Simple Two-dimensional Model Research Articles

Investigation of Fractal Characteristics of Karman Vortex for NACA0009 Hydrofoil

A Karman vortex is a phenomenon of fluid flow that can cause fluctuation and vibration. As a result, it leads to fatigue damage to structures and induces safety accidents. Therefore, the analysis of the shedding law and strength of the Karman vortex is significant. To further understand the laws of turbulent Karman vortex shedding and strength, this study conducts a numerical vorticity simulation of a Karman vortex at the trailing edge of a hydrofoil based on the two-dimensional simplified model of the NACA0009 hydrofoil under different Reynolds numbers. Combined with image segmentation technology, the fractal characteristics of a turbulent Karman vortex at the trailing edge of a hydrofoil are extracted, the number and total area of vortex cores are calculated, and the fractal dimension of the vortex is obtained. The results show that the fractal dimension can characterize the change in vortex shape and strength under different Reynolds numbers, and that the fractal analysis method is feasible and effective for the shedding analysis of a turbulent Karman vortex.

Hierarchy of anomalies in the simple rose model of water

The density, diffusion, and structural anomalies of the simple two-dimensional model of water were determined by Monte Carlo simulations. The rose model was used which is a very simple model for explaining the origin of water properties. Rose water molecules are modelled as two-dimensional Lennard-Jones disks with rose potentials for orientation dependent pairwise interactions mimicking formations of hydrogen bonds. The model can be seen also as a variance of silica-like models. Two parameters of potential in this work were selected in a way that (1) the model exhibits similar properties to Mercedes-Benz (MB) water model; and (2) that the model has real-like properties of water. Beside the known thermodynamic anomaly for the model we also found diffusion and structural anomalies. The orientational order parameters were calculated and maximum encountered for three and six-fold symmetry. For the MB parametrization, the anomalies occur in hierarchy order, which is a slight variation of the hierarchy order in real water. The diffusion anomaly region is the innermost in the hierarchy while for water it is the density anomaly region. In case of real water parametrization the most inner is the structural anomaly.

Failure Mechanism Research on Bending Fretting Fatigue of 6061-T6 Aluminum Alloy by Experiment and Finite Element Method.

The fatigue failure mechanism of bending fretting for cyclic softening material 6061-T6 aluminum alloy was researched by experiment and finite element method. The influence of cyclic load on bending fretting fatigue was researched and the damage characteristics under different cycles was discussed experimentally though SEM images. In the simulation, a normal load transformation method was employed to obtain a simplified two-dimensional model used for simulating the bending fretting fatigue from a three-dimensional model. An advanced constitutive equation with the Abdel-Ohno rule and isotropic hardening evolution was transplanted into ABAQUS by UMAT subroutine to consider the ratchetting behavior and cyclic softening characteristics. The peak stain distributions under various cyclic loads were discussed. Additionally, the bending fretting fatigue lives and crack initiation locations referring to a critical volume method were estimated using the Smith-Watson-Topper critical plane approach and reasonable results were obtained.

Parametric level-set inverse problems with stochastic background estimation

We study parametric shape reconstruction inverse problems in which the object of interest is embedded in a heterogeneous background medium that is known only approximately. We model the background medium as a Gaussian random field and pose shape reconstruction as a stochastic programming problem in which we seek to minimize the expected value, with respect to the background field, of a stochastic objective function. We develop a computationally efficient algorithm based on the sample average approximation that reduces the effect of uncertainty in the background medium on shape recovery. We demonstrate that by using accelerated stochastic gradient descent, we can apply our method to large-scale problems. The capabilities of our method are demonstrated on a simple two-dimensional model problem and in a more demanding application to a three-dimensional inverse conductivity problem in geophysical imaging.

Coseismic river avulsion on surface rupturing faults: Assessing earthquake-induced flood hazard.

Surface-rupturing earthquakes can produce fault displacements that abruptly alter the established course of rivers. Several notable examples of fault rupture-induced river avulsions (FIRAs) have been documented, yet the factors influencing these phenomena have not been examined in detail. Here, we use a recent case study from New Zealand's 2016 Kaikōura earthquake to model the coseismic avulsion of a major braided river subjected to ~7-m vertical and ~4-m horizontal offset. We demonstrate that the salient characteristics of the avulsion can be reproduced with high accuracy by running a simple two-dimensional hydrodynamic model on synthetic (pre-earthquake) and "real" (post-earthquake) deformed lidar datasets. With adequate hydraulic inputs, deterministic and probabilistic hazard models can be precompiled for fault-river intersections to improve multihazard planning. Flood hazard models that ignore present and potential future fault deformation may underestimate the extent, frequency, and severity of inundation following large earthquakes.

