Theoretical calculation of the conformation and crystal structure of poly-L-hydroxyproline

The intra-and intermolecular forces determining the conformation of poly-L-hydroxyproline have been examined. The vacuum conformation of the isolated molecule has the left-hand trans configuration of poly-L-proline II with Ψ = 295°. A second less favorable low-energy form is the right-hand superhelix, also previously described for polyproline. No cis conformation was found to be feasible. Introduction of intermolecular interaction functions shows that the conformation in the solid state is strongly modified to accommodate such interactions. The rotation angle corresponding to the minimum energy in the solid is found to be Ψ = 343°. The crystal structure predicted from these calculations is a hexagonal lattice with a₀ = 12.5 Å and c₀ = 9.1 Å with space group P3₂. Three helices are required in the fundamental structural unit. These results are in excellent agreement with X-ray evidence.     

Molecular conformation and liquid structure of 2-propanol through neutron diffraction

The neutron diffraction data analysis of deuterated liquid 2-propanol at room temperature to define its molecular conformation is presented. 2-Propanol being a large molecule with twelve atomic sites, the conformation analysis is tricky and an improved method of data analysis is given. The intermolecular structural correlations, i.e., hydrogen-bonded liquid structure, can be modelled accurately to extract the nature of the average hydrogen-bonded molecular association in liquid state at room temperature. Like other alcohols these are mostly hexamer ring chain (HRC) clusters. The cluster analysis of recent X-ray data available in the literature also support the same liquid structure.     

Electronic structure and conformation of ethene when adsorbed on transition and noble metals

Using the geometry of the ethene molecule when adsorbed on transition metal surfaces, as predicted by Felter and Weinberg [Surface Sci. 103 (1981) 265], but omitting molecular twist, a tight-binding model has been employed to predict the effect of chemisorption on the σ-levels of the molecule. The energy of the σ_CC-level changed appreciably from its free space value, and based on these calculations we have reinterpreted the experimental data and have revised the prediction of the geometry. The qualitative nature of the distortions, namely an increase in the C-C bond length and reduction of the C-C-H and H-C-H angles, remains intact. Secondly, the interaction of the π-orbitals of ethene with the d-band states of the metal surface has been studied, using a model of localized bonding between the metal and the molecule, within the Hartree-Fock approximation using an Anderson Hamiltonian. The conclusions are that as the strength of the metal-molecule interaction increases, the π-bond order decreases. Using experimental values of the chemisorption energy the model predicts that, for Ni and Cu, electrons are transferred from the molecule to the metal. This is in accord with the observed decrease in the work function for both these systems.     

On the structure and conformation of polymer chains in latex particles. I. Small-angle neutron scattering characterization of polystyrene latexes of small diameter

Polystyrene latexes with 40-60 nm diameter and molecular weights ranging from 6 × 10⁴ to 6 × 10⁶ g/mol were synthesized by a two-step equilibrium swelling method, with deuterated polymer forming either the first or second step. Below about 1 × 10⁶ g/mol, small-angle neutron scattering gave zero-angle scattering intensities much higher than expected on the basis of gel permeation chromatography molecular weights. Several models were examined, the leading model based on a core-shell latex structure. The development of such structure was found to depend on the ratio of the radius of gyration of the polymer chain to that of the diameter of the latex particle, reaching a maximum in the range where the polymer chain dimensions are about half that of the latex particle. For the highest molecular weights, normal scattering intensities were found. These results lead to the finding that the polymer chains were compressed in the latex particles with constraining in the range of one to four, for this molecular weight range.     

