Narrow Results

We develop a heterogeneous continuum model based upon a car-following model for a nonlane-based system taking lateral separation into account. The criterion for linear stability analysis and traveling wave solution of the homogeneous case is studied. The consideration of the lateral separation not only stabilizes the flow but also shrinks the critical region. For heterogeneous case, the fundamental diagram is examined for two different equilibrium speed-density functions and the effect of lane width is investigated for different compositions of heterogeneous traffic. The theoretical findings agree well with the results of numerical simulation which justifies the applicability of the model to a nonlane-based system.

A modified continuum traffic flow model is established in this paper based on an extended car-following model considering driver’s reaction time and distance. The linear stability of the model and the Korteweg–de Vries (KdV) equation describing the density wave of traffic flow in the metastable region are obtained. In the new model, the relaxation term and the dissipation term exist at the same time, thus the type and stability of equilibrium solution of the model can be analyzed on the phase plane. Based on the equilibrium point, the bifurcation analysis of the model is carried out, and the existence of Hopf bifurcation and saddle-node bifurcation is proved. Numerical simulations show that the model can describe the complex nonlinear dynamic phenomena observed in freeway traffic, such as local cluster effect. Various bifurcations of the model, such as Hopf bifurcation, saddle-node bifurcation, Limit Point bifurcation of cycles, Cusp bifurcation and Bogdanov–Takens bifurcation, are also obtained by numerical simulations, and the traffic behaviors of some bifurcations are studied. The results show that the numerical solution is consistent with the analytical solution. Consequently, some nonlinear traffic phenomena can be analyzed and predicted from the perspective of global stability.

Vehicles equipped with advanced driving assistance systems (ADAS) can acquire information about preceding and following vehicles, which will have an undeniable impact on the phase transition of traffic flow. Therefore, we establish a new heterogeneous continuum model of traffic flow considering the jerk effect mixed with human driving (HD) and ADAS vehicles. The neutral stability condition associated with the permeability of ADAS vehicle is inferred via stability analysis. According to simulation, shock wave occurs, implying that our model can emerge correct wave propagation trend. Moreover, the simulation of density evolution and flow changes also suggests that an increase in ADAS vehicle penetration and jerk effect can enhance traffic system stability and reduce energy consumption.

The ground-state energies of large polaron E_p and bipolaron E_B in three-dimensional lightly doped cuprates are calculated variationally taking into account the short- and long-range electron-phonon interactions and Coulomb correlation in the continuum model and adiabatic approximation. The binding energy of a large bipolaron and its stability region are determined as a function of the ratio of dielectric constants η = ε_∞/ε₀. It is found that the large bipolaron is stable in a broad region of η.

This study proposes a new nonlane-based continuum model derived from a two-sided lateral gap-following theory using the relation between microscopic and macroscopic variables. The model considers the effect of lateral gaps of the leading vehicles available on both sides of the following vehicle in multilane scenario. Linear stability analysis is performed to establish the neutral stability condition for the stable traffic flow. Nonlinear analysis is carried out at neutral stability line to derive the KdV–Berger equation, which describes density wave propagation. For that, one of the traveling wave solutions is also obtained. Numerical simulation results show that the two-sided lateral gap in the model improves the stability of the traffic flow by suppressing the traffic jams even at high-density conditions. The results implies that the proposed model is successful in replicating the properties of actual traffic jams in nonlane-based traffic environment.

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.

Drivers would adjust the speeds in response to not only the external environment, but also the anticipated traffic condition. In this paper, we propose a new continuum model considering the driver’s self-anticipative effect. Such effect is mainly reflected by the difference between the current speed and optimal speed within the anticipation time step. By applying the linear stability theory, the stability condition of the new model is obtained. Through the nonlinear analysis method, the KdV–Burgers equation of the model is provided. The solution describes the evolution of density waves near the neutral stability region. The simulation example verifies that the self-anticipative effect of the driver contributes to suppressing traffic congestion and reducing exhaust emissions effectively. We thus suggest that the traffic flow stability could be improved in an ad hoc manner.

The rapid adoption of sensor technology has upgraded the vehicular communication capacity, which enables the drivers to predict the traffic state (e.g. headway variation tendency (HVT)) based on the current traffic information. Meanwhile, in practice, the drivers would exhibit bounded rationality behavior in that they often perceive and respond to acceleration/deceleration only when the headway variation exceeds a certain threshold. The collective effect may greatly affect the driving behavior and traffic flow performance. In this study, we innovatively model the traffic flow macroscopically considering HVT and bounded rationality effect in the context of continuum model. Based on the linear stability theory, the stability condition of the above model is obtained. The KdV-Burgers equation of the model is derived to describe traffic jam propagation mechanism near the neutral stability line by applying the reductive perturbation method in nonlinear stability analysis. Results show that the HVT and bounded rationality behavior have a great impact on the traffic congestion and energy consumption.

