Improved Continuum Model Research Articles

A Physics-based Model Assisted by Machine-Learning for Sodium-ion Batteries with both Liquid and Solid Electrolytes

In the absence of experimental data of fully developed hierarchical 3D sodium solid-state batteries, we developed an improved continuum model by relying on Machine Learning-assisted parameter fitting to uncover the intrinsic material properties that can be transferred into different battery models. The electrochemical system simulated has sodium metal P2-type Na2/3[Ni1/3Fe1/12Mn7/12]O2 (NNFMO) as the cathode material, paired with two types of electrolytes viz, the organic liquid electrolyte and a solid polymer electrolyte. We implemented a 1D continuum model in COMSOL to suit both liquid and solid electrolytes, then used a Gaussian Process Regressor to fit and evaluate the electrochemical parameters in both battery systems. To enhance the generalizability of our model, the liquid cell and solid cell models share the same OCV input for the cathode materials. The resulting parameters are well aligned with their physical meaning and literature values. The continuum model is then used to understand the effect of increasing the thickness of the cathode and current density by analyzing the cathode utilization, and the overpotentials arising from transport and charge transfer. This 1D model and the parameter set are ready to be used in a 3D battery architecture design.

An improved continuum model for hypersonic thermal nonequilibrium flow in the near-continuum regime

In this work, the rarefied Couette flow of diatomic gases with thermal nonequilibrium effects is investigated by the direct simulation Monte Carlo (DSMC) method, and a macroscopic computational model is developed to consider the local rarefaction effects for diatomic gases in the near-continuum regime. The nonlinear transport properties of the diatomic gases are studied, indicating that effective viscosity and effective translational thermal conductivity in the shear nonequilibrium state are affected by translational nonequilibrium effects, which obey the same laws for both monatomic and diatomic gases. The transport coefficients of internal energy modes are affected by both translational nonequilibrium and internal energy relaxation, therefore, the effective rotational and vibrational thermal conductivities are related to the effective viscosity through a modified Eucken relation that accounts for internal energy relaxation. Conclusively, effective constitutive relations are newly established as a function of the shear nonequilibrium parameter and the modified Eucken factors for thermal nonequilibrium flows, and these are integrated into the macroscopic two-temperature model. Subsequently, it is assessed in the simulation of hypersonic flows over flat plates and cylinders at various Knudsen numbers. The results show that the surface shear stress and heat flux obtained by the proposed model agree well with the DSMC results, indicating significantly improved performance compared to the conventional Navier–Stokes two-temperature model for hypersonic flows in the near-continuum regime.

Bifurcation analysis of an extended macro model considering time delay and anticipation effect

In this paper, a novel macro traffic flow model is proposed integrating time delay and anticipation effect on the headway and velocity, which are indispensable factors in the course of driving. The stability condition of the novel model is derived by linear stability analysis method. The corresponding stability diagrams show that time delay deteriorates the stability of traffic flow, while anticipation effect is conducive to traffic flow stability. The existence and stability of Hopf bifurcations are discussed through bifurcation theory. Numerical results demonstrate that the improved continuum model presented can well describe the local cluster effect, fuel consumption and exhaust emissions. Considering the factor of anticipation and time delay has positive and negative impact on dynamic characteristic of macroscopic flow, respectively. In Hopf bifurcation simulation, partial data from Portable Emissions Measurement System (PeMS) is adopted to calibrate the parameters of the novel model. Meanwhile, the simulation results verify the existence of Hopf bifurcation. The occurrence of bifurcations brings a significant impact on the stability of traffic flow, in which the density wave of traffic flow arises equal-amplitude oscillations.

An improved continuum model for determining the behavior of suspension bridges during construction

Large deformation can be involved in the construction of suspension bridges, and thus the geometry nonlinearity plays an important role in this process. The available continuum model, which is based on the so called “deflection theory”, is proved to be inaccurate in the condition with high geometry nonlinearity. This paper proposes an improved continuum model based on the principle of complementary energy and variational calculus, and the weighted residual approach together with the nonlinear adjustment optimization is proposed to numerically solve the continuum model. The result comparisons among the finite element method, deflection theory and the improved model confirm that the proposed improved model can achieve the higher accuracy than the deflection theory. Also, the following parameter analyses indicate the improved model has considerable stability and applicability to the suspension bridge in a wide range.

Hypersonic Aerodynamics of Blunt Plates in Near-Continuum Regime by Improved Navier–Stokes Model

Hypersonic argon flows over circularly blunt flat plates in near-continuum regime are numerically investigated in this study. The flows are, respectively, simulated using the direct simulation Monte Carlo (DSMC) method, the Navier–Stokes–Fourier (NSF) equations, and the DSMC data-improved Navier–Stokes (DiNS) model that is an improved continuum model with consideration of local shear nonequilibrium effects. The influences of nose radius, angle of attack, and freestream density on the local nonequilibrium characteristics and body surface aerodynamics are investigated in detail. The numerical results show that both the nose radius and the angle of attack present significant influences on the local nonequilibrium effects. Furthermore, it is found that the inaccuracy of the NSF equations for predicting aerodynamics mainly results in the error of the axial force. Compared with the NSF equations, the DiNS model exhibits remarkable improvements for predicting surface aerodynamic properties, especially the axial force, in all the simulated cases.

