On the entropy and letter frequencies of ternary square-free words

We enumerate all ternary length-1 square-free words, which are words avoiding squares of words up to length 1, for 1<=24. We analyse the singular behaviour of the corresponding generating functions. This leads to new upper entropy bounds for ternary square-free words. We then consider ternary square-free words with fixed letter densities, thereby proving exponential growth for certain ensembles with various letter densities. We derive consequences for the free energy and entropy of ternary square-free words

Are galaxy distributions scale invariant? A perspective from dynamical systems theory

Unless there is evidence for fractal scaling with a single exponent over distances .1 <= r <= 100 h^-1 Mpc then the widely accepted notion of scale invariance of the correlation integral for .1 <= r <= 10 h^-1 Mpc must be questioned. The attempt to extract a scaling exponent \nu from the correlation integral n(r) by plotting log(n(r)) vs. log(r) is unreliable unless the underlying point set is approximately monofractal. The extraction of a spectrum of generalized dimensions \nu_q from a plot of the correlation integral generating function G_n(q) by a similar procedure is probably an indication that G_n(q) does not scale at all. We explain these assertions after defining the term multifractal, mutually--inconsistent definitions having been confused together in the cosmology literature. Part of this confusion is traced to a misleading speculation made earlier in the dynamical systems theory literature, while other errors follow from confusing together entirely different definitions of ``multifractal'' from two different schools of thought. Most important are serious errors in data analysis that follow from taking for granted a largest term approximation that is inevitably advertised in the literature on both fractals and dynamical systems theory.Comment: 39 pages, Latex with 17 eps-files, using epsf.sty and a4wide.sty (included) <[email protected]

Field-theoretical renormalization group analysis for the scaling exponents of star polymers

We review recent results of the field theoretical renormalization group analysis on the scaling properties of star polymers. We give a brief account of how the numerical values of the exponents governing the scaling of star polymers were obtained as well as provide some examples of the phenomena governed by these exponents. In particular we treat the interaction between star polymers in a good solvent, the Brownian motion near absorbing polymers, and diffusion-controlled reactions involving polymers.Зроблено огляд недавніх результатів аналізу методом теоретикопольової ренормалізаційної групи масштабних (скейлінґових) властивостей зіркових полімерів. Коротко пояснено, як були отримані чисельні значення показників скейлінґу зіркових полімерів. Приведено приклади явищ, які описуються цими показниками. Зокрема, розглядається взаємодія міз зірковими полімерами у доброму розчиннику, бровнівський рух біля полімерного абсорбера, керовані дифузією реакції за участю полімерів

Modelling Enhanced Gas Recovery by CO2_2 Injection in Partially-Depleted Reservoirs.

Carbon Capture and Storage (CCS) is considered as an important solution for CO$_2$ emission reduction, yet, the CO$_2$ capture process is highly costly. Thus, combining Enhanced Gas Recovery (EGR) with CCS could potentially offset the costs via additional production of natural gas. Therefore, the objective of this P.hD. is to build a numerical model to simulate CO$_2$-EGR in partially-depleted gas reservoirs; in particular Centrica Plc's North Morecame gas field. Our numerical model is based on the so-called Method of Lines (MOL) approach. MOL requires selecting a set of persistent Primary Dependent Variables (PDVs) to solve for. In this case, we chose to solve for pressure, temperature and component mass fractions. Additionally, MOL requires recasting of the governing equations in terms of the PDVs, which often requires the evaluation of partial derivative terms of the flow properties with respect to the PDVs. In this work, a method of analytical evaluation of these partial derivative terms is introduced. Furthermore, in a new approach, the mutual solubility correlations for mixtures of CO$_2$-H$_2$O and CH$_4$-H$_2$O, available in the literature, are joined together using straight lines as a ternary diagram, to form a ternary CO$_2$-CH$_4$-H$_2$O equilibrium model; the equilibrium-model's predictions matched well with the available experimental solubility data. 1D and 2D numerical simulations of CO$_2$-EGR were carried out. Overall, the 1D results were found to match very well with an existing analytical solution, predicting accumulation of a CH$_4$ bank ahead of the CO$_2$ plume and accurately locating the associated shock fronts while considering the partial miscibility of both CO$_2$ and CH$_4$ in H$_2$O. Based on the subsequent model predictions, in the North Morecambe field without drilling any additional wells, 0.6 out 2.3 BSCM, i.e., 26\% of the remaining gas can potentially be recovered using CO$_2$-EGR

On combinatorial properties of the Arshon sequence

AbstractWe consider combinatorial and algebraic properties of the language of factors of the infinite sequence on the three-letter alphabet built by S.E. Arshon in 1930s. This sequence never contains two successive equal words, i. e., avoids the number 2. The notion of avoidability is extended from integers to rational numbers. It is shown that the avoidability bound for the considered language is 74. This language is defined by two alternating morphisms; our method allows to study it like a formal language defined by one morphism. We also give a complete description of the syntactic congruence of the considered language