We propose a method for designing the bronchial tree where the branching process is stochastic and the diameter (d) of a branch is determined by its flow rate (Q). We use two principles: the continuum equation for flow division and a power-law relationship between d and Q, given by Q approximately dn, where n is the diameter exponent. The value of n has been suggested to be approximately 3. We ...

The analysis of the gas in a single expirate has long been used to estimate the degree of ventilation-perfusion (Va/Q) inequality in the lung. To further validate this estimate, we examined three measures of Va/Q inhomogeneity calculated from a single full exhalation in nine anesthetized mongrel dogs under control conditions and after exposure to aerosolized methacholine. These measurements wer...

We present results from the simulation of a two-coupling spin-1 model with states 0,±1 and nearest neighbour interaction. By a suitable choice of couplings we are able to drastically reduce the effects of corrections to scaling. Our estimates for the critical exponents are ν = 0.6299(3) and η = 0.0359(10). For the universal ratio Q = 〈m〉/〈m〉 we obtain Q = 0.6240(2). The universal ratio of parti...

Our final integration technique deals with the class of functions known as rational functions. Recall from Calculus I that DEFINITION 7.1. A rational function 1 is a function that is the ratio of two polynomials 1 Here 'rational' means 'ratio', as in 'the ratio of two polynomials.' r(x) = p(x) q(x) , where p(x) and q(x) are polynomials. (Remember a polynomial has the form p(x) = a n x n + a n−1...

We propose high precision measurements of the double ratio of polarization transfer coefficients, P ′ x and P ′ z, of the quasielastic He( e, e′ p ) H reaction with respect to the elastic H( e, e′ p ) reaction, at a Q of 0.8 (GeV/c) and 1.3 (GeV/c). Recently, measurements of this double ratio at both Mainz and JLab hinted at the need to include medium modifications of the proton form factors pr...

This paper describes two approaches to modelling lung disease: one based on a multicompartment statistical model with a log normal distribution of ventilation perfusion ratio ( _ V= _ Q) values; and the other on a bifurcating tree which emulates the anatomical structure of the lung. In the statistical model, the distribution becomes bimodal, when the _ V= _ Q values of a randomly selected numbe...

Enumeration of derangements in the symmetric group $\mathfrak{S}_n$ is classical. Extensions enumerative results to hyperoctahedral $B_n$ are combinatorially sound. That even-signed permutation $D_n$ remains largely unexplored. Let $d_n^D(q) = \sum_{\sigma \in \mathcal{D}_n^D} q^{\operatorname{maj}(\sigma)}$ be generating function by their major indices. We study this work properties $d_n^D(q)$...