On the structure and accuracy of programmed burn

Accurate computation of the evolution of a (typically curved) detonation front in a complex geometry, and of the state behind it, is a practical problem in the design of devices that use high-energy explosives. Direct numerical simulations are infeasible: accuracy demands high resolution of the smallest scale (the reaction zone), which is typically several orders of magnitude smaller than the device scale. Programmed burn is an engineering alternative that has been shown to produce acceptable results at a fraction of the cost. The underlying algorithm prescribes the trajectory of the detonation front a priori and replaces the actual reaction zone by a mock up that is a few computational cells thick and in which the reaction rate is taken to be a constant. The state of the explosive at the end of the reaction zone is thereby computed at a relatively modest cost, and the bulk of the computational effort is reserved for the region behind the reaction zone wherein the products of detonation perform useful work. The reasons for the remarkable fidelity to which the physical situation is captured by the programmed burn are not well-understood. This investigation, aimed at achieving such an understanding, considers a model problem for a steady, curved detonation propagating down a rate stick. It examines the pseudo-reaction-zone structure of the programmed burn, studies the sensitivity of the state of the reaction products to the choice of the reaction zone length, and compares the results to those for the actual, physical reaction zone. Conclusions are drawn as to the causes behind the success of the programmed-burn algorithm. The analysis is based on the asymptotic limits of small front curvature and small departures from the Chapman–Jouguet speed. Results are presented for ideal as well as nonideal explosives.     

On the formation of structure and electronic transport

By systematic studies of amorphous systems (and most of the results are transferable to liquid systems) we are able to show that structure formation at early stages is to a high degree the effect of self-organized and hence optimized resonances between macroscopic subsystems. There is, for example, a spherical-periodic resonance, based on momentum exchange between the valence electrons in total as one subsystem, and the forming static structure as the other one. It causes spherical structural periodicity of nearest-neighbour shells at medium distances and is a global effect, giving rise to similar effects as described by Bloch's theorem in crystals. Resonances based on an exchange of angular momentum became apparent too. Accordingly, together with the local quantum chemical effects, global resonances are important as well and both will cooperate to get the most optimal energetic situation for the total system. Occasionally, the global effects even dominate structure formation. We report on different scenarios where the total system is able to optimize the resonances. The resonance model explains major structural features of many liquid and amorphous systems of different types as there are pure elements, binary as well as ternary alloys, metallic glasses, glassy semiconductors, glassy Zintl systems, and light-weight Al–TM alloys (TM: from Ti to Cu). Spherical-periodic order causes pseudogaps or even gaps at the Fermi energy and hence has dramatic influences on any electronic transport. Accordingly, understanding structure formation on the basis of resonances also triggers a deeper understanding of electronic transport properties.     

On the electronic structure of graphite

Comprehending investigations of the electronic structure of polycrystalline as well as monocrystalline graphite have been performed by means of X-ray emission, self absorption and X-ray induced photoemission techniques. On the basis of these combined investigations a model for the determination of the relative cross sections for the photoemission process has been established and applied to graphite, where it yields _s / _p =32. The anisotropy and polarization of the CK-radiation of monocrystalline graphite is discussed in terms of the binding properties of the graphite lattice. The predictions are verified by measurements of the CK-emission employing a crystal monochromator which acts simultaneously as a nearly perfect analyzer for the polarization of the monochromatized radiation. By means of the self absorption technique the unoccupied part of the conduction band has been investigated.     

On the band structure of CdSb

The paper consists of two parts. Throughout the first part only the symmetry properties and the existence of the gap are employed for a study of electron bands in CdSb by means of group theory. A general structure of valence bands is obtained, the possible locations of extrema limiting the gap are discussed, and a criterion for the conservation of the gap after switching off the spin-orbit interaction is deduced.In the second part a simple version of thel-dependent pseudopotential suitable for crystals with many atoms in the elementary cell is proposed and the corresponding structure of energy levels in the point is calculated. The results indicate the starting approximation of free electrons to be reasonable and support the hypothesis that the gap arises even before the spin-orbit effects are accounted for.     

On the structure of analytic renormalization

A direct proof is given that analytic renormalization has an additive structure and hence may be implemented by counterterms in the Lagrangian.     

