An accurate numerical integration scheme for finite rotations using rotation vector parametrization

A numerical integration procedure for rotational motion using a rotation vector parametrization is explored from an engineering perspective by using rudimentary vector analysis. The incremental rotation vector, angular velocity and acceleration correspond to different tangent spaces of the rotation manifold at different times and have a non-vectorial character. We rewrite the equation of motion in terms of vectors lying in the same tangent space, facilitating vector space operations consistent with the underlying geometric structure. While any integration algorithm (that works within a vector space setting) may be used, we presently employ a family of explicit Runge-Kutta algorithms to solve this equation. While this work is primarily motivated out of a need for highly accurate numerical solutions of dissipative rotational systems of engineering interest, we also compare the numerical performance of the present scheme with some of the invariant preserving schemes, namely ALGO-C1, STW, LIEMIDEA] and SUBCYC-M. Numerical results show better local accuracy via the present approach vis-a-vis the preserving algorithms. It is also noted that the preserving algorithms do not simultaneously preserve all constants of motion. We incorporate adaptive time-stepping within the present scheme and this in turn enables still higher accuracy and a `near preservation' of constants of motion over significantly longer intervals. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Stereochemistry of peptides containing 1-aminocyclopentane carboxylic acid (Acc5). Solution and solid state conformations of Boc-Acc5-Acc5-NHMe.

The conformational analysis of a protected homodipeptide of 1-aminocyclopentanecarboxylic acid (Acc5) has been carried out. 1H-nmr studies establish a ?-turn conformation for Boc-Acc5-Acc5-NHMe in chloroform and dimethylsulfoxide solutions involving the methylamide NH in an intramolecular hydrogen bond. Supportive evidence for the formation of an intramolecular hydrogen bond is obtained from ir studies. X-ray diffraction studies reveal a type III ?-turn conformation in the solid state stabilized by a 4 ? 1 hydrogen bond between the Boc CO and methylamide NH groups. The ?,? values for both Acc5 residues are close to those expected for an ideal 310-helical conformation (?? ± 60°, ?? ±30°).

Conformations of the amino terminal tetrapeptide of emerimicins and antiamoebin in solution and in the solid state

The conformations of Boc-l-Phe-(AiB)3-OH (1) and Boc-l-Phe-(Aib)3-OMe (2) which correspond to the amino terminal sequence of the emerimicins and antiamoebins have been studied in solution using 270 MHz 1H n.m.r. In dimethyl sulphoxide solution both peptides show the presence of two strongly solvent shielded Aib NH groups, consistent with a consecutive β-turn conformation, involving the Aib(3) and Aib(4) NH groups in intramolecular 4 → I hydrogen bonds. This folded conformation is maintained for 2 in chloroform solution. Nuclear Overhauser effect studies provide evidence for a Type II Phe-Aib β-turn. An X-ray diffraction study of Boc-(d,l)-Phe-(Aib)3-OH establishes a single type III(III′) β-turn conformation with Aib(2)-Aib(3) as the corner residues. A single intramolecular 4 → I hydrogen bond between Phe(I) CO and Aib(4) NH groups is observed in the crystal. The solution conformation may incorporate a consecutive type II-III′ structure for the Phe(1)-Aib(2)-Aib(3) segment, with the initial type II β-turn being destabilized by intermolecular interactions in the solid state.

Precise measurement of hyperfine structure in the 2P(1/2) state of Li-7 using saturated-absorption spectroscopy

We report a precise measurement of the hyperfine interval in the 2P(1/2) state of Li-7. The transition from the ground state (D-1 line) is accessed using a diode laser and the technique of saturated-absorption spectroscopy in hot Li vapor. The interval is measured by locking an acousto-optic modulator to the frequency difference between the two hyperfine peaks. The measured interval of 92.040(6) MHz is consistent with an earlier measurement reported by us using an atomic-beam spectrometer Das and Natarajan, J. Phys. B 41, 035001 (2008)]. The interval yields the magnetic dipole constant in the P-1/2 state as A = 46.047(3), which is discrepant from theoretical calculations by > 80 kHz.

