh samples. • A lightweight deep neural network MQNet for mesh quality evaluation. • A MQNet-based meshing workflow for high-quality airfoil mesh generation. Evaluating mesh quality before solving is crucially important for error control in the numerical simulation of airfoils. Traditional mesh quality metrics are used to identify distorted mesh elements by analyzing their geometric shape information like angles and edges. However, these metrics fail to recognize numerical errors stemming from quality attributes such as improper mesh density or distribution. This deficiency has imposed a burden on intensive manual re-evaluation, which heavily increases the meshing cost. In this paper, we introduce deep neural networks to airfoil mesh quality evaluation to improve its automation and efficiency. Specifically, we propose a neural network-based evaluation model, MQNet, accompanied by the first large-scale mesh benchmark dataset, AirfoilSet. MQNet is trained on the dataset to learn the quality-related attributes including mesh orthogonality, smoothness, and density. Thereafter, the trained network can be used as a black box to automatically evaluate and output the overall quality of the airfoil mesh. To demonstrate the effectiveness and generalization behaviors of the proposed network, we establish an MQNet-based mesh generation workflow. Experimental results show that MQNet is small and accurate. It outperforms widely-used neural networks and can be a useful tool to guide the high-quality mesh generation process with minimal user intervention. [ABSTRACT FROM AUTHOR]

In this paper, we mainly study the propagation properties of solutions of the predator-prey system with nonlocal dispersal. More specifically, we explored the spreading speeds of the predator and the prey in two different situations, namely, the predator spreads faster than the prey and the predator spreads slower than the prey. The main difficulty lies in the fact that the comparison principle cannot be used for the predator-prey system. We use the comparison principle of the scalar equation and the method of upper and lower solutions to prove the results. In addition, we establish the comparison principle of nonlocal dispersal equations in space and time dependent environment. We conclude that the predator and the prey will eventually coexist by constructing a suitable Lyapunov functional. Finally, we use numerical simulations to illustrate the results. [ABSTRACT FROM AUTHOR]

In this paper, we revisit the Holling-Tanner model with constant-yield prey harvesting. It is shown that the highest codimension of a nilpotent cusp is 4, and the model can undergo degenerate Bogdanov-Takens bifurcation of codimension 4. Moreover, when the model has a center-type equilibrium, we show that it is a weak focus with order at least 3 and at most 4, and the model can exhibit Hopf bifurcation of codimension 3. Some algebraic methods including resultant elimination and pseudo-division are used to solve the semi-algebraic varieties of normal form coefficients or focal values. Our results indicate that constant-yield prey harvesting can cause not only richer dynamics and bifurcations, but also the coextinction of both populations with some positive initial densities. Finally, numerical simulations, including the coexistence of limit cycle and homoclinic cycle, and three limit cycles, are presented to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

• An approach is proposed for identification of bridge bending stiffness distribution using improved Gaussian peak function. • The improved Gaussian peak function allows for considering a wider range of stiffness variation models and thus is a general model. • The Levenberg-Marquardt (LM) method is proposed for parameter estimation and shows good robustness with different initial parameter values. • Numerical simulation and laboratory experiment are used to verify the effectiveness of the proposed method in identifying bridge bending stiffness distribution. Bridge damage and bending stiffness deterioration can lead to a decrease in the bearing capacity of a bridge, posing significant safety concerns. To ensure the safe operation of bridges, it is crucial to accurately identify bending stiffness deterioration and assess the bridge performance. The bridge influence line (IL), which reflects the deterioration of bending stiffness, was widely used in the assessment of bending stiffness deterioration. Existing IL-based methods mostly assume a uniform reduction in bending stiffness for identification. In reality, the deterioration of bridge bending stiffness is far more complex, which causes difficulty in accurately identifying the bending stiffness distribution using the uniform reduction model. This paper proposes a novel method for identifying bridge stiffness distribution using an improved Gaussian peak function model. The improved model incorporates additional parameters, allowing for considering a wider range of stiffness variation and thus addressing the limitations of traditional models. The parameters of the improved Gaussian peak function model are estimated by minimizing the residual between the predicted deflection influence line (DIL) and the actual DIL using the Levenberg-Marquardt (LM) algorithm. This approach enables the accurate identification of bending stiffness distribution without baseline information. Numerical simulation and laboratory experiment are used to verify the effectiveness of the proposed method in identifying bridge bending stiffness distribution. A comparison between the identified and actual bending stiffness distribution curves under various forms of damage assesses the applicability of the proposed method. [ABSTRACT FROM AUTHOR]

