A longstanding problem in biology has been the origin of pervasive quarter-power allometric scaling laws that relate many characteristics of organisms to body mass (M) across the entire spectrum of life from molecules and microbes to ecosystems and m
ammals. In particular, whole-organism metabolic rate, B=aM^b, where a is a taxon-dependent normalisation constant and b is approximately equal to 3/4 for both animals and plants. Recently Darveau et al. (hereafter referred to as DSAH) proposed a multiple-causes model for B as the sum of multiple contributors to metabolism, B_i, which were assumed to scale as M^(b_i). They obtained for average values of b: 0.78 for the basal rate and 0.86 for the maximally active rate. In this note we show that DSAH contains serious technical, theoretical and conceptual errors, including misrepresentations of published data and of our previous work. We also show that, within experimental error, there is no empirical evidence for an increase in b during aerobic activity as suggested by DSAH. Moreover, since DSAH consider only metabolic rates of mammals and make no attempt to explain why metabolic rates for other taxa and many other attributes in diverse organisms also scale with quarter-powers (including most of their input data), their formulation is hardly the unifying principle they claim. These problems were not addressed in commentaries by Weibel and Burness.
The phase diagram of the Gross-Neveu (G-N) model in 2+1 dimensions as a function of chemical potential and temperature has a simple curve separating the broken symmetry and unbroken symmetry phases, with chiral symmetry being restored both at high te
mperature and high density. We study, in leading order in the 1/N expansion, the dynamics of the chiral phase transition for an expanding plasma of quarks in the Gross-Neveu model in 2+1 dimensions assuming boost invariant kinematics. We compare the time evolution of the order parameter (mass of the fermion) for evolutions starting in the unbroken and broken phases. The proper time evolution of the order parameter resembles previous results in the 1+1 dimensional G-N model in the same approximation. The time needed to traverse the transition is insensitive to mu.
Many non-Hermitian but PT-symmetric theories are known to have a real positive spectrum. Since the action is complex for there theories, Monte Carlo methods do not apply. In this paper the first field-theoretic method for numerical simulations of PT-
symmetric Hamiltonians is presented. The method is the complex Langevin equation, which has been used previously to study complex Hamiltonians in statistical physics and in Minkowski space. We compute the equal-time one-point and two-point Greens functions in zero and one dimension, where comparisons to known results can be made. The method should also be applicable in four-dimensional space-time. Our approach may also give insight into how to formulate a probabilistic interpretation of PT-symmetric theories.
