Stability of Large-Amplitude Viscous Shock Profiles of Hyperbolic-Parabolic Systems

2004 ◽  
Vol 172 (1) ◽  
pp. 93-131 ◽  
Author(s):  
Corrado Mascia ◽  
Kevin Zumbrun
Keyword(s):  
Large Amplitude ◽  
Parabolic Systems ◽  
Shock Profiles

scholarly journals Analysis of large amplitude shock profiles for non-equilibrium radiative hydrodynamics: formation of Zeldovich spikes

Shock Waves ◽  
2012 ◽  
Vol 22 (3) ◽  
pp. 181-197 ◽  
Author(s):  
J.-F. Coulombel ◽  
T. Goudon ◽  
P. Lafitte ◽  
C. Lin
Keyword(s):  
Large Amplitude ◽  
Shock Profiles ◽  
Non Equilibrium

scholarly journals SHARP POINTWISE BOUNDS FOR PERTURBED VISCOUS SHOCK WAVES

2006 ◽  
Vol 03 (02) ◽  
pp. 297-373 ◽  
Author(s):  
PETER HOWARD ◽  
MOHAMMADREZA RAOOFI ◽  
KEVIN ZUMBRUN
Keyword(s):  
Shock Waves ◽  
Large Amplitude ◽  
Small Amplitude ◽  
Artificial Viscosity ◽  
Nonlinear Perturbation ◽  
Sharp Bounds ◽  
Shock Profiles ◽  
Viscous Shock Waves

Refining previous work of Zumbrun, Mascia–Zumbrun, Raoofi, Howard–Zumbrun and Howard–Raoofi, we derive sharp pointwise bounds on behavior of perturbed viscous shock profiles for large-amplitude Lax or overcompressive type shocks and physical viscosity. These extend well-known results of Liu obtained by somewhat different techniques for small-amplitude Lax type shocks and artificial viscosity, completing a program initiated by Zumbrun and Howard. As pointed out by Liu, the key to obtaining sharp bounds is to take account of cancellation associated with the property that the solution decays faster along characteristic than in other directions. Thus, we must here estimate characteristic derivatives for the entire nonlinear perturbation, rather than judicially chosen parts as in the work of Raoofi and Howard–Raoofi, a requirement that greatly complicates the analysis.

On nearly-commensurable periods in the restricted problem of three bodies, with calculations of the long-period variations in the interior 2:1 case

1966 ◽  
Vol 25 ◽  
pp. 197-222 ◽  
Author(s):  
P. J. Message
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Large Amplitude ◽  
Restricted Problem ◽  
Small Amplitude ◽  
Minor Planets ◽  
Long Period ◽  
Numerical Integrations ◽  
Period Variations ◽  
The Mean

An analytical discussion of that case of motion in the restricted problem, in which the mean motions of the infinitesimal, and smaller-massed, bodies about the larger one are nearly in the ratio of two small integers displays the existence of a series of periodic solutions which, for commensurabilities of the typep+ 1:p, includes solutions of Poincaré'sdeuxième sortewhen the commensurability is very close, and of thepremière sortewhen it is less close. A linear treatment of the long-period variations of the elements, valid for motions in which the elements remain close to a particular periodic solution of this type, shows the continuity of near-commensurable motion with other motion, and some of the properties of long-period librations of small amplitude.To extend the investigation to other types of motion near commensurability, numerical integrations of the equations for the long-period variations of the elements were carried out for the 2:1 interior case (of which the planet 108 “Hecuba” is an example) to survey those motions in which the eccentricity takes values less than 0·1. An investigation of the effect of the large amplitude perturbations near commensurability on a distribution of minor planets, which is originally uniform over mean motion, shows a “draining off” effect from the vicinity of exact commensurability of a magnitude large enough to account for the observed gap in the distribution at the 2:1 commensurability.

Information and estimation in image processing

1987 ◽  
Vol 45 ◽  
pp. 14-17
Author(s):  
B. Roy Frieden
Keyword(s):  
Image Processing ◽  
Optical System ◽  
Large Amplitude ◽  
Communication Theory ◽  
Image Data ◽  
Direct Approach ◽  
Ill Posed

Despite the skill and determination of electro-optical system designers, the images acquired using their best designs often suffer from blur and noise. The aim of an “image enhancer” such as myself is to improve these poor images, usually by digital means, such that they better resemble the true, “optical object,” input to the system. This problem is notoriously “ill-posed,” i.e. any direct approach at inversion of the image data suffers strongly from the presence of even a small amount of noise in the data. In fact, the fluctuations engendered in neighboring output values tend to be strongly negative-correlated, so that the output spatially oscillates up and down, with large amplitude, about the true object. What can be done about this situation? As we shall see, various concepts taken from statistical communication theory have proven to be of real use in attacking this problem. We offer below a brief summary of these concepts.

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