• A novel multi-extracting velocity-synchronous chirplet transform (MEVCT) for efficient and effective time–frequency analysis. • An adaptive chirp angle search method for improving computational efficiency and velocity synchronous basis accuracy. • A higher-order iterative extraction operator for eliminating the non-reassigned time–frequency points. • The improved IF accuracy and anti-noise capability of MEVCT provide ideal TFR for synchronous multi-component signals. • Demonstrated advantages of MEVCT by numerical simulations as well as experimental tests. In many engineering applications, the instantaneous frequency (IF) needs to be identified rapidly and precisely, especially in rotating machinery condition monitoring, where quasi-real-time analysis is a favorable option, and any error in shaft speed (identified from the instantaneous frequency) needs to be reduced to prevent it from accumulating with time. The modern time–frequency analysis (TFA) method provides a way for IF identification; however, sometimes, it still suffers from energy smearing and closely spaced frequency interference. In addition, many TFA methods based on the chirplet transform also present the problem of excessive computation when searching for the optimal parameters. To overcome these limitations, we propose the multi-extracting velocity-synchronous chirplet transform (MEVCT), an enhanced TFA method, in this paper. In the MEVCT, a refined chirp parameter search is developed first to reduce the computational cost while increasing time–frequency accuracy. Then, an iterative high-order IF estimator is constructed to allow the IF to achieve or approach the actual values even in highly nonlinear situations. After that, the obtained IF estimate is substituted into the simultaneous extraction operator to reduce energy dispersion further and eliminate non-reassigned points (NRPs). Simulated and experimental signal analyses demonstrate that MEVCT is able to eliminate NRPs completely. Furthermore, when handling synchronous multicomponent signals, the proposed method has higher IF accuracy with less computational cost and better anti-noise capability. [ABSTRACT FROM AUTHOR]

In this paper, we propose an extended model for the numerical simulation of evaporating droplets within the framework of interface capturing or interface tracking methods. Most existing works make several limiting assumptions that need to be overcome for a more accurate description of the evaporation of droplets. In particular, the variations of several physical variables with local temperature and mass fraction fields must be accounted for in order to perform more realistic computations. While taking into account the variations of some of these physical properties, as viscosity, seems rather obvious, variations of other variables, as density and surface tension, involve additional source terms in the fundamental equations for which a suitable discretization must be developed. The paper presents a numerical strategy to account for such an extended model along with several original test-cases allowing to demonstrate both the accuracy of the proposed numerical schemes and the strong interest in developing such an extended model for the simulation of droplet evaporation. In particular, the impact of thermo-capillary convection will be highlighted on the vapor film thickness between a superheated wall and a static Leidenfrost droplet levitating above this wall. • An extended model is proposed for the direct numerical simulation of evaporating droplets. • A suitable numerical framework is developed to solve this extended model. • Novel benchmarks are proposed to validate the extended model and the proposed numerical approach. • A significant impact of the density variations on the Nusselt number is reported for a moving and evaporating droplet. • A strong effect of the Marangoni convection is also reported for Leidenfrost droplets. [ABSTRACT FROM AUTHOR]

Projection methods are applicable in many fields. It is a natural and practical approach to devise the invariant-preserving schemes for conservative systems. The idea is to project the solution of any underlying numerical scheme onto the manifold determined by the invariant, and this process will be referred to as the projection integrator. Generally, the projection integrator chooses the gradient of invariant as its projection direction and has the same order as the underlying method. In this paper, we propose a different projection direction to construct a new projection integrator whose order is higher than the underlying method. According to this novel direction, we further summarize high-order projection integrators with superconvergence and rigorously prove the truncation error by utilizing the linear integral method as a central tool. Apart from the invariant-preserving property, symmetry is an important geometric property for reversible differential equations. The design and analysis of another high-order projection integrators with symmetry and superconvergence are also presented in this paper. Numerical experiments are provided to verify our theoretical results and illustrate that our proposed projection integrators have superior behaviors in a long time numerical simulation. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stability of traveling waves for a Keller-Segel model with singular chemotactic term and zero chemo-attractant diffusion, where the model and the waves are established to explain the propagation of bacteria pulses along a capillary tube observed in Adler's experiment [1]. By applying the detailed spectral analysis, Evans function method and special transformations and combining with some numerical simulations, in some range of the parameters all the waves are shown to be spectrally stable in some exponentially weighted spaces, and in other range of parameters all the waves are shown to be unstable in any exponentially weighted spaces. The local well-posedness of the classical positive solution to the Cauchy problem of the model is also obtained by applying semigroup argument and some special transformations. [ABSTRACT FROM AUTHOR]

This paper is mainly concerned with the new types of entire solutions which are different from pulsating fronts of Lotka-Volterra competition systems with asymmetric dispersal in spatially periodic habitats. The asymmetry of kernel function leads to a great influence on the profile of pulsating fronts and the sign of wave speeds, which gives rise to the properties of the entire solution more complex and diverse. We first give a relationship between the critical speeds c ⁎ (ξ) and c ⁎ (− ξ) , corresponding to the minimal speeds of two pulsating fronts propagating in the direction of ξ and − ξ , respectively. Then, the exponential behavior of pulsating fronts as they approach their limiting states is obtained. Finally, by considering the interactions of two different pulsating fronts coming from two opposite/same directions and applying the super-/subsolutions techniques as well as the comparison principle, we establish the existence and various qualitative properties of some different types of entire solutions defined for all time and whole space. Moreover, we give some numerical simulations to describe intuitively these obtained entire solutions. [ABSTRACT FROM AUTHOR]

