Ordering near the percolation threshold in models of two-dimensional interacting bosons with quenched dilution

Randomly diluted quantum boson and spin models in two dimensions combine the physics of classical percolation with the well-known dimensionality dependence of ordering in quantum lattice models. This combination is rather subtle for models that order in two dimensions but have no true order in one dimension, as the percolation cluster near threshold is a fractal of dimension between 1 and 2: two experimentally relevant examples are the O(2) quantum rotor and the Heisenberg antiferromagnet. We study two analytic descriptions of the O(2) quantum rotor near the percolation threshold. First a spin-wave expansion is shown to predict long-ranged order, but there are statistically rare points on the cluster that violate the standard assumptions of spin-wave theory. A real-space renormalization group (RSRG) approach is then used to understand how these rare points modify ordering of the O(2) rotor. A new class of fixed points of the RSRG equations for disordered one-dimensional bosons is identified and shown to support the existence of long-range order on the percolation backbone in two dimensions. These results are relevant to experiments on bosons in optical lattices and superconducting arrays, and also (qualitatively) for the diluted Heisenberg antiferromagnet La-2(Zn,Mg)(x)Cu1-xO4.

Air Fleet and Facility Planning via Optimal Control Models

A study is presented which is aimed at developing techniques suitable for effective planning and efficient operation of fleets of aircraft typical of the air force of a developing country. An important aspect of fleet management, the problem of resource allocation for achieving prescribed operational effectiveness of the fleet, is considered. For analysis purposes, it is assumed that the planes operate in a single flying-base repair-depot environment. The perennial problem of resource allocation for fleet and facility buildup that faces planners is modeled and solved as an optimal control problem. These models contain two "policy" variables representing investments in aircraft and repair facilities. The feasibility of decentralized control is explored by assuming the two policy variables are under the control of two independent decisionmakers guided by different and not often well coordinated objectives.

Air Fleet and Facility Planning via Optimal Control Models

A study is presented which is aimed at developing techniques suitable for effective planning and efficient operation of fleets of aircraft typical of the air force of a developing country. An important aspect of fleet management, the problem of resource allocation for achieving prescribed operational effectiveness of the fleet, is considered. For analysis purposes, it is assumed that the planes operate in a single flying-base repair-depot environment. The perennial problem of resource allocation for fleet and facility buildup that faces planners is modeled and solved as an optimal control problem. These models contain two "policy" variables representing investments in aircraft and repair facilities. The feasibility of decentralized control is explored by assuming the two policy variables are under the control of two independent decisionmakers guided by different and not often well coordinated objectives.

Nonsingular cosmological models: the massive scalar field case

The nonminimal coupling of a massive self-interacting scalar field with a gravitational field is studied. Spontaneous symmetry breaking occurs in the open universe even when the sign on the mass term is positive. In contrast to grand unified theories, symmetry breakdown is more important for the early universe and it is restored only in the limit of an infinite expansion. Symmetry breakdown is shown to occur in flat and closed universes when the mass term carries a wrong sign. The model has a naturally defined effective gravitational coupling coefficient which is rendered time-dependent due to the novel symmetry breakdown. It changes sign below a critical value of the cosmic scale factor indicating the onset of a repulsive field. The presence of the mass term severely alters the behaviour of ordinary matter and radiation in the early universe. The total energy density becomes negative in a certain domain. These features make possible a nonsingular cosm

Polypeptide models of collagen. II. Solution properties of (Pro-Gly-Phe)n

The conformation of (Pro-Gly-Phe)n in trifluoroethanol was investigated using CD, nmr and ir techniques. After making appropriate correction for the contribution of the phenylalanine chromophore to the observed CD spectra of the polytripeptide at several temperatures, it is found that (Pro-Gly-Phe)n can exist in a partially triple-helical conformation in this solvent a t low temperatures. The nmr and ir data support this conclusion. In conjunction with recent theoretical sutdies, our data offer an explanation for the preferential occurrence of the Phe residue in position 2 of the tripeptide sequence Gly-R2-R3, in collagen.

Synthetic peptide models for the redox-active disulfide loop of glutaredoxin. Conformational studies

Two cyclic peptide disulfides Boc-Cys-Pro-X-Cys-NHMe (X = L-Tyr or L-Phe) have been synthesized as models for the 14-membered redox-active disulfide loop of glutaredoxin. 'H NMR studies at 270 MHz in chloroform solutions establish a type I 0-turn conformation for the Pro-X segment in both peptides, stabilized by a 4-1 hydrogen bond between the Cys(1) CO and Cys(4) NH groups. Nuclear Overhauser effects establish that the aromatic ring in the X = Phe peptide is oriented over the central peptide unit. In dimethyl sulfoxide solutions two conformational species are observed in slow exchange on the NMR time scale, for both peptides. These are assigned to type I and type I1 p-turn structures with -Pro-Tyr(Phe)-as the corner residues. The structural assignments are based on correlation of NMR parameters with model 14-membered cyclic cystine peptides with Pro-X spacers. Circular dichroism studies based on the -S-Sn- u* transition suggest a structural change in the disulfide bridge with changing solvent polarity, establishing conformational coupling between the peptide backbone and the disulfide linkage in these systems.

