Fractal Dimensions of Confined Clusters in Two-Dimensional Directed Percolation

The fractal structure of directed percolation clusters, grown at the percolation threshold inside parabolic-like systems, is studied in two dimensions via Monte Carlo simulations. With a free surface at y=\pm Cx^k and a dynamical exponent z, the surface shape is a relevant perturbation when k<1/z and the fractal dimensions of the anisotropic clusters vary continuously with k. Analytic expressions for these variations are obtained using a blob picture approach.Comment: 6 pages, Plain TeX file, epsf, 3 postscript-figure

About the screening of the charge of a proton migrating in a metal

The amount of screening of a proton in a metal, migrating under the influence of an applied electric field, is calculated using different theoretical formulations. First the lowest order screening expression derived by Sham (1975) is evaluated. In addition 'exact' expressions are evaluated which were derived according to different approaches. For a proton in a metal modeled as a jellium the screening appears to be 15 +/- 10 %, which is neither negligible not reconcilable with the controversial full-screening point of view of Bosvieux and Friedel (1962). In reconsidering the theory of electromigration, a new simplified linear-response expression for the driving force is shown to lead to essentially the same result as found by Sorbello (1985), who has used a rather complicated technique. The expressions allow for a reduction such that only the scattering phase shifts of the migrating impurity are required. Finally it is shown that the starting formula for the driving force of Bosvieux and Friedel leads exactly to the zero-temperature limit of well-established linear response descriptions, by which the sting of the controversy has been removed.Comment: 14 pages, 5 figure

Surface Shape and Local Critical Behaviour in Two-Dimensional Directed Percolation

Two-dimensional directed site percolation is studied in systems directed along the x-axis and limited by a free surface at y=\pm Cx^k. Scaling considerations show that the surface is a relevant perturbation to the local critical behaviour when k<1/z where z=\nu_\parallel/\nu is the dynamical exponent. The tip-to-bulk order parameter correlation function is calculated in the mean-field approximation. The tip percolation probability and the fractal dimensions of critical clusters are obtained through Monte-Carlo simulations. The tip order parameter has a nonuniversal, C-dependent, scaling dimension in the marginal case, k=1/z, and displays a stretched exponential behaviour when the perturbation is relevant. The k-dependence of the fractal dimensions in the relevant case is in agreement with the results of a blob picture approach.Comment: 13 pages, Plain TeX file, epsf, 6 postscript-figures, minor correction

Critical behaviour near multiple junctions and dirty surfaces in the two-dimensional Ising model

We consider m two-dimensional semi-infinite planes of Ising spins joined together through surface spins and study the critical behaviour near to the junction. The m=0 limit of the model - according to the replica trick - corresponds to the semi-infinite Ising model in the presence of a random surface field (RSFI). Using conformal mapping, second-order perturbation expansion around the weakly- and strongly-coupled planes limits and differential renormalization group, we show that the surface critical behaviour of the RSFI model is described by Ising critical exponents with logarithmic corrections to scaling, while at multiple junctions (m>2) the transition is first order. There is a spontaneous junction magnetization at the bulk critical point.Comment: Old paper, for archiving. 6 pages, 1 figure, IOP macro, eps

Tautomeric mutation: A quantum spin modelling

A quantum spin model representing tautomeric mutation is proposed for any DNA molecule. Based on this model, the quantum mechanical calculations for mutational rate and complementarity restoring repair rate in the replication processes are carried out. A possible application to a real biological system is discussed.Comment: 7 pages (no figures

Long-term regulation of proximal tubule acid–base transporter abundance by angiotensin II

In the proximal tubule, angiotensin II (Ang-II) regulates HCO−3 reabsorption and H+ secretion by binding the type 1 Ang-II (AT1) receptor, stimulating Na+/HCO−3 cotransport and Na+/H+ exchange. Studies were carried out to determine if long-term changes in Ang-II receptor occupation alter the abundance of the basolateral Na+/HCO−3 cotransporter (NBC1) or the apical membrane type 3Na+/H+ exchanger (NHE3). In the first set of experiments, rats eating a low-sodium diet were infused with the AT1 blocker, candesartan, or vehicle. In the second, lisinopril-infused rats were infused with either Ang II or vehicle. Transporter abundances were determined in whole kidney homogenates (WKH) and in brush border membrane (BBM) preparations by semiquantitative immunoblotting. Tissue distribution of transporters was assessed by immunocytochemistry. Blockade of the AT1 receptor by candesartan caused decreased abundance of NBC1 in WKH (59±9% of control; P<0.05) and Ang-II infusion increased abundance (130±7% of control; P<0.05). Changes in NBC1 in response to candesartan were confirmed immunohistochemically. Neither candesartan nor Ang II infusion affected the abundance of NHE3 in WKH or cortical homogenates. Candesartan decreased type 2 sodium-phosphate cotransporter abundance in both WKH (52±7% of control; P<0.05) and BBM (32±7% of control; P<0.05). Serum bicarbonate was decreased by candesartan and increased by Ang-II. Candesartan also decreased urinary ammonium excretion (P<0.05). The long-term effects of Ang-II in the proximal tubule may be mediated in part by regulation of NBC1 abundance, modifying bicarbonate reabsorption

Nonequilibrium critical dynamics of the two-dimensional Ising model quenched from a correlated initial state

The universality class, even the order of the transition, of the two-dimensional Ising model depends on the range and the symmetry of the interactions (Onsager model, Baxter-Wu model, Turban model, etc.), but the critical temperature is generally the same due to self-duality. Here we consider a sudden change in the form of the interaction and study the nonequilibrium critical dynamical properties of the nearest-neighbor model. The relaxation of the magnetization and the decay of the autocorrelation function are found to display a power law behavior with characteristic exponents that depend on the universality class of the initial state.Comment: 6 pages, 5 figures, submitted to Phys. Rev.

Quantum first order phase transitions

The scaling theory of critical phenomena has been successfully extended for classical first order transitions even though the correlation length does not diverge in these transitions. In this paper we apply the scaling ideas to quantum first order transitions. The usefulness of this approach is illustrated treating the problems of a superconductor coupled to a gauge field and of a biquadratic Heisenberg chain, at zero temperature. In both cases there is a latent energy associated with their discontinuous quantum transitions. We discuss the effects of disorder and give a general criterion for it's relevance in these transitions.Comment: 6 pages, 2 figures, misprints corrected and a reference added. Version published in PHYSICA

Surface Magnetization of Aperiodic Ising Systems: a Comparative Study of the Bond and Site Problems

We investigate the influence of aperiodic perturbations on the critical behaviour at a second order phase transition. The bond and site problems are compared for layered systems and aperiodic sequences generated through substitution. In the bond problem, the interactions between the layers are distributed according to an aperiodic sequence whereas in the site problem, the layers themselves follow the sequence. A relevance-irrelevance criterion introduced by Luck for the bond problem is extended to discuss the site problem. It involves a wandering exponent for pairs, which can be larger than the one considered before in the bond problem. The surface magnetization of the layered two-dimensional Ising model is obtained, in the extreme anisotropic limit, for the period-doubling and Thue-Morse sequences.Comment: 19 pages, Plain TeX, IOP macros + epsf, 6 postscript figures, minor correction