Direct Numerical Calculations of a Neutral Stability Curve for One-Dimensional Detonations

1996 ◽  
Vol 17 (4) ◽  
pp. 814-829 ◽  
Author(s):  
Wei Cai ◽  
Wonho Oh ◽  
Youlan Zhu
Keyword(s):  
Numerical Calculations ◽  
Neutral Stability ◽  
Neutral Stability Curve ◽  
Stability Curve ◽  
One Dimensional

A new lattice hydrodynamic model for bidirectional pedestrian flow with consideration of pedestrians’ honk effect

2020 ◽  
Vol 31 (02) ◽  
pp. 2050031 ◽  
Author(s):  
Cong Zhai ◽  
Weitiao Wu
Keyword(s):  
Stability Analysis ◽  
Hydrodynamic Model ◽  
Mkdv Equation ◽  
Neutral Stability ◽  
Neutral Stability Curve ◽  
Lattice Hydrodynamic Model ◽  
Pedestrian Flow ◽  
Stability Curve ◽  
The Stability ◽  
Honk Effect

Understanding the pedestrian behavior contributes to traffic simulation and facility design/redesign. In practice, the interactions between individual pedestrians can lead to virtual honk effect, such as urging surrounding pedestrians to walk faster in a crowded environment. To better reflect the reality, this paper proposes a new lattice hydrodynamic model for bidirectional pedestrian flow with consideration of pedestrians’ honk effect. To this end, the concept of critical density is introduced to define the occurrence of pedestrians’ honk event. In the linear stability analysis, the stability condition of the new bidirectional pedestrian flow model is given based on the perturbation method, and the neutral stability curve is also obtained. Based on this, it is found that the honk effect has a significant impact on the stability of pedestrian flow. In the nonlinear stability analysis, the modified Korteweg–de Vries (mKdV) equation of the model is obtained based on the reductive perturbation method. By solving the mKdV equation, the kink-antikink soliton wave is obtained to describe the propagation mechanism and rules of pedestrian congestion near the neutral stability curve. The simulation example shows that the pedestrians’ honk effect can mitigate the pedestrians crowding efficiently and improve the stability of the bidirectional pedestrian flow.

Instability of a gravity-modulated fluid layer with surface tension variation

2001 ◽  
Vol 434 ◽  
pp. 243-271 ◽  
Author(s):  
J. RAYMOND LEE SKARDA
Keyword(s):  
Surface Tension ◽  
Fluid Layer ◽  
Modulation Frequency ◽  
Galerkin Approximation ◽  
Neutral Stability ◽  
Modulation Amplitude ◽  
Neutral Stability Curve ◽  
Stability Curve ◽  
The Stability ◽  
Rayleigh Benard

Gravity modulation of an unbounded fluid layer with surface tension variations along its free surface is investigated. The stability of such systems is often characterized in terms of the wavenumber, α and the Marangoni number, Ma. In (α, Ma) parameter space, modulation has a destabilizing effect on the unmodulated neutral stability curve for large Prandtl number, Pr, and small modulation frequency, Ω, while a stabilizing effect is observed for small Pr and large Ω. As Ω → ∞ the modulated neutral stability curves approach the unmodulated neutral stability curve. At certain values of Pr and Ω, multiple minima are observed and the neutral stability curves become highly distorted. Closed regions of subharmonic instability are also observed. In (1/Ω, g1Ra)-space, where g1 is the relative modulation amplitude, and Ra is the Rayleigh number, alternating regions of synchronous and subharmonic instability separated by thin stable regions are observed. However, fundamental differences between the stability boundaries occur when comparing the modulated Marangoni–Bénard and Rayleigh–Bénard problems. Modulation amplitudes at which instability tongues occur are strongly influenced by Pr, while the fundamental instability region is weakly affected by Pr. For large modulation frequency and small amplitude, empirical relations are derived to determine modulation effects. A one-term Galerkin approximation was also used to reduce the modulated Marangoni–Bénard problem to a Mathieu equation, allowing qualitative stability behaviour to be deduced from existing tables or charts, such as Strutt diagrams. In addition, this reduces the parameter dependence of the problem from seven transport parameters to three Mathieu parameters, analogous to parameter reductions of previous modulated Rayleigh–Bénard studies. Simple stability criteria, valid for small parameter values (amplitude and damping coefficients), were obtained from the one-term equations using classical method of averaging results.