Activity–Composition Relations in the Nickel Oxide–Magnesium Oxide System at 1300 K by the Solid-State Galvanic Cell Technique

The activity of NiO in NiO-MgO rock salt solid solution has been measured at 1300 K by employing a solid-state galvanic cell: Pt,Ni+ NiO||(CaO)ZrO2||Ni + (Nix,Mgl-x)O, Pt. A high-density tube of Zr02-15 mol% CaO has been used as the solid electrolyte for the emf measurements. The activities of the component oxides in the rock salt solid solution exhibit negative deviation from ideality at the temperature of investigation. The solid solution obeys regular solution behavior at 1300 K. The value of the regular solution parameter is found to be -12000 ((l000) J mol-1. The composition dependence of ΔGEx obtained in this study agrees reasonably well with the calorimetric data reported in the literature for NiO-MgO solid solution.

Analysis of performance of a hot gas injection thrust vector control system

The complex three-dimensional flowfield produced by secondary injection of hot gases in a rocket nozzle for thrust vector control is analyzed by solving unsteady three-dimensional Euler equations with appropriate boundary conditions. Various system performance parameters like secondary jet amplification factor and axial thrust augmentation are deduced by integrating the nozzle wall pressure distributions obtained as part of the flowfield solution and compared with measurements taken in actual static tests. The agreement is good within the practical range of secondary injectant flow rates for thrust vector control applications.

A Hybrid Multilevel Inverter Topology for an Open-End Winding Induction-Motor Drive Using Two-Level Inverters in Series With a Capacitor-Fed H-Bridge Cell

In this paper, a new five-level inverter topology for open-end winding induction-motor (IM) drive is proposed. The open-end winding IM is fed from one end with a two-level inverter in series with a capacitor-fed H-bridge cell, while the other end is connected to a conventional two-level inverter. The combined inverter system produces voltage space-vector locations identical to that of a conventional five-level inverter. A total of 2744 space-vector combinations are distributed over 61 space-vector locations in the proposed scheme. With such a high number of switching state redundancies, it is possible to balance the H-bridge capacitor voltages under all operating conditions including overmodulation region. In addition to that, the proposed topology eliminates 18 clamping diodes having different voltage ratings compared with the neutral point clamped inverter. On the other hand, it requires only one capacitor bank per phase, whereas the flying-capacitor scheme for a five-level topology requires more than one capacitor bank per phase. The proposed inverter topology can be operated as a three-level inverter for full modulation range, in case of any switch failure in the capacitor-fed H-bridge cell. This will increase the reliability of the system. The proposed scheme is experimentally verified on a four-pole 5-hp IM drive.

Inertial effects in solvation dynamics

The dynamics of solvation of newly created charged species in dense dipolar liquids can proceed at a high speed with time constants often in the subpicosecond domain. The motion of the solvent molecules can be in the inertial limit at such short times. In this paper we present a microscopic study of the effects of inertial motion of solvent molecules on the solvation dynamics of a newly created ion in a model dipolar liquid. Interesting dynamical behavior emerges when the relative contribution of the translational modes in the wave-vector-dependent longitudinal relaxation time is significant. Especially, the theory predicts that the time correlation function of the solvation energy can become oscillatory in some limiting situations. In general, the dynamics becomes faster in the presence of the inertial contribution. We discuss the experimental situations where the inertial effects can be noticeable.

