[en] We give statistical definitions of the length, l, of a loose prime knot tied into a long, fluctuating ring macromolecule. Monte Carlo results for the equilibrium, good solvent regime show that (l) ∼ N^t, where N is the ring length and t ≅ 0.75 is independent of the knot type. In the collapsed regime below the theta temperature, length determinations based on the entropic competition of different knots within the same ring show knot delocalization (t ≅ 1). (letter to the editor)

[en] We consider directed walk models of a homopolymer (in two dimensions) interacting with two immiscible liquids. The polymer is subject to a force, normal to the interface between the two liquid phases. We first consider the case where, in the absence of a force, the polymer is delocalized into the preferred bulk phase, but is pulled into the less favourable bulk phase by the applied force. We examine the temperature dependence of the critical force as a function of the relative quality of the two solvents. When both solvents are poor the polymer can localize at the interface and we also consider the temperature dependence of the critical force needed to pull the polymer out of the interface and into a bulk phase

[en] When a polymer molecule is subjected to a force (such as a tensile force) it responds and this response gives information about the thermodynamics and structural properties of the polymer. In recent years there have been a number of experimental developments, such as atomic force microscopy and optical tweezers, that allow individual polymer molecules to be pulled in various ways. This has resulted in a renewed theoretical interest in how polymers respond to applied forces. This review will focus on some particular aspects of this field. We shall be primarily interested in tensile forces and consider various scenarios, such as pulling an adsorbed polymer from a surface and pulling a polymer from one phase to another. In order to make theoretical progress one needs a model of the polymer and we shall focus on lattice models. Our emphasis will be on exactly solvable models such as Dyck and Motzkin paths, and on rigorous results for self-avoiding walk models and some relatives, though we shall also discuss scaling theories and some selected numerical results. (topical review)

[en] We study cold dilute gases made of bosonic atoms, showing that in the mean-field one-dimensional regime they support stable out-of-equilibrium states. Starting from the 3D Boltzmann–Vlasov equation with contact interaction, we derive an effective 1D Landau–Vlasov equation under the condition of a strong transverse harmonic confinement. We investigate the existence of out-of-equilibrium states, obtaining stability criteria similar to those of classical plasmas. (paper: disordered systems, classical and quantum)

[en] We investigate partially directed walk models of polymers adsorbed at a surface under the influence of an applied force. The force can be applied at various angles (from perpendicular to parallel to the surface) and the critical force-temperature curves are strongly angle-dependent. We observe some interesting differences between the two- and three-dimensional cases associated with the degeneracy of the ground state in three dimensions.

[en] We discuss self-averaging of thermodynamic properties in some random lattice models. In particular, we investigate when self-averaging (in an almost sure sense) of the free energy implies self-averaging of the energy and heat capacity, and we discuss the connection between self-averaging in the almost sure sense, and self-averaging in an L^p sense. Under quite general conditions we show that the average of the finite size heat capacity converges to the second derivative of the limiting quenched average free energy. We consider the application of these ideas to the problem of adsorption of a random copolymer at a surface, and to some related systems. (author)

[en] We analyse directed walk models of random copolymer adsorption and localization. Ideally we would like to solve the quenched problem, but it appears to be intractable even for simple directed models. The annealed approximation is solvable, but is inadequate in the strong interaction regime for the adsorption problem and gives a qualitatively incorrect phase diagram for the localization problem. In this paper, we treat these directed models using an approximation suggested by Morita (1964 J. Math. Phys. 5 1401-5) in which the proportion of each comonomer is fixed. We find that the Morita approximation leads to behaviour that is closer to that of the quenched average model and this is particularly interesting in the localization problem where the phase diagram is (at least qualitatively) very similar to that of the quenched average problem. We also show that the phase boundaries in the Morita approximation are bounds on the locations of the phase boundaries of the quenched model. (author)

[en] Helium atoms are believed to be strongly bound within the interstitial channels in bundles of carbon nanotubes. In a recent paper [F. Ancilotto et al., Phys. Rev. B 70, 165422 (2004)] inhomogeneity in the size distribution of nanotube radii was shown to make a system of ⁴He atoms in such an environment effectively a four-dimensional Bose gas, thus permitting a Bose-Einstein condensation (BEC) of the adsorbed atoms into the minimum energy state. This surprising result was obtained for a model of noninteracting atoms in a continuum distribution of (virtually) infinite interstitial channels. Here we investigate how the singular thermal properties of the ideal system and the occurrence of BEC are affected by a more realistic modeling of a bundle of nanotubes where (i) the number of nanotubes is finite and where (ii) ⁴He atoms adsorbed within the same interstitial channel interact among themselves. Also in this case we observe an anomalous heat capacity close to the ideal condensation temperature, suggesting the persistence of the condensation transition for interacting ⁴He atoms, which might be experimentally observed

[en] We consider several different directed walk models of a homopolymer adsorbing at a surface when the polymer is subject to an elongational force which hinders the adsorption. We use combinatorial methods for analyzing how the critical temperature for adsorption depends on the magnitude of the applied force and show that the crossover exponent φ changes when a force is applied. We discuss the characteristics of the model needed to obtain a re-entrant phase diagram

[en] We use Monte Carlo methods to study knotting in polygons on the simple cubic lattice with a stiffness fugacity. We investigate how the knot probability depends on stiffness and how the relative frequency of trefoils and figure eight knots changes as the stiffness changes. In addition, we examine the effect of stiffness on the writhe of the polygons. (letter to the editor)