In this paper, we study a model for opinion dynamics where the influence weights of agents evolve in time via an equation which is coupled with the opinions' evolution. We explore the natural question of the large population limit with two approaches: the now classical mean-field limit and the more recent graph limit. After establishing the existence and uniqueness of solutions to the models that we will consider, we provide a rigorous mathematical justification for taking the graph limit in a general context. Then, establishing the key notion of indistinguishability , which is a necessary framework to consider the mean-field limit, we prove the subordination of the mean-field limit to the graph one in that context. This actually provides an alternative proof for the mean-field limit. We conclude by showing some numerical simulations to illustrate our results. [ABSTRACT FROM AUTHOR]

• A novel numerical method was proposed to solve the rocking response of TSRBs. • It has favorable stability, acceptable accuracy, and high computational efficiency. • It does well in impact point identification and rocking pattern judgement. • Free and forced vibration experiments were conducted to verify its accuracy. • Parametric analysis was performed to guide the design of structures like TSRBs. A system of two stacked rigid blocks (TSRBs), such as a statue on a pedestal, is extensively constructed and utilized. However, the numerical simulation of its dynamic response has been a crucial and challenging problem due to the diversity of motion patterns and the nonlinearity in the impacts. Therefore, a high-accuracy and appropriate numerical simulation approach for solving the rocking response of TSRBs was proposed in this paper. First, their rocking patterns were presented, and the judgment diagram of their transitions was defined. Then, the rocking equations of the motion and the formulas of the post-impact angular velocities were introduced. Next, to solve the rocking response of TSRBs, a novel numerical method stemming from the Rosenbrock method and the substep-two-step method was proposed and preliminarily verified. Moreover, free and forced vibration experiments were conducted to verify its accuracy further, and the regularity of the motion was summarized. Finally, parametric analyses of the applications was performed on statue-pedestal systems to investigate the influence of the wall thicknesses and height-to-width ratios of the pedestals on the dynamic response. The results indicate that the proposed method has favorable stability, acceptable accuracy, and high computational efficiency due to its accurate impact point identification and rocking pattern determination. In practice, to reduce the dynamic response of statues, it is preferred to place pedestals with smaller wall thicknesses and larger height-to-width ratios under statues. [ABSTRACT FROM AUTHOR]

During the past years, numerical simulations of Nucleate Boiling have attracted increasing attention. If significant advances have already been performed on the conception of accurate numerical schemes accounting for jump conditions at a non-isothermal interface, further studies are required on the modeling of the heat flux in the vicinity of the contact line. Especially, at very low scale (<500 nm) the formation of a micro-region can be assumed, since the observed apparent contact angle can be higher than the microscopic contact angle and depend on the wall superheat. This variation of the apparent contact angle can be related to a temperature discontinuity between the saturation temperature and the local wall temperature at the contact line inducing a micro-region heat flux and an evaporation mass flow rate. Whereas this micro-region acts at very low scale, existing theoretical models suggest a strong influence of the micro-region heat flux on the global heat flux, and so on the overall bubble growth phenomenon. However, the numerical description of this micro-region in the framework of Direct Numerical Simulation (DNS) of nucleate boiling is a major issue due to the large range of spatial scales involved in the whole process. In the present paper, we propose a coupling methodology between an existing micro-region theoretical model and a larger scale DNS solver for Nucleate Boiling in axisymmetric configurations. Several benchmarks are proposed to show the consistency and the accuracy of the proposed method and to highlight the quantitative effect of the micro-region at the bubble scale. • A coupling between a DNS solver for nucleate boiling and micro-region model is proposed. • A specific boundary condition on the heat flux is proposed in the cells that contain the contact line. • A smoothing technique is proposed to spread the micro-region mass flow rate along the interface. • A novel benchmark based on experimental data is proposed to show the strong effect of the micro-region. • Nucleate boiling simulations in the micro-layer regime with micro-region at the contact line are presented. [ABSTRACT FROM AUTHOR]