Modeling Polycrystalline Electrode-electrolyte Interfaces: The Differential Capacitance

We present and analyze a model for polycrystalline electrode surfaces based on an improved continuum model that takes finite ion size and solvation into account. The numerical simulation of finite size facet patterns allows to study two limiting cases: While for facet size diameter we get the typical capacitance of a spatially homogeneous but possible amorphous or liquid surface, in the limit , an ensemble of non-interacting single crystal surfaces is approached. Already for moderate size of the facet diameters, the capacitance is remarkably well approximated by the classical approach of adding the single crystal capacities of the contributing facets weighted by their respective surface fraction. As a consequence, the potential of zero charge is not necessarily attained at a local minimum of capacitance, but might be located at a local capacitance maximum instead. Moreover, the results show that surface roughness can be accurately taken into account by multiplication of the ideally flat polycrystalline surface capacitance with a single factor. In particular, we find that the influence of the actual geometry of the facet pattern in negligible and our theory opens the way to a stochastic description of complex real polycrystal surfaces.

Capturing transient granular rheology with extended fabric tensor relations

We present an improved continuum model for transient processes in granular simple shearing, which predicts the coupled evolution of the effective friction coefficient and fabric tensor. Specifically, the model gives the transient strength associated to the kinematics and the structure of the granular media for the quasi-static regime. The results of the continuum model were compared against molecular dynamic simulations. The comparison for the modulus and the angle of the principal directions of the fabric tensor showed a very good agreement for all the cases analyzed. The new fabric evolution model is capable of capturing the abrupt fall in the fabric modulus and in the effective friction coefficient at the beginning of reversal processes, when the network is destroyed. The model also predicts the right spin direction of the fabric angle, when the force chains move from one steady state to another, during reversal. Improvement in modeling the stress is obtained by relating the friction coefficient to the fabric and the unit shear rate tensors.

An improved anisotropic continuum model considering the driver’s desire for steady driving

With the consideration of the driver’s desire for steady driving, an improved car-following model is developed by incorporating the difference between the steady and history headways into the full velocity difference model. And then by using the connection method of macro–micro variables, an improved anisotropic continuum model is derived from the improved car-following model. The stability analysis of the improved continuum model is discussed by the linear analysis method. Numerical simulations are carried out to investigate the improved anisotropic continuum traffic model, which explores how the driver’s desire for steady driving affected the shock waves, rarefaction waves, and the stabilities of velocity and density. Numerical results demonstrate that the continuum model presented herein can well describe the developments of shock waves and rarefaction waves, and considering the factor of driver’s desire for steady driving have a positive impact on the dynamic characteristic of macroscopic flow.

Nonlinear analysis of an improved continuum model considering mean-field velocity difference

Based on the velocity gradient model, an extended continuum model with consideration of the mean-field velocity difference is proposed in this paper. By using the linear stability theory, the linear stability criterion of the new model is gained, which proved that mean-field velocity difference has significant influence on stability of traffic flow. The KdV–Burgers equation is derived by using non-linear analysis method and the evolution of density wave near the neutral stability line is explored. Numerical simulations are carried out how mean-field velocity difference affect the stability of traffic flow, and energy consumption is also studied for this new macro model. At the same time, complicated traffic phenomena such as local cluster effects, shock waves and rarefaction waves can be reproduced in the new model by numerical simulation. Numerical results are consistent with the theoretical analysis, which indicates that the mean-field velocity difference not only suppresses traffic jam, but also depresses energy consumption.

An extended macro model accounting for acceleration changes with memory and numerical tests

Considering effect of acceleration changes with memory, an improved continuum model of traffic flow is proposed in this paper. By applying the linear stability theory, we derived the new model’s linear stability condition. Through nonlinear analysis, the KdV–Burgers equation is derived to describe the propagating behavior of traffic density wave near the neutral stability line. Numerical simulation is carried out to study the extended traffic flow model, which explores how acceleration changes with memory affected each car’s velocity, density and fuel consumption and exhaust emissions. Numerical results demonstrate that acceleration changes with memory have significant negative effect on dynamic characteristic of traffic flow. Furthermore, research results verify that the effect of acceleration changes with memory will deteriorate the stability of traffic flow and increase cars’ total fuel consumptions and emissions during the whole evolution of small perturbation.