Direct stability evaluation of power systems with detailed generator models using structure-preserving energy functions

Energy-based direct methods for transient stability analysis are potentially useful both as offline tools for planning purposes as well as for online security assessment. In this paper, a novel structure-preserving energy function (SPEF) is developed using the philosophy of structure-preserving model for the system and detailed generator model including flux decay, transient saliency, automatic voltage regulator (AVR), exciter and damper winding. A simpler and yet general expression for the SPEF is also derived which can simplify the computation of the energy function. The system equations and the energy function are derived using the centre-of-inertia (COI) formulation and the system loads are modelled as arbitrary functions of the respective bus voltages. Application of the proposed SPEF to transient stability evaluation of power systems is illustrated with numerical examples.

Peptide models for b-turns.A circular dichroism study

The circular dichroism spectra of four 0-turn model peptides, Z-Aib-Pro-Aib-Pro- OMe (l), Piv-Pro-Aib-NHMe (2), Piv-Pro-D-Ala-NHMe (3) and Piv-Pro-Val-NHMe (4) have been examined under a wide range of solvent conditions, using methanol, hexafluoroisopropanol and cyclohexane. Type I and Type I1 0-turns have been observed for peptides 1 and 2 respectively, in the solid state, while the Pro-D-Ala sequence adopts a Type I1 Sturn in a related peptide crystal structure. A class C spectrum is observed for 1 in various solvents, suggesting a variant of a Type I(II1) structure. The Type I1 f3-turn is characterized by a CD spectrum having two positive CD bands at - 230 nm and - 202 nm, a feature observed in Piv-Pro- D-Ala-NHMe in cyclohexane and methanol and for Piv-Pro-Aib-NHMe in methanol. Peptide 2 exhibits solvent dependent CD spectra, which may be rationalized by considering Type 11, I11 and V reverse turn structures. Piv-Pro- Val-NHMe adopts nonaturn structures in polar solvents, but exhibits a class B spectrum in cyclohexane suggesting a population of Type I &turns.

On the models for deuterium long-range isotope effects in13C NMR spectroscopy

The long-range deuterium isotope effects on13C nuclear shielding are physically not yet completely understood. Two existing models for explaining these effects, vibrational and substituent, are compared here. The vibrational model is based on the Born-Oppenheimer approximation, but it can explain only one-bond deuterium effects. To the contrary, the substituent model may explain many long-range isotope effects, but it is controversial due to the assumption of some distinct electronic properties of isotopes. We explain how long-range deuterium isotope effects may be rationalized by the subtle electronic changes induced by isotope substitution, which does not violate the Born-Oppenheimer approximation.

Models for spin-state transitions in solids

The model for spin-state transitions described by Bari and Sivardiere (1972) is static and can be solved exactly even when the dynamics of the lattice are included; the dynamic model does not, however, show any phase transition. A coupling between the octahedra, on the other hand, leads to a phase transition in the dynamical two-sublattice displacement model. A coupling of the spin states to the cube of the sublattice displacement leads to a first-order phase transition. The most reasonable model appears to be a two-phonon model in which an ion-cage mode mixes the spin states, while a breathing mode couples to the spin states without mixing. This model explains the non-zero population of high-spin states at low temperatures, temperature-dependent variations in the inverse susceptibility and the spin-state population ratio, as well as the structural phase transitions accompanying spin-state transitions found in some systems.

A Deterministic Optimization Approach to Protein Sequence Design Using Continuous Models

Determining the sequence of amino acid residues in a heteropolymer chain of a protein with a given conformation is a discrete combinatorial problem that is not generally amenable for gradient-based continuous optimization algorithms. In this paper we present a new approach to this problem using continuous models. In this modeling, continuous "state functions" are proposed to designate the type of each residue in the chain. Such a continuous model helps define a continuous sequence space in which a chosen criterion is optimized to find the most appropriate sequence. Searching a continuous sequence space using a deterministic optimization algorithm makes it possible to find the optimal sequences with much less computation than many other approaches. The computational efficiency of this method is further improved by combining it with a graph spectral method, which explicitly takes into account the topology of the desired conformation and also helps make the combined method more robust. The continuous modeling used here appears to have additional advantages in mimicking the folding pathways and in creating the energy landscapes that help find sequences with high stability and kinetic accessibility. To illustrate the new approach, a widely used simplifying assumption is made by considering only two types of residues: hydrophobic (H) and polar (P). Self-avoiding compact lattice models are used to validate the method with known results in the literature and data that can be practically obtained by exhaustive enumeration on a desktop computer. We also present examples of sequence design for the HP models of some real proteins, which are solved in less than five minutes on a single-processor desktop computer Some open issues and future extensions are noted.