On the structure of symmetry generators

In a field theoretic framework we investigate generators of symmetry transformations induced by conserved local, not necessarily translationally covariant currents. Assuming the invariance of the vacuum and a mass gap, it is shown that the generator on one-particle states in general can be any polynomial of the generators of the Poincaré group and the internal symmetries. We give an example showing that the generator, defined as an integral over a conserved current, in spite of leaving the vacuum invariant, need not be self-adjoint.Supported by a DAAD grant     

On the structure of DeWitt supermanifolds

We show that for a wide and most natural class of (possibly infinite-dimensional) Grassmannian algebras of coefficients, the structure sheaf of every smooth DeWitt supermanifold is acyclic (i.e. its cohomology vanishes in positive degree). This result was previously known for finite-dimensional ground algebras and is new even for the original DeWitt algebra of supernumbers /GL∞. From here we deduce that (equivalence classes of) smooth DeWitt supermanifolds over a fixed ground algebra and of graded smooth manifolds are in a natural bijection with each other. However, contrary to what was stated previously by some authors, this correspondence fails to be functorial; so it happens, for instance, for Rogers' ground algebra B∞. Finally, we observe that every DeWitt super Lie group is a deformation of a graded Lie group over the spectrum Spec /GL of the ground algebra.     

On the fine structure constant

In the framework of a particle model based on a classical minimum action principle a number α′ is derived which is shown to be the analogue of the fine structure constant $\text{α = e}{}^2\text{/}\text{h}\text{?}\text{c}$. To compute α′, a pair of coupled partial differential equations of the second order must be solved. No exact result has been obtained as yet, but it is likely that α′ ? 1. The analogy between α′ and α opens a clear insight into the meaning of the fine structure constant.     

On the structure of Bethe vectors

The structure of Bethe vectors for generalised models associated with the rational and trigonometric R-matrix is investigated. The Bethe vectors in terms of two-component and multi-component models are described. Consequently, their structure in terms of local variables and operators is provided. This, as a consequence, proves the equivalence of coordinate and algebraic Bethe ansatzes for the Heisenberg spin chains. Hermitian conjugation of the elements of the monodromy matrix for the spin chains is studied.     

On the structure of space-time caustics

Caustics formed by timelike and null geodesics in a space-timeM are investigated. Care is taken to distinguish the conjugate points in the tangent space (T-conjugate points) from conjugate points in the manifold (M-conjugate points). It is shown that most nonspacelike conjugate points are regular, i.e. with all neighbouring conjugate points having the same degree of degeneracy. The regular timelikeT-conjugate locus is shown to be a smooth 3-dimensional submanifold of the tangent space. Analogously, the regular nullT-conjugate locus is shown to be a smooth 2-dimensional submanifold of the light cone in the tangent space. The smoothness properties of the null caustic are used to show that if an observer sees focusing in all directions, then there will necessarily be a cusp in the caustic. If, in addition, all the null conjugate points have maximal degree of degeneracy (as in the closed Friedmann-Robertson-Walker universes), then the space-time is closed.     

On the structure of competitive societies

We model the dynamics of social structure by a simple interacting particle system. The social standing of an individual agent is represented by an integer-valued fitness that changes via two offsetting processes. When two agents interact one advances: the fitter with probability p and the less fit with probability 1-p. The fitness of an agent may also decline with rate r. From a scaling analysis of the underlying master equations for the fitness distribution of the population, we find four distinct social structures as a function of the governing parameters p and r. These include: (i) a static lower-class society where all agents have finite fitness; (ii) an upwardly-mobile middle-class society; (iii) a hierarchical society where a finite fraction of the population belongs to a middle class and a complementary fraction to the lower class; (iv) an egalitarian society where all agents are upwardly mobile and have nearly the same fitness. We determine the basic features of the fitness distributions in these four phases.     

On the non-classical structure of the vacuum

Given any three causally separated space-time regions there are observables associated with these regions which do not possess a joint distribution in the vacuum state. This result extends to any state with the Reeh-Schlieder property. This non-classical structure of the vacuum implies, due to the vacuum asymptotic condition, the genericity of non-classical structure for all density matrices in the vacuum sector.     

On the structure of the alpha particle

Using very high resolution electron scattering data, we demonstrate that the ground state structure of⁴He has C_3v point group symmetry.     

On the connectedness structure of the CoulombS-matrix

The forward direction singularity of the non-relativistic CoulombS-matrix is examined and discussed. The relativistic CoulombS-matrix to order α is shown to have a similar singularity.