Simple rose model of water in constant electric field.

A simple two-dimensional statistical mechanical water model, called the rose model, was used in this work. We studied how a homogeneous constant electric field affects the properties of water. The rose model is a very simple model that helps explain the anomalous properties of water. Rose water molecules are represented as two-dimensional Lennard-Jones disks with potentials for orientation-dependent pairwise interactions mimicking formations of hydrogen bonds. The original model is modified by addition of charges for interaction with the electric field. We studied what kind of influence the electric field strength has on the model's properties. To determine the structure and thermodynamics of the rose model under the influence of the electric field we used Monte Carlo simulations. Under the influence of a weak electric field the anomalous properties and phase transitions of the water do not change. On the other hand, the strong fields shift the phase transition points as well as the position of the density maximum.

Performance Analysis of rotating pole shoe superconducting machine with dual coils

With the improvement of high temperature superconducting (HTS) materials, HTS machines have shown better competitive advantages in wind power generation and other fields. However, the conventional structure of superconducting machines has led to low reliability of the machines due to the complex structures such as brush and rotating dewar. Based on the analysis of the properties of second-generation high-temperature superconducting strips — YBCO strips, a kind of rotating pole shoe superconducting machine (RPHTSM) with dual HTS coils is proposed in this paper, which avoids the use of brush and rotating dewar used in the conventional HTS machine. The three-dimensional model for magnetic field analysis of the RPHTSM is established and the structure of the RPHTSM is optimized according to the calculation. A two-dimensional simplified model was developed and based on which the output performance of the machine was calculated. By comparing with the conventional HTS machine, it is concluded that the dual-coil RPHTSM has great advantage in reducing the consumption of superconducting strips and the inertia of the rotor.

Effect of boundary dimension on energy absorption behaviour of shear thickening fluids under impact

This study examined the effect of boundary dimension on the energy absorption behaviour of concentrated shear thickening fluids (STFs). STFs were filled into a steel container with various depths and diameters and were impacted by a cylindrical striker. It was found that the energy absorption behaviour showed a response time after which an effective impact-resistant performance was demonstrated. Then, a simplified two-dimensional model was proposed to clarify the characteristics and mechanism of energy absorption behaviour of the impacted STF. For a relatively shallow STF, the energy absorption is mainly achieved by the axial compression of a semi-ellipsoid like jamming region underneath the striker with less radial boundary confinement. Therefore, an increase in depth weakens the energy absorption performance because of the delayed response time for the effective energy absorption. By comparison, the increase in diameter causes the reduction of interaction between the jamming region and the surrounding liquid-STF, slightly degrading the energy absorption performance. For a deep STF, this jamming region reaches to the lateral boundary prior to the effective energy absorption which is primarily achieved by both the compression and bending of the jamming layer supported by the underneath liquid-STF. Thus, an increase in diameter leads to a decrease in the energy absorption performance.

Application of artificial neural networks for modeling of electronic excitation dynamics in 2D lattice: Direct and inverse problems

Machine learning (ML) approaches are attracting wide interest in the chemical physics community since a trained ML system can predict numerical properties of various molecular systems with a small computational cost. In this work, we analyze the applicability of deep, sequential, and fully connected neural networks (NNs) to predict the excitation decay kinetics of a simple two-dimensional lattice model, which can be adapted to describe numerous real-life systems, such as aggregates of photosynthetic molecular complexes. After choosing a suitable loss function for NN training, we have achieved excellent accuracy for a direct problem—predictions of lattice excitation decay kinetics from the model parameter values. For an inverse problem—prediction of the model parameter values from the kinetics—we found that even though the kinetics obtained from estimated values differ from the actual ones, the values themselves are predicted with a reasonable accuracy. Finally, we discuss possibilities for applications of NNs for solving global optimization problems that are related to the need to fit experimental data using similar models.

