ABSTRACT
We report computations of the short- and long-distance (scaling) contributions to the square-lattice Ising susceptibility. Both computations rely on summation of correlation functions, obtained using nonlinear partial difference equations. In terms of a temperature variable tau, linear in T/Tc-1, the short-distance terms have the form tau(p)(ln/tau/)q with p> or =q2. A high- and low-temperature series of N = 323 terms, generated using an algorithm of complexity O(N6), are analyzed to obtain the scaling part, which when divided by the leading /tau/(-7/4) singularity contains only integer powers of tau. Contributions of distinct irrelevant variables are identified and quantified at leading orders /tau/(9/4) and /tau/(17/4).
ABSTRACT
In anaesthetized cats, in which the cerebrospinal fluid bicarbonate concentration was varied by a ventriculocisternal perfusion technique, the ventilatory response to CO2 during hyperoxia could be satisfactorily described by VE = S(PCSFCO2 -B). Both the slope S and the intercept B were positively and linearly related to the CSF bicarbonate concentration. Assuming that the PCSFCO2 is equal to the PCO2 in extracellular fluid, it can be shown that VE is a linear, but not a unique function of the [H+] at the site of the chemoreceptors; the slope of this relation varies with the bicarbonate concentration at that site, possibly due to chemical complex formation between HCO-3 and Ca2+ or Mg2+. Changes in the B-value were related to the location of the central chemoreceptors with the models of Pappenheimer and Berndt aand their coworkers. It was found that changes in the CSF bicarbonate concentration are reflected for 60 per cent at the site of the central chemoreceptors, and that this was independent of the cerebral perfusion. Using Berndt's model a distance between CSF and central chemoreceptors of approximately 100 micron was found; this calculated distance is relatively insensitive to relationship (logarithmic or not) between ventilation and H+ concentration and to changes in cerebral perfusion, owing to the approximate nature of the diffusion model.