In this paper, we derived a model which describes the swelling dynamics of a gel and study the system in one-dimensional geometry with a free boundary. The governing equations are hyperbolic with a weakly dissipative source. Using a mass-Lagrangian formulation, the free boundary is transformed into a fixed boundary. We prove the existence of long-time C¹-solutions to the transformed fixed boundary problem.

Stability analysis of carbon nanotubes (CNT) under initial bend is conducted using continuum elastic beam models for both single wall nanotube (SWNT) and double wall nanotube (DWNT). A discrete beam model is proposed for simulating the mechanism of kink instability, a local buckling phenomenon, of CNTs. Theoretical analysis of the critical axial load for kink instability is carried out with the elastic beam model. Based on the theoretical analysis, the size effect of CNTs on the critical axial force is studied. By setting the initial bend to be zero, the current model can be used to predict the buckling load of a straight CNT as well.

A non-local elastic shell model is proposed for the first time in this study for considering the small-scale effect in axi-symmetric wave propagation in carbon nanotubes (CNTs). Two coupled radial and longitudinal modes, and one decoupled torsional mode, are derived from the developed non-local shell model. The small-scale effect on wave propagation is numerically studied and discussed. In addition, the cut-off frequency based on the non-local shell model is obtained, which is found to be free of the small-scale effect. It is interesting to note that only one asymptotic phase velocity exists in the CNTs using the non-local shell model, whereas two asymptotic phase velocities can be predicted using the classical or local elastic shell model. It is hoped the research presented herein can be used as a benchmark for future studies on the wave propagation of CNTs with non-local continuum models.

Buckling and postbuckling behaviors of multi-walled carbon nanotubes (MWCNTs) under a compressive force are studied. MWCNTs are modeled by Donnell's shallow shell nonlinear theory with the allowance of van der Waals (vdW) interaction between the walls. It is shown herein that the buckling load decreases while the buckling strain increases as the innermost radius of MWCNT increases. For the postbuckling behavior, the shortening-load curves show an initial steep gradient that gradually level up when the radius of the innermost tube changes from a small value to a large value. However, the deflection-load curves are almost level for various radii of MWCNTs. In addition, the analytical results showed that the shortening-load curves are almost linear but the deflection-load curves are nonlinear and the stability of MWCNTs can be enhanced by adding tubes.

Classical plate theory (CLPT) and first-order shear deformation plate theory (FSDT) of plates are reformulated using the nonlocal elasticity theory. Developed nonlocal plate theories have been applied to study buckling behavior of nanoplates. Nonlocal elasticity theory, unlike traditional elasticity theory introduces a length scale parameter into the formulation to take into account the discrete structure of the material to some extent. Both single-layered and multilayered nanoplates have been included in the analysis. Navier's approach has been used to obtain exact solutions for buckling loads for simply supported boundary conditions. Dependence of the small scale effect on various geometrical and material parameters has been investigated. Present study reveals the presence of significant small scale effect on the buckling response of nanoplates. The theoretical development and the numerical results presented in the present work are expected to promote the use of nonlocal theories for more accurate prediction of stability behavior of nanoplates and nanoshells.

The rail–wheel interaction can induce train and track vibrations and consequently lead to noise impact, passengers’ discomfort, high maintenance cost, etc. Due to the complexity of the rail–wheel interaction and the high cost of field tests, as well as the difficulties in data collection, numerical analyses have been widely resorted to for predicting the train and track vibrations, for which numerous numerical models have been developed. According to track modeling approaches, numerical models can be generally divided into two categories, i.e. beam models and continuum finite element (FE) models. In this paper, these two models are systematically compared and discussed. First, a typical beam model of Wu and Thompson [T. X. Wu and D. Thompson, On the parametric excitation of the wheel/track system, J. Sound Vib.278(4) (2004) 725–747.] is introduced, based on which a modified model is then established. Secondly, a plane continuum FE model with high mesh quality is established, in which the transition mesh generation, contact treatment and element size determination are presented. Numerical tests are conducted to validate the proposed plane FE model. Finally, both the beam and the plane continuum FE models are examined through typical rail–wheel interaction examples, in which the linear response of the track as well as the rail–wheel vibrations under both a single rolling wheel and two rolling wheels are analyzed. The results show that most of the vibration trends obtained from the two models agree well with each other. Nevertheless, it is noteworthy that the continuum FE model has superiorities, especially for analyzing vibrations at higher frequencies. The present study can be of considerable help for designers and engineers in the railway industry to achieve the trade-off between the simulation demands and the computational cost.