Molecular hydrodynamic theory of non‐Markovian collective orientational relaxation in dense dipolar liquids

A microscopic study of the non‐Markovian (or memory) effects on the collective orientational relaxation in a dense dipolar liquid is carried out by using an extended hydrodynamic approach which provides a reliable description of the dynamical processes occuring at the molecular length scales. Detailed calculations of the wave‐vector dependent orientational correlation functions are presented. The memory effects are found to play an important role; the non‐Markovian results differ considerably from that of the Markovian theory. In particular, a slow long‐time decay of the longitudinal orientational correlation function is observed for dense liquids which becomes weaker in the presence of a sizeable translational contribution to the collective orientational relaxation. This slow decay can be attributed to the intermolecular correlations at the molecular length scales. The longitudinal component of the orientational correlation function becomes oscillatory in the underdamped limit of momenta relaxations and the frequency dependence of the friction reduce the frictional resistance on the collective excitations (commonly known as dipolarons) to make them long lived. The theory predicts that these dipolarons can, therefore, be important in chemical relaxation processes, in contradiction to the claims of some earlier theoretical studies.

Molecular theory of dielectric relaxation in a dense binary dipolar liquid

A molecular theory of dielectric relaxation in a dense binary dipolar liquid is presented. The theory takes into account the effects of intra- and interspecies intermolecular interactions. It is shown that the relaxation is, in general, nonexponential. In certain limits, we recover the biexponential form traditionally used to analyze the experimental data of dielectric relaxation in a binary mixture. However, the relaxation times are widely different from the prediction of the noninteracting rotational diffusion model of Debye for a binary system. Detailed numerical evaluation of the frequency-dependent dielectric function epsilon-(omega) is carried out by using the known analytic solution of the mean spherical approximation (MSA) model for the two-particle direct correlation function for a polar mixture. A microscopic expression for both wave vector (k) and frequency (omega) dependent dielectric function, epsilon-(k,omega), of a binary mixture is also presented. The theoretical predictions on epsilon-(omega) (= epsilon-(k = 0, omega)) have been compared with the available experimental results. In particular, the present theory offers a molecular explanation of the phenomenon of fusing of the two relaxation channels of the neat liquids, observed by Schallamach many years ago.

Photochromism of alkylisophthalaldehydes in the solid state: structure–reactivity correlations

The crystal and molecular structures of the photochromic compounds 2,5-dimethylisophthalaldehyde (I) and 5-isopropyl-2-methylisophthalaldehyde (II) have been determined by single crystal X-ray analyses. The intramolecular gamma-hydrogen abstraction process involved in the photoenolisation of I and II in the solid state has been rationalised in the light of relevant geometrical parameters.

A simple n-state model for water

A simple n-state configurational excitation model which takes into account the presence of weakly connected pentamer units in liquid water is proposed. The model has features of both the “continuum” and “mixture” models. Calculations based on this model satisfactorily account for the important, diagnostic thermodynamic properties of water such as the density maximum, fraction of monomers and so on.

Pes study of spin-state transitions in d6 transition metal complexes and oxides

Transitions from the low-to the high-spin state in Fe2+ and Co3+ compounds have been examined by X-ray and UV photoelectron spectroscopy. It has been shown that the core-level bands in XPES, in particular the metal 3s band, as well as the valence bands, are diagnosis in the study of spin-state transitions.

Thermodynamics Of Aluminum Strontium Alloys

The activity of strontium in liquid Al-Sr alloys (X(Sr) less-than-or-equal-to 0.17) at 1323 K has been determined using the Knudsen effusion-mass loss technique. At higher concentrations (X(Sr) greater-than-or-equal-to 0.28), the activity of strontium has been determined by the pseudoisopiestic technique. Activity of aluminium has been derived by Gibbs-Duhem integration. The concentration - concentration structure factor of Bhatia and Thornton at zero wave vector has been computed from the thermodynamic data. The behaviour of the mean square thermal fluctuation in composition and the thermodynamic mixing functions suggest association tendencies in the liquid state. The associated solution model with Al2Sr as the predominant complex can account for the properties of the liquid alloy. Thermodynamic data for the intermetallic compunds in the Al-Sr system have been derived using the phase diagram and the Gibbs' energy and enthalpy of mixing of liquid alloys. The data indicate the need for redetermination of the phase diagram near the strontium-rich corner.

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.