Non-universal Features Research Articles

Analytic reference interaction site model-mean spherical approximation theory of flexible polymer blends: Effects of spatial and fractal dimensions

Recently developed methods for obtaining exact and approximate analytical solutions of the reference interaction site model-mean spherical approximation (RISM-MSA) integral equations for liquid mixtures composed of long, flexible polymers are applied to study the critical temperature Tc for phase separation of symmetric isotopic binary blends as a function of degree of polymerization N, spatial dimension D, and fractal dimension df of the individual macromolecules. For ideal random walk coils, the theory predicts a nonclassical behavior given by Tc∝N(D−2)/2 in two and three dimensions, and the classical Flory–Huggins mean field Tc∝N law is recovered in four and higher dimensions. For arbitrary interpenetrating polymeric fractals, the theory predicts Tc∝N(D−df)/df for spatial dimensions below 2df and Flory–Huggins behavior for D>2df. These novel scaling laws for isotopic mixtures are a consequence of a consistent treatment of chain connectivity on all length scales, intermolecular excluded volume, and a short range unfavorable interaction between hydrogenated and deuterated polymers. A general, closure-independent physical argument based on a renormalization of the bare chi parameter by relatively long range correlated fluctuations in the blend is proposed which reproduces all the qualitative predictions of the RISM-MSA integral equation theory. Analogies with nonclassical critical fluctuation effects are established. Application of the analytical approach to purely athermal blends is also presented. The magnitude and composition dependence of the effective chi parameter is found to be a sensitive function of both spatial and fractal dimensions, and also local nonuniversal features. The various theoretical predictions are favorably compared with recent small angle neutron scattering measurements on binary polymer alloys.

Mean Field Theory of Normal and Superconducting Heavy Fermion Systems and Oxide Superconductors

Normal heavy fermion systems may be assumed to have infinitely strong short range electron-electron interaction U within the f-orbital. Formulating the Anderson lattice model in terms of slave bosons and working in mean field approximation the very high masses, high specific heats and high susceptibilities of these materials may be simply understood. Allowing U to be large but finite, a generalisation of the theory allows for the possibility of superconductivity. In an isotropic model estimates of Tc give values close to experiment. Gap and Hc take BCS values in the weak coupling limit. In a more realistic model, the gap is found to be anisotropic with zeros and other nonuniversal features developing. The model is also applied to high-Tc oxide superconductors.

Universal features of hydrogen absorption in amorphous transition-metal alloys.

We propose that all ${A}_{1\mathrm{\ensuremath{-}}x}$${B}_{x}$ glasses [where A (B) is a late (early) transition metal] are structurally isomorphic, chemically random alloys which store hydrogen in tetrahedral interstitial sites ${A}_{4\mathrm{\ensuremath{-}}n}$${B}_{n}$ (in decreasing order n=4,3,2,. . . ). The maximum absorbed hydrogen-to-metal atomic ratio within each type of interstitial site is ${1.9(}_{n}^{4}$)${x}^{n}$(1-x${)}^{4\mathrm{\ensuremath{-}}n}$ [${(}_{n}^{4}$)=4!/n!(4-n)!] independent of alloy and temperature. The chemical potential as a function of hydrogen concentration within a single site type n is also independent of composition and temperature. The only nonuniversal feature is the dependence of the typical site energies ${E}_{n}$ of the type-n sites on the A and B atoms, which may, however, be estimated from crystalline hydride properties. This model agrees with our electrochemical measurements of hydrogen in Ni-Zr, Pd-Ti, and Ni-Ti, predicts total H/M ratios for Ni-Zr and Cu-Ti alloys in excellent agreement with literature gas-phase data over a wide range of compositions and thermodynamic conditions, and is consistent with literature H/M data on other alloys at isolated compositions. We show theoretically that infinite near-neighbor hydrogen-hydrogen interactions (blocking) in a glass dominated by fivefold rings of tetrahedral units predicts the observed x dependence of H/M with a prefactor of 1.9--2.1, in excellent agreement with the observed factor of 1.9. This result supports theoretical models of icosahedral ordering in glasses.

Thermodynamic properties of the low-dimensional perfect Bose gas

Abstract The chemical potential, the specific heat and the correlation function are obtained for the perfect Bose gas at a constant volume at low spatial dimensionalities. The Bose-Einstein condensation occurs only at zero temperature. Some nonuniversal features of this condensation are discussed.

On the exponential flattening of current sheets near neutral X-points in two-dimensional ideal MHD flow

It is shown that the flattening of current sheets which has been observed near neutral X-points in numerical simulations of ideal MHD flow in two dimensions can be obtained from an asymptotic expansion of the dynamical equations. This asymptotic expansion suggests that exponential self-similar flattening proceeds forever and that there is no finite time singularity for ideal two-dimensional MHD flows. The equation for the spatial structure of the self-similar solution is reduced, via a hodograph transformation, to a nonlinear wave equation involving interactions with distant parts of the fluid and therefore non-universal features.

Bifurcation sequences and tree interactions in some Hamiltonian systems

The behavior of fixed points on the surface of sections of two differential equations were studied. The first one, a particle in a standing wave field, exhibits universal bifurcation sequences, followed by the restabilization of some fixed points. The second, the undamped driven Duffing oscillator, produces more complex behavior with remerging bifurcations and other nonuniversal features. Some of these features can be ascribed to interactions between separate periodic orbits and bifurcation trees.

The Essential Contributions of Formal Instruction in Adult Second Language Learning

One way of investigating what happens to the language learning capacity at puberty is to examine what the essential contributions of formal instruction are: since formal instruction is so useful for the adult and non-essential for the child language learner, it is probably the case that the main contributions formal instruction makes are in just those areas where the LAD is affected at puberty. A feature-type comparison of language teaching methods known to be successful in helping adults learn language reveals that the universal and presumably crucial ingredients of formal instruction are (1) the isolation of rules and lexical items of the target language, and (2) the possibility of error detection or correction. This hypothesis predicts that any new system that produces significant increases in second language proficiency for adults will contain these two features. It also predicts that adults who seem to be able to learn second languages in informal linguistic environments have some means of approaching rules and lexical items one at a time and are getting feedback. The analysis also points out direction for determining which values of non-universal features might be most useful for adult language learning instruction.