Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations

We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Regarding regularity, we show that the RG map, defined on a suitable space of interactions (= formal Hamiltonians), is always single-valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description of first-order phase transitions. On the pathological side, we make rigorous some arguments of Griffiths, Pearce and Israel, and prove in several cases that the renormalized measure is not a Gibbs measure for any reasonable interaction. This means that the RG map is ill-defined, and that the conventional RG description of first-order phase transitions is not universally valid. For decimation or Kadanoff transformations applied to the Ising model in dimension $d \ge 3$, these pathologies occur in a full neighborhood $\{ \beta > \beta_0 ,\, |h| < \epsilon(\beta) \}$ of the low-temperature part of the first-order phase-transition surface. For block-averaging transformations applied to the Ising model in dimension $d \ge 2$, the pathologies occur at low temperatures for arbitrary magnetic-field strength. Pathologies may also occur in the critical region for Ising models in dimension $d \ge 4$. We discuss in detail the distinction between Gibbsian and non-Gibbsian measures, and give a rather complete catalogue of the known examples. Finally, we discuss the heuristic and numerical evidence on RG pathologies in the light of our rigorous theorems.Comment: 273 pages including 14 figures, Postscript, See also ftp.scri.fsu.edu:hep-lat/papers/9210/9210032.ps.

Stick-release pattern in stretching single condensed polyelectrolyte toroids

Using Langevin dynamics simulations, we study elastic response of single semiflexible polyelectrolytes to an external force pulling on the chain ends, to mimic the stretching of DNA molecules by optical tweezers. The linear chains are condensed by multivalent counterions into toroids. The force-extension curve shows a series of sawtooth-like structure, known as the stick-release patterns in experiments. We demonstrate that these patterns are a consequence of the loop-by-loop unfolding of the toroidal structure. Moreover, the dynamics, how the internal structure of chain varies under tension, is examined. At the first stage of the stretching, the toroidal condensate decreases its size until the loss of the first loop in the toroid and then, oscillates around this size for the rest of the unfolding process. The normal vector of the toroid is pulled toward the pulling-force direction and swings back to its early direction repeatedly when the toroidal chain looses a loop. The results provide new and valuable information concerning the elasticity and the microscopic structure and dynamic pathway of salt-condensed DNA molecules being stretched.Comment: 13 pages, 5 figures, accepted for publication in Macromolecule

Characterization of a K+-induced conformational switch in a human telomeric DNA oligonucleotide using 2-aminopurine fluorescence

Human telomeric DNA consists of tandem repeats of the DNA sequence d(GGGTTA). Oligodeoxynucletotide telomere models such as d[A(GGGTTA)(3)GGG] (Tel22) fold in a cation-dependent manner into quadruplex structures consisting of stacked G-quartets linked by d(TTA) loops. NMR has shown that in Na(+) solutions Tel22 forms a ‘basket’ topology of four antiparallel strands; in contrast, Tel22 in K(+) solutions consists of a mixture of unknown topologies. Our previous studies on the mechanism of folding of Tel22 and similar telomere analogs utilized changes in UV absorption between 270 and 325 nm that report primarily on G-quartet formation and stacking showed that quadruplex formation occurs within milliseconds upon mixing with an appropriate cation. In the current study, we assessed the dynamics and equilibria of folding of specific loops by using Tel22 derivatives in which the dA residues were serially substituted with the fluorescent reporter base, 2-aminopurine (2-AP). Tel22 folding induced by Na(+) or K(+) assessed by changes in 2-AP fluorescence consists of at least three kinetic steps with time constants spanning a range of ms to several hundred seconds. Na(+)-dependent equilibrium titrations of Tel22 folding could be approximated as a cooperative two-state process. In contrast, K(+)-dependent folding curves were biphasic, revealing that different conformational ensembles are present in 1 mM and 30 mM K(+). This conclusion was confirmed by (1)H NMR. Molecular dynamics simulations revealed a K(+) binding pocket in Tel22 located near dA1 that is specific for the so-called hybrid-1 conformation in which strand 1 is in a parallel arrangement. The possible presence of this topologically specific binding site suggests that K(+) may play an allosteric role in regulating telomere conformation and function by modulating quadruplex tertiary structure

Squaring the investment cycle

The present paper replaces the standard behavioral axioms by structural axioms and applies these to the analysis of the accumulation and decumulation of capital. This yields a coherent view of the interrelations of real and nominal saving–investment, of profit–loss, of money–credit, and of internal–external financing. The main result is that asymmetric growth is indispensable for the viability of the market system

An analysis of the indoor air quality and mould growth in a multi-zone building

The effects of poor indoor air quality and mould growth in working environment are major problems in built environment, and there is a need to look for improvement of the health, comfort and productivity of the building occupants. Airborne mould sampling studies were conducted in a reference building located in Rockhampton, Central Queensland, Australia. Both indoor culturable and mould spore levels were observed. It was found through the indoor–outdoor ratios of the species that indoor concentrations are mostly related to the outdoor mould levels. The moulds differ in their relative humidity and temperature requirements to support surface growth. Indoor humidity has a significant effect on occupants comfort, perceived air quality, occupants’ health, building durability, emissions and energy efficiency. Practical hygrothermal simulation models are employed to analyse the combined heat and moisture behaviour within the built environment. A review of the current modelling options available to predict building performance based on energy and mass transport simulation is presented, and then a case study is presented with the assessment of indoor built environment to avoid mould problem