Brownian Motion Simulation for Estimating Chloride Diffusivity of Cement Paste

Chloride ion diffusion properties are important factors that affect the durability of cementitious materials. Researchers have conducted much exploration in this field, both experimentally and theoretically. Numerical simulation techniques have been greatly improved as theoretical methods and testing techniques have been updated. Researchers have modeled cement particles mostly as circular shapes, simulated the diffusion of chloride ions, and derived chloride ion diffusion coefficients in two-dimensional models. In this paper, a three-dimensional random walk method based on Brownian motion is employed to evaluate the chloride ion diffusivity of cement paste with the use of numerical simulation techniques. Unlike previous simplified two-dimensional or three-dimensional models with restricted walks, this is a true three-dimensional simulation technique that can visually represent the cement hydration process and the diffusion behavior of chloride ions in cement paste. During the simulation, the cement particles were reduced to spheres, which were randomly distributed in a simulation cell with periodic boundary conditions. Brownian particles were then dropped into the cell and permanently captured if their initial position in the gel fell. Otherwise, a sphere tangential to the nearest cement particle was constructed, with the initial position as the center. Then, the Brownian particles randomly jumped to the surface of this sphere. The process was repeated to derive the average arrival time. In addition, the diffusion coefficient of chloride ions was deduced. The effectiveness of the method was also tentatively confirmed by the experimental data.

Control of Electromagnetic Formation Flight of Two Satellites in Low Earth Orbits

Electromagnetic formation flight uses the electromagnetic interaction between satellites to provide maneuver control for formation satellites, with the advantages of no propellant consumption, long life, and high flexibility. However, high-precision control for electromagnetic formation flight is challenging because of the nonlinear and coupling characteristics of the dynamics, optimal assignment of magnetic dipoles, model uncertainties, and the angular momentum management issues caused by the geomagnetic field. This paper studies the 6-DOF control problem of two-satellite electromagnetic formation flight in low-Earth orbit. A new electromagnetic frame is introduced to promote the decoupling of the translation dynamics model and the electromagnetic model. The electromagnetic model can be expressed as a simple two-dimensional model in this electromagnetic frame. The proposed electromagnetic force envelope diagram can intuitively show the relationship between electromagnetic force and magnetic dipoles, providing practical guidance for dipole assignment. The frequency division multiplexing method is designed for angular momentum management considering the effect of the earth’s magnetic field on the electromagnetic satellites, and the active disturbance rejection control method is used to solve the 6-DOF stability problem with external disturbance and model uncertainties. Numerical simulation verifies the effectiveness of the proposed control method and angular momentum management strategy.

Prediction of comprehensive mechanical properties of thermoplastic vulcanizate (TPV) with various composition ratios based on a micromechanical method

In the field of thermoplastic vulcanizate (TPV), experimental methods cannot quantify the relationship between the internal structure and performance of TPV, and are not conducive to the accurate design of TPV structure and performance, which is one of the problems to be solved in this field. In this study, a simple and effective two-dimensional micromechanical model was established based on the real microstructure of TPV by using the micromechanical method and the mechanical properties of TPV with different ethylene propylene diene monomer (EPDM) mass fractions were studied. The results show that with the increase of EPDM content, the maximum stress distribution area of TPV would change, the elastic modulus of TPV would gradually decrease, while the maximum stress of polypropylene (PP) phase would first decrease and then increase and strain corresponding to elastic–plastic change would also increase. The resilience of TPV increases with the increase of EPDM content and decreases with the increase of strain load. When the EPDM content is higher than 70%, the “S” bending deformation would occur at the thinnest part of PP matrix ligament.

Nonlinear two-dimensional analysis of manifold marine inflated membrane structures using vector form intrinsic finite element method

This study aims to investigate the two-dimensional nonlinear deformation of manifold marine inflatable membrane structures. The vector form intrinsic finite element method is adopted and the pseudo-dynamic stiffness damping is introduced to better get a steady-state solution for quasi-static problems. Three typical marine membrane structures, including the partially submerged pontoon, water-filled dam and finger-bag skirt of a hovercraft, are simulated with rod elements, the spatial varied fluid loads and interaction with deformed structures are considered via user-defined functions. Satisfactory deformation results can be obtained with a simplified two-dimensional profile model. Furthermore, a preliminary analysis of the effects of internal and external pressure on the dam is performed, more accurate hovercraft skirt tension can be obtained than traditional analytical method and the hazardous tuck-under behavior of the skirt is simulated. The models and simulations using vector form intrinsic finite element method are beneficial for understanding the deformation behavior and providing a reference for the design of marine membrane structures.

