Nonlinear Stability of Shock Fronts for a Relaxation System in Several Space Dimensions

1999 ◽  
pp. 693-702
Author(s):  
Tao Luo ◽  
Zhouping Xin
Keyword(s):  
Nonlinear Stability ◽  
Relaxation System ◽  
Shock Fronts

Nonlinear Stability for Multidimensional Fourth-Order Shock Fronts

2006 ◽  
Vol 181 (2) ◽  
pp. 201-260 ◽  
Author(s):  
Peter Howard ◽  
Changbing Hu
Keyword(s):  
Fourth Order ◽  
Nonlinear Stability ◽  
Shock Fronts

Self-action effects for wave beams containing shock fronts

2004 ◽  
Vol 174 (9) ◽  
pp. 973 ◽  
Author(s):  
Oleg V. Rudenko ◽  
Oleg A. Sapozhnikov
Keyword(s):  
Action Effects ◽  
Shock Fronts

scholarly journals Detection of Magnetohydrodynamic Shocks in the L1551 Outflow

1994 ◽  
Vol 140 ◽  
pp. 222-223
Author(s):  
M. Barsony ◽  
N. Z. Scoville ◽  
C. J. Chandler
Keyword(s):  
Near Infrared ◽  
Resolution Single ◽  
Shock Fronts ◽  
Magnetohydrodynamic Shocks

AbstractWe report the results of CO J=l—+0 mapping of portions of the blue outflow lobe of L1551 with ~ 7” (N-S) × 4” (E-W) resolution, obtained with the 3-element OVRO millimeter array. Comparison of our interferometer mosaic with lower resolution single-dish data shows that we resolve the strongest single-dish emission regions into filamentary structures, such as are characteristic of shock fronts mapped via their near-infrared H2 emission in other outflow sources.

scholarly journals Nonlinear stability of two-layer shallow water flows with a free surface

2020 ◽  
Vol 476 (2236) ◽  
pp. 20190594
Author(s):  
Francisco de Melo Viríssimo ◽  
Paul A. Milewski
Keyword(s):  
Free Surface ◽  
Initial Data ◽  
Nonlinear Stability ◽  
Mathematical Proof ◽  
Passive Layer ◽  
Physical Parameters ◽  
Immiscible Fluid ◽  
Dimensional System ◽  
The Cauchy Problem ◽  
The Difference

The problem of two layers of immiscible fluid, bordered above by an unbounded layer of passive fluid and below by a flat bed, is formulated and discussed. The resulting equations are given by a first-order, four-dimensional system of PDEs of mixed-type. The relevant physical parameters in the problem are presented and used to write the equations in a non-dimensional form. The conservation laws for the problem, which are known to be only six, are explicitly written and discussed in both non-Boussinesq and Boussinesq cases. Both dynamics and nonlinear stability of the Cauchy problem are discussed, with focus on the case where the upper unbounded passive layer has zero density, also called the free surface case. We prove that the stability of a solution depends only on two ‘baroclinic’ parameters (the shear and the difference of layer thickness, the former being the most important one) and give a precise criterion for the system to be well-posed. It is also numerically shown that the system is nonlinearly unstable, as hyperbolic initial data evolves into the elliptic region before the formation of shocks. We also discuss the use of simple waves as a tool to bound solutions and preventing a hyperbolic initial data to become elliptic and use this idea to give a mathematical proof for the nonlinear instability.

Weakly nonlinear stability of Hartmann boundary layers

2003 ◽  
Vol 22 (4) ◽  
pp. 345-353 ◽  
Author(s):  
P. Moresco ◽  
T. Alboussière
Keyword(s):  
Boundary Layers ◽  
Nonlinear Stability ◽  
Weakly Nonlinear

Analysis of Single Buffer Random Polling System With State-Dependent Input Process and Server/Station Breakdowns

2018 ◽  
Vol 9 (1) ◽  
pp. 22-50 ◽  
Author(s):  
Thomas Y.S. Lee
Keyword(s):  
Steady State ◽  
Linear Model ◽  
Repair Process ◽  
Polling System ◽  
Steady State Analysis ◽  
Relaxation System ◽  
Polling Model ◽  
State Dependent ◽  
Non Linear ◽  
State Analysis

Models and analytical techniques are developed to evaluate the performance of two variations of single buffers (conventional and buffer relaxation system) multiple queues system. In the conventional system, each queue can have at most one customer at any time and newly arriving customers find the buffer full are lost. In the buffer relaxation system, the queue being served may have two customers, while each of the other queues may have at most one customer. Thomas Y.S. Lee developed a state-dependent non-linear model of uncertainty for analyzing a random polling system with server breakdown/repair, multi-phase service, correlated input processes, and single buffers. The state-dependent non-linear model of uncertainty introduced in this paper allows us to incorporate correlated arrival processes where the customer arrival rate depends on the location of the server and/or the server's mode of operation into the polling model. The author allows the possibility that the server is unreliable. Specifically, when the server visits a queue, Lee assumes that the system is subject to two types of failures: queue-dependent, and general. General failures are observed upon server arrival at a queue. But there are two possibilities that a queue-dependent breakdown (if occurs) can be observed; (i) is observed immediately when it occurs and (ii) is observed only at the end of the current service. In both cases, a repair process is initiated immediately after the queue-dependent breakdown is observed. The author's model allows the possibility of the server breakdowns/repair process to be non-stationary in the number of breakdowns/repairs to reflect that breakdowns/repairs or customer processing may be progressively easier or harder, or that they follow a more general learning curve. Thomas Y.S. Lee will show that his model encompasses a variety of examples. He was able to perform both transient and steady state analysis. The steady state analysis allows us to compute several performance measures including the average customer waiting time, loss probability, throughput and mean cycle time.

Evolution of nonlinear stationary formations in a quantum plasma at finite temperature

2021 ◽  
Vol 76 (4) ◽  
pp. 329-347
Author(s):  
Swarniv Chandra ◽  
Chinmay Das ◽  
Jit Sarkar
Keyword(s):  
Finite Temperature ◽  
Acoustic Waves ◽  
Quantum Plasma ◽  
Quantum Hydrodynamics ◽  
Stationary Structure ◽  
Gradual Evolution ◽  
Layer Structures ◽  
Model Equations ◽  
Electron Acoustic ◽  
Shock Fronts

Abstract In this paper we have studied the gradual evolution of stationary formations in electron acoustic waves at a finite temperature quantum plasma. We have made use of Quantum hydrodynamics model equations and obtained the KdV-Burgers equation. From here we showed how the amplitude modulated solitons evolve from double layer structures through shock fronts and ultimately converging into solitary structures. We have studied the various parametric influences on such stationary structure and also showed how the gradual variations of these parameter affect the transition from one form to another. The results thus obtained will help in the generation and structure of the structures in their respective domain. Much of the experiments on dense plasma will benefit from the parametric study. Further we have studied amplitude modulation followed by a detailed study on chaos.

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