The interference pattern of the sound field of a broadband source in a shallow water waveguide is studied theoretically and experimentally in this paper. In the ocean waveguide, the sound source generates the interference pattern of the intensity distribution (interferogram) in the frequency–time domain. The mathematical theory of the interferogram structure is developed. The source interferogram consists of a set of quasi-parallel interference fringes in the frequency–time domain. It is shown that the slope of the interference fringes depends on the distance, velocity, and direction of motion of the sound source. The relationship between the slope angle of the interference fringes in the interferogram and the source parameters is derived in the paper. The two-dimensional Fourier transform (2D-FT) is used to analyze the interferogram. The result of the 2D-FT is called the Fourier hologram (hologram). It is shown that the hologram consists of a few focal spots in a relatively small area. The presence of these focal spots is the result of the interference of acoustic modes with different wavenumbers. The mathematical theory of the hologram structure is developed in this paper. The relationship between the coordinates of the focal spots on the hologram and the source parameters is considered. Consequently, the position of the focal spots can be used to estimate the source parameters (range, velocity, and direction of motion). The theoretical conclusions are verified in the context of computer modeling and the results of the acoustic experiment on the Pacific shelf (Yellow Sea, April, 2004) in the band 180–220 Hz. • Moving source interferogram consists of a set of parallels in frequency–time domain. • Relationship between the fringes slope angle and the source parameters. • Hologram (2D-FT of interferogram) consists of a few focal spots in a small area. • Derivation of relationship between the spots coordinates and the source parameters. • Verification of theoretical results by computer modeling and in real experiments. [ABSTRACT FROM AUTHOR]

The complex dynamics of a frictional contact interface have been the subject of many research investigations. However, a comprehensive model has not been proposed that can be easily solved and considers the effect of all parameters of interest, i.e., the variation in contact pressure, the interaction of normal and tangential direction mechanisms, and contact surface degradation. This paper proposes a generalized slip model based on the original Valanis model with the ability to generate non-symmetric hysteresis loops for frictional contact interface modelling and identification. Various numerical and simulation results are used to show the capability of the generalized Valanis model. The advantages of the model presented in this paper are its simplicity and accuracy. The model offers an explicit solution for the Hysteresis loop and is Lipschitz continuous, making it an ideal choice for real-time analyses, such as in digital twins' applications. The model can represent both point-to-point contacts in a joint interface and the joint interface as a whole. The latter application is considered in this paper. [ABSTRACT FROM AUTHOR]

• A new method to derive rail roughness spectra, independent of vehicle speed. • Model-based transfer function based on stiffness estimates from the P2 resonance. • Improved estimates by accounting for multiple wheels on the same rail. • Application of a comb filter to remove the effect of wheel roughness. • Evaluation via numerical simulation and measurement trials. Railways require frequent inspection to maintain acceptable levels of rail roughness. Accelerometers mounted on in-service railway vehicles potentially offer a cost-effective method of near-continuous roughness monitoring by using a transfer function in the frequency domain to derive rail roughness spectra from measurements of axle-box vibration. This paper addresses two phenomena that currently limit the effectiveness of such a method: the variation in track support stiffness along the track, which is the least known property of the vehicle-track system, resulting in a variable transfer function; and the vibration coupling between wheels, which limits the effectiveness of a transfer function based on a single wheel. A new method is presented that estimates the track stiffness by curve-fitting a transfer function to the peak in the axle-box acceleration spectrum associated with the so-called 'P2' resonance of the wheel-rail system. Wheel-to-wheel coupling is addressed by refining the transfer function to account for multiple wheels running on the same rail. Axle-box acceleration is also affected by wheel roughness, and the use of a comb filter is briefly demonstrated to mitigate this effect. The developments are evaluated by both numerical simulation and measurement trials conducted on London Underground's Victoria line. [ABSTRACT FROM AUTHOR]

The detection and localization of damage in metallic structures using acoustic emission (AE) monitoring and artificial intelligence technology such as deep learning has been widely studied. However, a current challenge of this approach is the difficulty of obtaining sufficient labeled historical AE signals for the training process of deep learning models. This problem can be approached through the implementation of transfer learning. The innovation of this paper lies in the development of a transfer learning approach for AE source localization on a stainless-steel structure when no historical labeled AE signals are available for training. A finite element model is developed to generate numerical AE signals for the training. Unsupervised domain adaptation (UDA) technology is utilized to reduce the distribution difference between the numerical and the realistic AE signals and to derive the localization results of the unlabeled realistic AE signals. The results suggest that the proposed approach is capable of localizing AE signals with high accuracy in the absence of labeled training data. [ABSTRACT FROM AUTHOR]

• Novel method is proposed for eliminating mass loading effect during impact force identification. • Proposed method introduces pseudo-forces to re-express accelerometer mass loading effects. • Proposed method can simultaneously identify impact force and accelerometer masses. • Application of proposed sparse regularization-based method is effective and robust. Identifying impact force from measured structural responses has been extensively studied. Contact sensors such as accelerometers are often applied for recording the structural responses. Masses of the contact sensors would change the structural dynamic properties, especially for lightweight structures. To eliminate the effects of additional masses in force identification, this paper proposes a novel method for reconstructing the impact force. The proposed method is developed from existing sparse regularization-based method. In the process of forward analysis, a key step is to introduce some pseudo-forces for simulation of the additional mass loading effects. The measured responses are regarded as the sum of two components. One is induced by the impact force, and the other one is caused via pseudo-forces. In the process of inverse analysis, impact force identification involving notable sensor mass is treated as a problem of multi-force identification, in which both impact force and pseudo-forces are simultaneously identified. The impact force is identified via sparse regularization which determines more accurate results insensitive to noise. Masses of installed sensors are estimated from the identified pseudo-forces because the pseudo-forces are a translated expression of mass loading effects. Therefore, the effects of additional masses can be eliminated in force identification. Numerical simulations and experimental studies on a cantilever beam are carried out. Cases studies show that the proposed method can be applied for estimating the impact force and additional masses with high accuracy and strong robustness. Some related issues are discussed as well. [ABSTRACT FROM AUTHOR]

