Non-linear interaction of elastic waves in rocks

A minimal model of cerebral blood flow and respiratory control was developed to describe hypocapnic and hypercapnic responses. Important non-linear properties such as cerebral blood flow changes with arterial partial pressure of carbon dioxide (PaCO2) and associated time dependent circulatory time delays were included. It was also necessary to vary cerebral metabolic rate as a function of PaCO2. The cerebral blood flow model was added to a previously developed respiratory control model to simulate central and peripheral controller dynamics for humans. Model validation was based on previously collected data. The variable time delay due to brain blood flow changes in hypercapnia was an important determinant of predicted instability due to non-linear interaction in addition to linear loop gain considerations. Peripheral chemoreceptor gains above a critical level, but within normal limits, was necessary to produce instability. Instability was observed in recovery from hypercapnia and hypocapnia. The 20 sec breath-hold test appears to be a simple test of brain blood flow mediated instability in hypercapnia. Brain blood flow was predicted to play an important role with non-linear properties. There is an important interaction predicted by the current model between central and peripheral control mechanisms related to instability in hypercapnia recovery. Post hyperventilation breathing pattern can also reveal instability tied to brain blood flow. Previous data collected in patients with chronic obstructive lung disease was closely fitted with the current model and instability predicted. Brain vascular volume was proposed as a potential cause of instability despite cerebral autoregulation promoting constant brain flow.

Download Full-text

NON-LINEAR INTERACTION BETWEEN ULTRASONIC SHEAR WAVES AND DISLOCATIONS IN ALUMINIUM

Le Journal de Physique Colloques ◽

10.1051/jphyscol:1981558 ◽

1981 ◽

Vol 42 (C5) ◽

pp. C5-387-C5-392 ◽

Cited By ~ 2

Author(s):

Y. T. Wang ◽

W. G.B. Britton ◽

R. W.B. Stephens

Keyword(s):

Shear Waves ◽

Linear Interaction ◽

Non Linear ◽

Ultrasonic Shear

Download Full-text

A stochastic model for two interacting populations

Journal of Applied Probability ◽

10.2307/3211937 ◽

1970 ◽

Vol 7 (3) ◽

pp. 544-564 ◽

Cited By ~ 14

Author(s):

Niels G. Becker

Keyword(s):

Stochastic Model ◽

Linear Models ◽

Death Process ◽

Linear Component ◽

Birth And Death Process ◽

Linear Interaction ◽

Interacting Populations ◽

Non Linear ◽

The Subject ◽

Interaction Component

To explain the growth of interacting populations, non-linear models need to be proposed and it is this non-linearity which proves to be most awkward in attempts at solving the resulting differential equations. A model with a particular non-linear component, initially proposed by Weiss (1965) for the spread of a carrier-borne epidemic, was solved completely by different methods by Dietz (1966) and Downton (1967). Immigration parameters were added to the model of Weiss and the resulting model was made the subject of a paper by Dietz and Downton (1968). It is the aim here to further generalize the model by introducing birth and death parameters so that the result is a linear birth and death process with immigration for each population plus the non-linear interaction component.

Download Full-text