Analytical Solution of Congested Traffic Pattern Formation for a Viscous High-Order Model

2011 ◽  
Vol 97-98 ◽  
pp. 546-549
Author(s):  
Xing Li Li ◽  
Tao Song ◽  
Hua Kuang
Keyword(s):  
Flow Model ◽  
Kdv Equation ◽  
Neutral Stability ◽  
Neutral Stability Curve ◽  
Equilibrium Flow ◽  
Order Model ◽  
Stability Curve ◽  
Traffic Pattern ◽  
Congested Traffic ◽  
Real Traffic

In this paper, a new viscous vehicular flow model proposed by Song et al is discussed from the perspective of the capability to reproduce nonlinear traffic behavors observed in real traffic. The linear stability condition for stationary and equilibrium flow is derived. Near the neutral stability curve, the Korteweg–de Vries (KdV) equation describing congested traffic pattern is derived with use of the reduction perturbation method. And the corresponding analytical soliton solution is obtained.

The stability of steady and time-dependent plane Poiseuille flow

1968 ◽  
Vol 34 (1) ◽  
pp. 177-205 ◽  
Author(s):  
Chester E. Grosch ◽  
Harold Salwen
Keyword(s):  
Reynolds Number ◽  
Steady Flow ◽  
Poiseuille Flow ◽  
Time Dependent ◽  
Wave Number ◽  
Neutral Stability ◽  
Neutral Stability Curve ◽  
Plane Poiseuille Flow ◽  
Stability Curve ◽  
Wave Numbers

The linear stability of plane Poiseuille flow has been studied both for the steady flow and also for the case of a pressure gradient that is periodic in time. The disturbance streamfunction is expanded in a complete set of functions that satisfy the boundary conditions. The expansion is truncated after N terms, yielding a set of N linear first-order differential equations for the time dependence of the expansion coefficients.For the steady flow, calculations have been carried out for both symmetric and antisymmetric disturbances over a wide range of Reynolds numbers and disturbance wave-numbers. The neutral stability curve, curves of constant amplification and decay rate, and the eigenfunctions for a number of cases have been calculated. The eigenvalue spectrum has also been examined in some detail. The first N eigenvalues are obtained from the numerical calculations, and an asymptotic formula for the higher eigenvalues has been derived. For those values of the wave-number and Reynolds number for which calculations were carried out by L. H. Thomas, there is excellent agreement in both the eigenvalues and the eigenfunctions with the results of Thomas.For the time-dependent flow, it was found, for small amplitudes of oscillation, that the modulation tended to stabilize the flow. If the flow was not completely stabilized then the growth rate of the disturbance was decreased. For a particular wave-number and Reynolds number there is an optimum amplitude and frequency of oscillation for which the degree of stabilization is a maximum. For a fixed amplitude and frequency of oscillation the wave-number of the disturbance and the Reynolds number has been varied and a neutral stability curve has been calculated. The neutral stability curve for the modulated flow shows a higher critical Reynolds number and a narrower band of unstable wave-numbers than that of the steady flow. The physical mechanism responsible for this stabiIization appears to be an interference between the shear wave generated by the modulation and the disturbance.For large amplitudes, the modulation destabilizes the flow. Growth rates of the modulated flow as much as an order of magnitude greater than that of the steady unmodulated flow have been found.

On the neutral stability curve for shallow conical shells subjected to lateral pressure

2017 ◽  
Vol 23 (5) ◽  
pp. 727-747
Author(s):  
Ciprian D Coman ◽  
Andrew P Bassom
Keyword(s):  
Perturbation Methods ◽  
Lateral Pressure ◽  
Neutral Stability ◽  
Neutral Stability Curve ◽  
Eighth Order ◽  
Conical Shells ◽  
Stability Curve ◽  
Singular Perturbation Methods ◽  
Boundary Eigenvalue ◽  
Theoretical Results

This work presents a detailed asymptotic description of the neutral stability envelope for the linear bifurcations of a shallow conical shell subjected to lateral pressure. The eighth-order boundary-eigenvalue problem investigated originates in the Donnell shallow-shell theory coupled with a linear membrane pre-bifurcation state, and leads to a neutral stability curve that exhibits two distinct growth rates. By using singular perturbation methods we propose accurate approximations for both regimes and explore a number of other novel features of this problem. Our theoretical results are compared with several direct numerical simulations that shed further light on the problem.

On the stability of a shear layer

1959 ◽  
Vol 6 (4) ◽  
pp. 518-522 ◽  
Author(s):  
J. Menkes
Keyword(s):  
Shear Layer ◽  
Transition Layer ◽  
Density Variation ◽  
Neutral Stability ◽  
Neutral Stability Curve ◽  
Horizontal Shear ◽  
Stability Curve ◽  
Wave Numbers ◽  
The Stability ◽  
Small Disturbances

The effects of density variation in the absence of gravity on the stability of a horizontal shear layer between two streams of uniform velocities is investigated. The density is assumed to decrease exponentially with height and the velocity is represented by U(y) = tanh y.The method of small disturbances is employed to obtain the neutral stability curve. It is demonstrated that disturbances with wave-numbers larger than the width of the transition layer are attenuated.Qualitative agreement with experimental evidence is obtained.

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