Fast Identification of Micro-Health Parameters for Retired Batteries Based on a Simplified P2D Model by Using Padé Approximation

Better performance consistency of regrouped batteries retired from electric vehicles can guarantee the residual value maximized, which greatly improves the second-use application economy of retired batteries. This paper develops a fast identification approach for micro-health parameters characterizing negative electrode material and electrolyte in LiFePO4 batteries on the basis of a simplified pseudo two-dimensional model by using Padé approximation is developed. First, as the basis for accurately identifying micro-health parameters, the liquid-phase and solid-phase diffusion processes of pseudo two-dimensional model are simplified based on Padé approximation, especially according to enhanced boundary conditions of liquid-phase diffusion. Second, the reduced pseudo two-dimensional model with the lumped parameter is proposed, the target parameters characterizing negative electrode material (εn, Ds,n) and electrolyte (De, Ce) are grouped with other unknown but fixed parameters, which ensures that no matter whether the target parameters can be achieved, the corresponding varying traces is able to be effectively and independently monitored by lumped parameters. Third, the fast identification method for target micro-health parameters is developed based on the sensitivity of target parameters to constant-current charging voltage, which shortens the parameter identification time in comparison to that obtained by other approaches. Finally, the identification accuracy of the lumped micro-health parameters is verified under 1 C constant-current charging condition.

Nonlinear planar and non-planar vibrations of viscoelastic fluid-conveying pipes with external and internal resonances

In this study, nonlinear vibrations of a viscoelastic fluid-conveying pipe under in-plane and out-of-plane transverse excitations are investigated, with emphasis on external and internal resonances. For this purpose, a three-dimensional pipe model that couples the in-plane and out-of-plane vibrations is developed based on the Euler–Bernoulli beam theory together with the Kelvin–Voigt viscoelasticity. The Galerkin method is performed on the nonlinear governing equations, and the resultant discretized equations are solved via the pseudo-arclength continuation method and a direct integration method. The dynamical responses of the pipe are examined in both sub- and super-critical regions and presented by plotting the frequency–amplitude curves, force–amplitude curves, basins of the attraction, time histories, and phase portraits. A comparison between the simplified two-dimensional model and the present three-dimensional model is presented to showcase the possibility of the in-plane and out-of-plane vibrations in regions of primary and principal parametric resonances, highlighting the modal interaction between the in-plane and out-of-plane transverse modes. In the presence of a two-to-one internal resonance, in addition to typical jumping and hysteresis, the two-peak resonance behavior is observed. The numerical results not only show complex nonlinear dynamics of the fluid–structure interaction system, but also provide hints for safe design and novel application of such structures.

The electric field changes the anomalous properties of the Mercedes Benz water model.

The influence of a homogeneous constant electric field on water properties was assessed. We used a simple two-dimensional statistical mechanical model called the Mercedes-Benz (MB) model of water in the study. The MB water molecules are two-dimensional disks with Gaussian arms that mimic the formation of hydrogen bonds. The model is modified with added charges for interaction with the electric field. The influence of the strength of the electric field on the water's properties was studied using Monte Carlo simulations. The structure and thermodynamics of the water were determined as a function of the strength of the electric field. We observed that the properties and phase transitions of the water in the low strength electric field does not change. In contrast, the high strength electric field shifts boiling and melting points as well as the position of the density maxima. After further increasing the strength of the electric field the density anomaly disappears.

Validating a double Gaussian source model for small proton fields in a commercial Monte-Carlo dose calculation engine

