Finite speed of propagation and local boundary conditions for wave equations with point interactions

We show that the boundary conditions entering in the definition of the self-adjoint operator describing the Laplacian plus a finite number of point interactions are local if and only if the corresponding wave equation has finite speed of propagation.

     

Proof of gridlock in a polymer model

It has been suggested that some lattice models of polymers, especially ones that incorporate more realistic excluded volume interactions extending to further neighbors, may be subject to gridlock. A model is defined to have the property of gridlock if it cannot melt at any temperature unless a density decrease is allowed. Classical theories of polymer melting are incompatible with the property of gridlock. This paper proves rigorously that a two-dimensional square-lattice model of polymer chains that have nearest-neighbor excluded volume interactions (called the X1S model) has the gridlock property. The proof uses elementary concepts from graph theory. Also, different interpretations of the X1S model are given in terms of real polymers. This leads to a discussion of a number of different classes of melting depending upon whether the intramolecular rotameric energies and the attractive intermolecular energies are antagonistic to or supportive of the melting transition.     

Application of Pitzer's equations on the system HCl+MnCl2+H2O at various temperatures. V.

Activity coefficients of hydrochloric acid in mixed solutions of manganous chloride at twelve ionic strengths, from 0.1 to 5.0 mole-kg^–1, were obtained from emf measurements of cells without liquid junction at five temperatures from 5 to 45°C. The data were interpreted in terms of the simple and convenient Pitzer treatment. Activity coefficients for manganous chloride in the mixtures were also derived using Pitzer's equations. Hydrochloric acid follows Harned's rule fromI=0.1 to 3.0 mole-kg^–1, as concluded by Downes, whereas quadratic terms are warranted fromI=3.5 to 5.0 mole-kg^–1. Contrary to Downes' conclusion, Harned's rule clearly does not hold true for manganous chloride at most ionic strengths.     

Velocity autocorrelation function for the motion of long-chain molecules in the free draining limit

The thermal motion of a long-chain molecule dispersed in a solvent is examined in terms of the velocity autocorrelation, in a reference frame attached to a subunit of the chain.     

On the quasi-chemical theory of solutions

The classical canonical partition function for a one-dimensional, two-component system is examined for the case of nearest-neighbor interactions. The quasi-chemical model of solid solutions is found to be a natural consequence of the definition of the partition function when one replaces the normal configurational energy with a configurational free energy. Consequently, the quasi-chemical theory may be viewed as a consequence of the definition of the partition function and not as merely a physically pleasing model.     

Phase diagrams of Ising models on Husimi trees II. Pair Wand multisite interaction systems

We continue an earlier study of multisite interaction Ising spin models on Husimi trees. In particular, attention is given to systems with both a nearestneighbor pair interaction and three-site interactions. We use our calculations of the phase diagrams of the systems on Husimi trees as approximations of systems with the same interactions but on a regular lattice, e.g., the triangle lattice. Specific models where exact results are available are used as test cases. All of the work involves computation of quantities, such as the magnetization, by iterative processes. Hence we are dealing with a discrete map and for certain values of the interaction strengths we obtain for the magnetization diagram results involving period doubling, chaos, period-three windows, etc., all phenomena of recent interest in connection with dynamical systems and now associated with certain Ising spin systems.     

Quantum chromodynamics corrections to polarised deep-inelastic electron-nucleon scattering

Quantum chromodynamics corrections to orderα _s (the running coupling constant), using the quark-parton approach are calculated for the spin-dependent structure functions in deep-inelastic polarised electron-nucleon scattering. Consequences of these corrections for the Bjorken sum rule and the asymmetry in the case of longitudinally polarised (with respect to the beam) nucleons is discussed which could provide possible tests of quantum chromodynamics. Comparison of our results with the moments of the flavour non-singlet contribution to the structure functions obtained using operator product expansion is also given. An erratum to this article is available at .     

Three-level Doppler-free two- and three-photon resonances

Summary We analyse saturated-absorption and two-photon absorption line shapes in Doppler-broadened three-level systems with nearly degenerate resonance frequencies. The two counterpropagating equal-frequency laser beams of arbitrary intensity irradiating the sample are allowed to couple to both atomic transitions. Various Doppler-free resonances associated to two- and three-photon effects occur. Their saturating behaviour is analysed. A comparison is made with experiments by Woerdmann and Schuurmans and by Himbertet al. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Macromolecular Crowding and the Sizes of Neutral Flexible Polymer Chains: The Role of Colloids Sizes and Concentrations

In the present work, we revisit the effect of macromolecular crowding on the sizes of flexible neutral polymer chains. Motivated by recent experimental measurements on crowding effects on neutral flexible polymers chains, we perform Monte Carlo simulations on a model system consisting of hard spheres (HS) and a neutral flexible polymer chain. We find that, depending on the ratio of the sizes of the colloidal particles to the sizes of the polymer chain, and thus, on the extent of the colloid partitioning among the chain segments and the solution, the flexible polymeric coil may be either continuously compressed, or initially compressed followed by a reswelling at high enough colloid concentration. The chain behavior is thus nonmonotonic, a point which, apart from the work of Khalatur et al., has not so far been stressed in simulations of flexible polymer chains under crowding conditions. A thermodynamic model for the polymer–colloid interactions based on the Gibbs–Duhem equation and on a “Flory‐type” argument is also presented, emphasizing the indirect influence of macromolecular crowding on the monomers chemical potential. We show explicitly that under crowding conditions, the colloids are driven into the most compact coil states. These analytical results are compared with the results of the potential of mean force between the chain center of mass and the colloids obtained from the Monte Carlo simulations, and a reasonable agreement is found. The implications of the aforementioned results are further discussed in the context of biological systems, specially those for which macromolecular crowding is supposed to play the important role of including preferentially other (charged) macromolecules into the colloid‐compressed polymer phase.