The investigation on water entry and exit of rigid bodies is of great significance to prevent the marine equipment from hydrodynamic impact in ocean engineering. It is challenging to simulate this kind of problems in the framework of immersed boundary method because the rigid bodies are not always immersed in the fluid domain. In this paper, we propose a new method for simulating water entry and exit problems, by means of coupling the immersed boundary-lattice Boltzmann method with the single-phase free surface model. The key treatment in present method is the artificially filling interior algorithm, which is firstly developed in this paper to keep complete implementation of the immersed boundary condition. The accuracy, flexibility and effectiveness of the present method are verified through the water entry of a circular cylinder, the water entry of a wedge, and the water exit of a circular cylinder. The present numerical results are in good agreement with reference solutions. Additionally, for the water entry of a bow-flare section with various roll angles, severe numerical oscillations of impact forces appear in the solutions of traditional bounce-back lattice Boltzmann method, while the present method can accurately predict the impact forces with few oscillations. These numerical results well demonstrate that the present method is an effective tool for simulating the water entry and exit of rigid body problems. [ABSTRACT FROM AUTHOR]

• Time-dependent dynamic model of linear guideway with crowning is established. • The idea of coordinate transformation is used to propose the five DOF model. • The possible contact states of each ball are considered due to load distribution. • The ball passage vibration in five directions is predicted. The motion accuracy of linear guideway is adversely affected by ball passage vibration (BPV) when rolling balls within carriage move in a loop. Reduced vibration amplitude can be realized by a carriage with crowning design by now. However, few dynamic models are availability for the BPV analysis when linear guideway is subjected to actual external load in five directions. In this paper, a nonlinear dynamic model is proposed to investigate the periodic micro fluctuation of linear guideway with crowning subjected to load in five directions. The idea of coordinate transformation is adopted for the easier derivations of time-dependent and piecewise restoring force function. The different contact states of each ball are described in detail due to load distribution. The numerical simulation is employed to deal with equation of motion and discuss the effects of ball grouping, external load, preload and carriage speed. Experiment is also conducted for the verification of proposed model. The analytical model developed here is promising to clarify the mechanism of BPV from a dynamic perspective and serve the walking parallelism accuracy monitoring of linear guideway. [ABSTRACT FROM AUTHOR]

Consider a multivariate linear regression model where the sample size is n and the dimensions of the predictors and the responses are p and m , respectively. We know that the limiting distribution of the likelihood ratio test (LRT) in multivariate linear regressions is different in the case of finite and high dimensions. In traditional multivariate analysis, when the dimension parameters (p , m) are fixed, the limiting distribution of the LRT is a χ 2 distribution. However, in the high-dimensional setting, the χ 2 approximation to the LRT may be invalid. In this paper, based on He et al. (2021), we give the moderate deviation principle (MDP) results for the LRT in a high dimensional setting, where the dimension parameters (p , m) are allowed to increase with the sample size n. The performance of the numerical simulation confirms our results. [ABSTRACT FROM AUTHOR]

Estimation and variable selection in partially linear models for massive data has been discussed by several authors. However, there does not seem to exist an established procedure for other semiparametric models, such as the semiparametric varying-coefficient linear model, the single index regression model, the partially linear errors-in-variables model, etc. In this paper, we propose a general procedure for variable selection in high-dimensional general semiparametric models by penalized semiparametric estimating equations. Under some regularity conditions, the oracle property is established, which the number of parameters is allowed to diverge. Furthermore, we also propose a split-and-conquer variable selection procedure for high-dimensional general semiparametric models with massive data. Under some weak regularity conditions, we establish the oracle property of the proposed procedure when the number of subsets does not grow too fast. What is more, the split-and-conquer procedure enjoys the oracle property as the penalized estimator by using all the dataset, and can substantially reduce computing time and computer memory requirements. The performance of the proposed method is illustrated via a real data application and numerical simulations. [ABSTRACT FROM AUTHOR]