PurposeThe primary fluence of a proton pencil beam exiting the accelerator is enveloped by a region of secondaries, commonly called “spray”. Although small in magnitude, this spray may affect dose distributions in pencil beam scanning mode e.g., in the calculation of the small field output, if not modelled properly in a treatment planning system (TPS). The purpose of this study was to dosimetrically benchmark the Monte Carlo (MC) dose engine of the RayStation TPS (v.10A) in small proton fields and systematically compare single Gaussian (SG) and double Gaussian (DG) modeling of initial proton fluence providing a more accurate representation of the nozzle spray. MethodsThe initial proton fluence distribution for SG/DG beam modeling was deduced from two-dimensional measurements in air with a scintillation screen with electronic readout. The DG model was either based on direct fits of the two Gaussians to the measured profiles, or by an iterative optimization procedure, which uses the measured profiles to mimic in-air scan-field factor (SF) measurements. To validate the DG beam models SFs, i.e. relative doses to a 10 × 10 cm2 field, were measured in water for three different initial proton energies (100MeV, 160MeV, 226.7MeV) and square field sizes from 1×1cm2 to 10×10cm2 using a small field ionization chamber (IBA CC01) and an IBA ProteusPlus system (universal nozzle). Furthermore, the dose to the center of spherical target volumes (diameters: 1cm to 10cm) was determined using the same small volume ionization chamber (IC). A comprehensive uncertainty analysis was performed, including estimates of influence factors typical for small field dosimetry deduced from a simple two-dimensional analytical model of the relative fluence distribution. Measurements were compared to the predictions of the RayStation TPS. ResultsSFs deviated by more than 2% from TPS predictions in all fields <4×4cm2 with a maximum deviation of 5.8% for SG modeling. In contrast, deviations were smaller than 2% for all field-sizes and proton energies when using the directly fitted DG model. The optimized DG model performed similarly except for slightly larger deviations in the 1×1cm2 scan-fields. The uncertainty estimates showed a significant impact of pencil beam size variations (±5%) resulting in up to 5.0% standard uncertainty. The point doses within spherical irradiation volumes deviated from calculations by up to 3.3% for the SG model and 2.0% for the DG model. ConclusionProperly representing nozzle spray in RayStation’s MC-based dose engine using a DG beam model was found to reduce the deviation to measurements in small spherical targets to below 2%. A thorough uncertainty analysis shows a similar magnitude for the combined standard uncertainty of such measurements.

Tube wall deformation behaviour of tensile-loaded blind-bolted connections in octagonal hollow section tubes

The structural behaviour of octagonal hollow section (OctHS) tubes under lateral tensile loads applied through blind-bolted T-stubs were experimentally and numerically investigated in this study. Two series of T-stub connections – single-side and double-side bolted T-stub connections, were tested to investigate the influence of the tube geometry and boundary conditions on the failure modes, deformation, and strength. Finite element (FE) models were developed and validated against the test results. Based on the validated FE models, parametric studies were conducted to further assess the influence of width-to-thickness ratios, tube length-to-width ratios and boundary conditions on the tube deformation and strength. Furthermore, the applicability of the tube deformation of 3% of a tube width to be the ultimate state criterion for OctHS tubes was evaluated using tube-face component shell FE models. A simplified two-dimensional analytical model was developed, and the calculation equations were proposed based on either small deformation assumption or large deformation assumption. The comparison of the strengths obtained from the proposed equations, numerical simulations and tests demonstrated that the proposed equations are able to give reasonable predictions on the yield and ultimate strengths of blind-bolted OctHS tube connections under tensile loading.

De Sitter Bubbles from Anti-de Sitter Fluctuations.

Cosmological acceleration is difficult to accommodate in theories of fundamental interactions involving supergravity and superstrings. An alternative is that the acceleration is not universal but happens in a large localized region, which is possible in theories admitting regular black holes with de Sitter-like interiors. We considerably strengthen this scenario by placing it in a global anti-de Sitter background, where the formation of "de Sitter bubbles" will be enhanced by mechanisms analogous to the Bizoń-Rostworowski instability in general relativity. This opens an arena for discussing the production of multiple accelerating universes from anti-de Sitter fluctuations. We demonstrate such collapse enhancement by explicit numerical work in the context of a simple two-dimensional dilaton-gravity model that mimics the spherically symmetric sector of higher-dimensional gravities.

Bayesian optimization of discrete dislocation plasticity of two-dimensional precipitation-hardened crystals

Discovering relationships between materials' microstructures and mechanical properties is a key goal of materials science. Here, we outline a strategy exploiting Bayesian optimization to efficiently search the multidimensional space of microstructures, defined here by the size distribution of precipitates (fixed impurities or inclusions acting as obstacles for dislocation motion) within a simple two-dimensional discrete dislocation dynamics model. The aim is to design a microstructure optimizing a given mechanical property, e.g., maximizing the expected value of shear stress for a given strain. The problem of finding the optimal discretized shape for a distribution involves a norm constraint, and we find that sampling the space of possible solutions should be done in a specific way in order to avoid convergence problems. To this end, we propose a general mathematical approach that can be used to generate trial solutions uniformly at random while enforcing an Euclidean norm constraint. Both equality and inequality constraints are considered. A simple technique can then be used to convert between Euclidean and other Lebesgue $p$-norm (the 1-norm in particular) constrained representations. Considering different dislocation-precipitate interaction potentials, we demonstrate the convergence of the algorithm to the optimal solution and discuss its possible extensions to the more complex and realistic case of three-dimensional dislocation systems where also the optimization of precipitate shapes could be considered.