Nonlinear analysis of an improved continuum model considering headway change with memory

Considering the effect of headway changes with memory, an improved continuum model of traffic flow is proposed in this paper. By means of linear stability theory, the new model’s linear stability with the effect of headway changes with memory is obtained. Through nonlinear analysis, the KdV–Burgers equation is derived to describe the propagating behavior of traffic density wave near the neutral stability line. Numerical simulation is carried out to study the improved traffic flow model, which explores how the headway changes with memory affected each car’s velocity, density and energy consumption. Numerical results show that when considering the effects of headway changes with memory, the traffic jams can be suppressed efficiently. Furthermore, research results demonstrate that the effect of headway changes with memory can avoid the disadvantage of historical information, which will improve the stability of traffic flow and minimize car energy consumption.

An improved continuum model for traffic flow considering driver's memory during a period of time and numerical tests

Considering effect of driver's memory during a period of time, an improved continuum model for traffic flow is proposed in this paper. By means of linear stability theory, the improved model's linear stability with driver's memory is obtained, which demonstrates that driver's memory have significant influence stability of traffic flow. The KdV–Burgers equation is deduced to describe the propagating behavior of traffic density wave near the neutral stability line by nonlinear analysis. Numerical results show that driver's memory has negative impact on stability of traffic flow, which will lead to traffic congestion.

Improved Continuum Model for Free Vibration Analysis of Suspension Bridges

AbstractAn improved continuum model of three-span suspension bridges has been developed to study the effects of hanger extensibility on free vertical vibrations. This model can be applied to both h...

Properties of lipid electropores I: Molecular dynamics simulations of stabilized pores by constant charge imbalance

Molecular dynamics (MD) simulations have become a powerful tool to study electroporation (EP) in atomic detail. In the last decade, numerous MD studies have been conducted to model the effect of pulsed electric fields on membranes, providing molecular models of the EP process of lipid bilayers. Here we extend these investigations by modeling for the first time conditions comparable to experiments using long (μs–ms) low intensity (~kV/cm) pulses, by studying the characteristics of pores formed in lipid bilayers maintained at a constant surface tension and subject to constant charge imbalance. This enables the evaluation of structural (size) and electrical (conductance) properties of the pores formed, providing information hardly accessible directly by experiments. Extensive simulations of EP of simple phosphatidylcholine bilayers in 1M NaCl show that hydrophilic pores with stable radii (1–2.5nm) form under transmembrane voltages between 420 and 630mV, allowing for ionic conductance in the range of 6.4–29.5nS. We discuss in particular these findings and characterize both convergence and size effects in the MD simulations. We further extend these studies in a follow-up paper (Rems et al., Bioelectrochemistry, Submitted), by proposing an improved continuum model of pore conductance consistent with the results from the MD simulations.

Pasternak Model Formulation of Elastic Displacements in the Case of a Rigid Circular Foundation

The classical Winkler model has often been used in many engineering fields. However, it has some shortcomings, because the adjacent displacements are discontinuous. In this paper, the Pasternak model — an improved continuum model — is applied to the surface displacement distribution analysis of an elastic layer with a finite depth in an axisymmetric condition. The parameters of the Pasternak model are determined by comparing its surface displacement distributions with those of a finite element analysis. On the basis of the results, the author proposes the non–dimensional characteristic values for the Pasternak model with a simple closed–form formulation of surface displacement distributions in the case of a rigid circular foundation on an elastic layer with a finite depth. The author then discusses the accuracy of the approximate formulation and the limits of its applicability.

CJ 88-17. A study of diffusion wear in the milling of titanium alloys : By Wang Min and Zhang Youzhen (Nanjing Institute of Aeronautics, Nanjing, China). Chinese J. Mech. Engng24, No. 3 (Sept. 1988), pp. 1–9

In this paper, a novel macro traffic flow model is proposed integrating time delay and anticipation effect on the headway and velocity, which are indispensable factors in the course of driving. The stability condition of the novel model is derived by linear stability analysis method. The corresponding stability diagrams show that time delay deteriorates the stability of traffic flow, while anticipation effect is conducive to traffic flow stability. The existence and stability of Hopf bifurcations are discussed through bifurcation theory. Numerical results demonstrate that the improved continuum model presented can well describe the local cluster effect, fuel consumption and exhaust emissions. Considering the factor of anticipation and time delay has positive and negative impact on dynamic characteristic of macroscopic flow, respectively. In Hopf bifurcation simulation, partial data from Portable Emissions Measurement System (PeMS) is adopted to calibrate the parameters of the novel model. Meanwhile, the simulation results verify the existence of Hopf bifurcation. The occurrence of bifurcations brings a significant impact on the stability of traffic flow, in which the density wave of traffic flow arises equal-amplitude oscillations.

Calculations of the moments of the range and damage distributions for low keV light ion bombardment of amorphous solids

The range and deposited energy distributions of low energy 4He ions in Nb have been calculated both by an improved continuum model based on Boltzmann transport theory, and by a discrete model using the computer simulation program MARLOWE. The calculations were performed for infinite targets in both models and equivalent electronic stopping powers were used. Good agreement in the mean values and standard deviations of the range and damage distributions were observed in the energy interval 100 eV to 20 keV.