High-order gas-kinetic scheme (HGKS) has become a workable tool for the direct numerical simulation (DNS) of turbulence. In this paper, to accelerate the computation, HGKS is implemented with the graphical processing unit (GPU) using the compute unified device architecture (CUDA). Due to the limited available memory size, the computational scale is constrained by single GPU. For large-scale DNS of turbulence, we develop a multi-GPU HGKS simulation using message passing interface (MPI) and CUDA. The benchmark cases for compressible turbulence, including Taylor-Green vortex and turbulent channel flows, are presented to assess the numerical performance of HGKS with Nvidia TITAN RTX and Tesla V100 GPUs. For single-GPU computation, compared with the parallel central processing unit (CPU) code running on the Intel Core i7-9700 with open multi-processing (OpenMP) directives, 7x speedup is achieved by TITAN RTX and 16x speedup is achieved by Tesla V100. For multiple-GPU computation, multiple-GPU accelerated HGKS code scales properly with the increasing number of GPU. The computational time of parallel CPU code running on 1024 Intel Xeon E5-2692 cores with MPI is approximately 3 times longer than that of GPU code using 8 Tesla V100 GPUs with MPI and CUDA. Numerical results confirm the excellent performance of multiple-GPU accelerated HGKS for large-scale DNS of turbulence. Besides reducing memory access pressure, we also exploit single precision floating point arithmetic to accelerate HGKS on GPUs. Reasonably, compared to the computation with FP64 precision, the efficiency is improved and the memory cost is reduced with FP32 precision. Meanwhile, the differences in accuracy for statistical turbulent quantities appear. For turbulent channel flows, difference in long-time statistical turbulent quantities is acceptable between FP32 and FP64 precision solutions. While the obvious discrepancy in instantaneous turbulent quantities can be observed, which shows that FP32 precision is not safe for DNS in compressible turbulence. The choice of precision should be depended on the requirement of accuracy and the available computational resources. • To conduct DNS of turbulence, the HGKS is developed with single GPU+CUDA, and multiple GPUs using MPI+CUDA. • For multiple-GPU computation, multiple-GPU accelerated HGKS code scales properly with No. of GPU. • Efficiency of single Tesla V100 GPU is comparable with the MPI code using 300 CPU cores. • Efficiency of GPU code with 8 Tesla V100 GPUs approximately equals to MPI code with 3000 cores. • Efficiency is improved with FP32 precision, but differences in accuracy appear with the long-time computing. [ABSTRACT FROM AUTHOR]

This paper presents a new semi-active piezoelectric damping strategy for the vibration suppression of integrally bladed disk (blisk). The main novelty is the networking of the synchronized switch damping (SSD). Different from the independently shunted SSD broadly studied in the literature, in our approach the piezoelectric materials distributed to different blade sectors are first connected in few electric networks. The blades in the same network share a single SSD circuit. In this way, additional electrical energy channels are established, and the vibration energy can be thereby dissipated and redistributed globally. In addition, the overall number of the SSD circuits will be drastically reduced, decreasing the complexity of the system. To illustrate and demonstrate such an idea, numerical and experimental studies are conducted. First, We presents the governing equations of a general discrete blisk model with the SSD network and derive a linearization method to solve the steady-state solutions. Next, the optimal topologies of the SSD network for different vibrational modes are summarized through numerical simulation. The proposed network exhibits better performance than other candidates for the mistuned case. Then, through the Mont–Carlo simulation, statistical results prove that the network is also effective for the suppression of the amplitude magnification due to mistuning. Eventually, these findings are validated experimentally through a dummy blisk. • The SSD network can establish additional energy channels among non-adjacent sectors. • The vibration energy of the blisk can then be dissipated and redistributed globally. • The optimal network topology is only determined by the vibration mode of blisk. • The method is effective both for the tuned and mistuned blisks. • Over 20% amplitude drop is achieved even with weakly coupled piezoelectric patches. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new finite element approach to simulate the time-dependent Ginzburg-Landau equations under the temporal gauge, and design an efficient preconditioner for the Newton iteration of the resulting discrete system. The new approach solves the magnetic potential in H (curl) space by the lowest order of the second kind Nédélec element. This approach offers a simple way to deal with the boundary condition, and leads to a stable and reliable performance when dealing with the superconductor with reentrant corners. The comparison in numerical simulations verifies the efficiency of the proposed preconditioner, which can significantly speed up the simulation in large-scale computations. • Energy stability is analyzed for the new approach under the temporal gauge. • The boundedness and coercivity are analyzed to motivate the design of preconditioner. • The preconditioner is efficient and can significantly speed up large-scale simulations. • Extensive numerical experiments are provided. [ABSTRACT FROM AUTHOR]

• Both essential and non-essential genes differ from random sequences the same in length. • The composition of nucleotides within sequences differs in these groups. • The distribution of nucleotides within sequences differs in these groups. • Essential genes constitute a representative group of genes for each bacterium. Proteins encoded by genes are engaged in most of the processes within a cell. Typing a minimal set of genes required for survival is still a challenging task. Essential genes seem to be more conservative and are usually responsible for basic functions, for instance, genetic information flow or energy production. Despite persistent advances in experimental methods, computer predictions may constitute an important part of this investigation. Firstly, they may embrace a huge amount of data and provide some characteristic patterns. Furthermore, they enable scientists to build models for predicting essential genes which are not yet verified experimentally. Some papers indicate interesting dependencies within essential genes sequences using different computer models. In this paper, an author took a three-step analysis for a deeper understanding of the fundamentals of essential and non-essential genes. Beginning from a simple nucleotide composition and finishing at long-range correlations, presents some characteristic patterns that are expected to be developed in future studies. [ABSTRACT FROM AUTHOR]