In multi-storey buildings, unforeseen foundation rotations can change the building’s behavior. Therefore, these effects should be taken into account in the analysis. In the studies conducted in the literature, the impact of the rotation of the foundation on the building behavior under static loads has been investigated. In this study, an approach is proposed to determine the dynamic behavior of buildings under the effect of foundation rotation, regardless of the type of bearing system. The multi-storey building was modeled as an equivalent flexural-shear beam in the study. In the study, the axial displacements of the columns, which are neglected in the flexural-shear beam model, are also considered, which is different from the literature. The equation of motion representing the dynamic analysis of the equivalent flexural-shear beam was solved with the help of the Differential Transform Method. The period coefficients, effective mass ratio and peak displacement coefficient for five cases were determined and plotted. A code was prepared using Matlab for the analysis with the Differential Transform Method. As a result of the study, the dynamic characteristics obtained depending on the dimensionless building behavior coefficient have been graphed. Using the given graphs, the dynamic characteristics of the buildings under the effect of foundation rotation can be determined quickly and practically. The method presented in this study can be used for Response spectrum analysis of all systems with pure shear beam, pure bending beam and bending-shear beam behavior. In addition, an approach has been proposed to consider $P-\mathrm{\Delta }$ effects within the scope of the study. The results obtained in the study were interpreted, and the impact of rotation on dynamic characteristics was discussed. At the end of the study, for the convenience of the presented method, two examples, one for wall-frame and the other for frame systems, were solved with the proposed method, and the results were compared with the SAP2000 program.

We developed a generic numerical procedure using the finite element method (FEM) for modeling wrinkles on an elastic thin membrane. The geometric characterization of wrinkles formed in an elastic membrane, which is caused by a crawling cell, may help in understanding the forces acting between a cell and its compliant substrate. In this study, the equivalent nodal forces, obtained from the virtual changes in the element internal energy, were differentiated to calculate the stiffness matrix. Micro-wrinkles can be computed as a function of membrane thickness which affects the stiffness matrix. This model may be used for applications in cell mechanobiology.

Understanding the relationship between coronary arterial blood pressure, plaque morphology and composition, and sites of fibrous cap (FC) bursting, has been the focus of many recent studies. Instability of atherosclerotic plaques, defined as the propensity for FCs to burst, has been thought to occur at places where FCs are thin and necrotic core (NC) areas are large and highly compliant. However, here we show quantitatively, using a fiber-reinforced, anisotropic and hyperelastic FE model, that FC thickness and NC size and compliance alone are limited in predicting vulnerable and high-risk plaques. We suggest that plaque instabilities primarily occur at sites of high and concentrated mechanical stresses irrespective of fibrous cap thickness or NC area and compliance. Also, limitations of imaging techniques, such as intravascular ultrasound and optical coherence tomography, for providing input into (FE) models of atherosclerosis are discussed. The proposed model can be used to predict vulnerable plaque sites and rupture risks in patients. The current study also provides a framework for future research in which three-dimensional platform and viscoelastic properties of plaque composition can be considered in time-dependent and fatigue studies.

In this study, we apply a novel numerical technique for modeling the propagation of mechanical wave in the human arteries using the multiscale method. We define a particle region characterized by molecular dynamics (MD) method which is surrounded by a continuous region characterized by a finite element (FE) method. The interface between the two models are defined so as to minimize spurious reflections at the interface. This is a preliminary work for the modeling of the mechanical stability of atherosclerosis plaques using multiscale method. The model offered has extensive application in cell mechanics.

This paper discusses a simple two-species ripple model with avalanching. The effect of the avalanching term is investigated numerically, and is found to be crucial in producing realistic ripple profiles.

Granular surface flows are common in industrial practice and natural systems, however, theoretical description of such flows is at present incomplete. Two prototype systems involving surface flow are compared: heap formation by pouring at a point and rotating cylinders. Continuum models for analysis of these flows are reviewed, and experimental results for quasi-2D systems are presented. Experimental results in both systems are well described by continuum models.