[Display omitted] • Proposing a high precision method for measuring five dimensional blade tip movement. • The actual position of measuring point can be tracked and the BTT displacement can be converted into the five dimensional displacement in real time. • The way to determine each dimension displacement range that can be measured by a certain measuring point is given. • The method has been verified by the numerical simulation, test-rig, industrial axial fan and engine fan to be effective and highly accurate. As a non-intrusive blade vibration measurement technology, Blade Tip Timing (BTT) has been widely studied and developed in recent years. However, there are still many potential uncertainties in BTT technique, which reduce the correlation of the BTT measurements against the Finite Element (FE) predictions and the Strain Gauge (SG) measurements. One of the main ones is that the BTT sensor only measures the displacement of the blade tip in the direction of rotation. But blade tip movements other than rotation direction including axial, lean, bend, untwist, and sweep will change the position of the measuring point relative to the blade tip. In this paper, a method for measuring the five dimensional blade tip movements is proposed. This method uses BTT data, blade tip profile equation, and the initial measuring point position to track the actual measuring point position relative to the blade tip during blade rotation, so as to determine the blade axial, lean, bend, untwist, and sweep. Simulation results have proven the effectiveness and accuracy of the proposed method. Experiments were carried out on the test rig, industrial axial fan, and engine fan, results show that the method can effectively and accurately measure these types of blade tip movements. The relative error of blade untwist angle measurement is 3.6%. The work in this paper can improve the reliability of BTT measurements, and is of great significance to the comprehensive perception of operation state and accurate evaluation of dynamic stress of rotating blades. [ABSTRACT FROM AUTHOR]

In this paper, a novel gradient index (GRIN) structural lens based on the concept of generalized Luneburg lens (GLL) is proposed. This lens allows for the realization of double foci and localization of energy flow between the two focal spots, thereby achieving ultralong focusing. The double-foci GRIN lens consists of two concentric circular regions with varying thickness defined in a thin plate structure. The two concentric circular regions are designed to realize continuous change of refractive indices with different profiles. Numerical simulations and experimental studies are performed to obtain the maximum displacement amplitude, full length at half maximum (FLHM), and full width at half maximum (FWHM) of the focal region of the lens. The results demonstrate that ultralong subwavelength focusing can be achieved for a broadband frequency range. In addition, our results show that the FLHM and FWHM can be tailored through the design of the focal length of the GLL. This offers a simple and flexible approach of engineering the GLL focusing characteristics and energy distributions for many applications. [ABSTRACT FROM AUTHOR]

• A new complex structure-preserving method is proposed to investigate the dynamic response of the Space Manipulator Systems. • The effects of the parameters of the step-variable cross-section for the manipulator on the stable vibration amplitudes of which are reproduced. • The symmetry breaking of the dynamic model for the Space Manipulator Systems is presented. Decreasing the vibration amplitude of the manipulator in the Space Manipulator Systems (SMS) with a given mass limitation is an effective way to reduce the control costs for the SMS. In this paper, the dynamic response of the SMS modeled by a flexible hub-beam with a step-variable cross-section excited by an external torque is investigated employing a new complex structure-preserving method. The dynamic model of the flexible hub-beam with a step-variable cross-section is deduced firstly. Then, a new structure-preserving method connecting the symplectic precise integration method and the generalized multi-symplectic method is proposed, in which, the time-consuming iteration is avoided and the simulation time is saved. In the numerical simulations, several simple cases for the step-variable cross-section are considered and the stable vibration amplitudes of the flexible beam at the free end are reported. The main contribution of this work is proposing a structure-preserving method for the solving the coupling dynamic problems of the hub-beam system to provide some suggestions on the structure design for the SMS directly. [ABSTRACT FROM AUTHOR]

Liquid steel storage tanks equipped with floating roofs are critical components of industrial facilities because they often store hazardous material. Major earthquakes have caused large vertical displacements of floating roofs. Consequently, roof failure and/or content loss has occurred, which has seriously endangered the surrounding environment and community. Therefore, research interest in this topic remains high, giving rise to experimental campaigns and investigatory studies concerning design and assessment approaches. The present paper aims to validate a simplified model (SM) using both a refined finite element (FE) model and experimental data. This model could later be used in the vulnerability and risk assessment framework based on numerous seismic analyses. The first part of the paper briefly introduces a shaking table test performed on a scaled steel storage tank equipped with a floating roof. This test provided useful experimental data about the vertical displacement histories of floating roofs subject to seismic loading. Subsequently, both a SM and a refined FE model aimed at simulating the shaking table test are introduced and described. Relevant experimental and numerical outcomes are then presented and discussed. Finally, in order to highlight the most relevant parameters involved, we performed a parametric study related to the SM. It is shown that both the refined FE model and the SM were capable of simulating the roof vertical displacement histories observed in the shaking table test. The former model has higher fidelity but appears to be excessively time-consuming, whilst the latter is more suitable for risk assessment purposes. • The seismic response of the Floating Roof (FR) in unanchored storage tanks is analysed. • Results of an experimental test were used to calibrate a 3D FE model of the entire tank. • A simplified non-linear model of the FR was proposed, calibrated and validated. • Both FE and simplified models were able to successfully simulate vertical displacements of the roof. • The limited computational effort renders the simplified model feasible for risk analysis of tanks with FR. [ABSTRACT FROM AUTHOR]

• A new iteration regularization algorithm is proposed. • The proposed iteration regularization algorithm is strictly proved. • The present method is powerful for load identification for stochastic structure. • The newly developed method saves computational cost remarkably compared with MCS. • Numerical simulations validate the obtained theoretical results. In this paper, we propose a novel fast convergence iterative regularization method on the basis of a new iterative regularization operator to solve the dynamic load identification of stochastic structures. Firstly, the validity and convergence of the proposed algorithm is proved by strict mathematical theory and numerical results of engineering example. Secondly, the dynamic load identification of uncertain structures can be transformed into a series of deterministic inverse problems by the matrix perturbation method. Finally, we also assess the statistical characteristics of identified loads using the statistical theory. Particularly, the proposed method successfully solves the dynamic load identification of stochastic structure. Numerical simulations are given to validate the feasibility of the presented method in this paper. [ABSTRACT FROM AUTHOR]

• Model of pounding tuned rotary mass damper considering friction effect is derived. • An optimal range of rolling friction coefficient is studied for a numerical example. • Elastic restitution coefficient and contact stiffness are identified by the impact test. • Rolling friction coefficients are measured by high-speed camera technology. • Rolling friction influence on vibration reduction is conducted by shaking table test. The pounding tuned rotary mass damper (PTRMD) has the characteristics of both tuned damper and impact energy dissipation, which is one of the effective ways to improve the control performance of traditional tuned mass damper (TMD). The rolling friction problem on PTRMD which has not been involved in the previous studies has a great impact on the energy dissipation and vibration reduction performance. Therefore, theoretical and experimental studies on the rolling friction problem in PTRMD are carried out in this paper. The motion model and control equation considering rolling friction energy dissipation of the PTRMD are derived based on Lagrange principle. Afterwards, the influence of the rolling friction on damping performance of PTRMD is analyzed by a numerical example. Additionally, a one-story frame structure equipped with PTRMD under different friction materials is designed and made for the impact performance test, rolling friction coefficient measurement and shaking table test to discuss the friction influence on PTRMD. The numerical and experimental results show that the friction effect between the oscillator and the track in PTRMD can greatly improve its energy dissipation and vibration reduction performance. For all the excitations, the greater the rolling friction coefficient of the track in a certain range, the better the control effect of PTRMD. There is an optimal range of rolling friction coefficient for the damper, but the optimal interval is not a fixed interval for different cases, which is related to the structural form, excitation type and intensity, as well as the parameters of the PTRMD itself. The vibration control performance of PTRMD will decrease when this parameter deviates from the optimum. [ABSTRACT FROM AUTHOR]

Investigating the sound field in and around ducts is an important topic in acoustics, e.g. when simulating musical instruments or the human vocal tract. In this paper a method that is based on the boundary element method in 3D combined with a formulation for infinitely thin elements is presented. The boundary integral equations for these elements are presented, and numerical experiments are used to illustrate the behavior of the thin elements. Using the example of a closed benchmark duct, boundary element solutions for thin elements and surface elements are compared with the analytic solution, and the accuracy of the boundary element method as function of element size is investigated. As already shown for surface elements in the literature, an accumulation of the error along the duct can also be found for thin elements, but in contrast to surface elements this effect is not as big and a damping of the amplitude cannot be seen. In a second experiment, the impedance at the open end of a half open duct is compared with formulas for the radiation impedance of an unflanged tube, and a good agreement is shown. Finally, resonance frequencies of a tube open at both ends are calculated and compared with measured spectra. For sufficiently small element sizes frequencies for lower harmonics agree very well, for higher frequencies a difference of a few Hertz can be observed, which may be explained by the fact that the method does not consider dampening effects near the duct walls. The numerical experiments also suggest, that for duct simulations the usual six to eight elements per wavelength rule is not enough for accurate results. • Thin boundary elements are used to simulate the acoustics of ducts and tubes. • Modeling of the acoustics for thin and thick walled ducts is possible. • Sound radiation from open ducts can be easily modeled. • An accumulation of the error along the duct can be found. • More than 10 elements per wavelength are necessary for accurate results. [ABSTRACT FROM AUTHOR]