First-order hyperpolarizabilities of octupolar aromatic molecules: symmetrically substituted triazines

The first hyperpolarizabilities of some symmetrically substituted triazines have been measured and compared with those of the corresponding symmetrically substituted benzenes. The octupolar triazines have higher quadratic polarizabilities than the corresponding octupolar benzenes. The triazine ring seems to be a better central acceptor than the benzene ring, but if it acts as a donor as in sym-triphenyl triazine, the nonlinearity improves further.

First-Order Hyperpolarizabilities of Sulfophthalein Dyes

In this paper we report the first hyperpolarizabilities (beta) of 12, sulfophthalein dyes. Since these dyes are ionic in nature, their second-order nonlinearities were measured by the hyper-Rayleigh scattering technique in solution. The measured beta values are large and highly solvent dependent. Inclusion of solvent polarity in ab initio estimates of static second-order polarizability does not fully account for the experimental beta values. Contributions from the dissociated forms of the dye in different solvents seem to play an important role in enhancing beta in these systems.

Partial instantiation methods for inference in first-order logic

Satisfiability algorithms for propositional logic have improved enormously in recently years. This improvement increases the attractiveness of satisfiability methods for first-order logic that reduce the problem to a series of ground-level satisfiability problems. R. Jeroslow introduced a partial instantiation method of this kind that differs radically from the standard resolution-based methods. This paper lays the theoretical groundwork for an extension of his method that is general enough and efficient enough for general logic programming with indefinite clauses. In particular we improve Jeroslow's approach by (1) extending it to logic with functions, (2) accelerating it through the use of satisfiers, as introduced by Gallo and Rago, and (3) simplifying it to obtain further speedup. We provide a similar development for a "dual" partial instantiation approach defined by Hooker and suggest a primal-dual strategy. We prove correctness of the primal and dual algorithms for full first-order logic with functions, as well as termination on unsatisfiable formulas. We also report some preliminary computational results.

First-order structural transition in the magnetically ordered phase of Fe(1.13)Te

Specific heat, resistivity, magnetic susceptibility, linear thermal expansion (LTE), and high-resolution synchrotron x-ray powder diffraction investigations of single crystals Fe(1+y) Te (0.06 <= y <= 0.15) reveal a splitting of a single, first-order transition for y <= 0.11 into two transitions for y >= 0.13. Most strikingly, all measurements on identical samples Fe(1.13)Te consistently indicate that, upon cooling, the magnetic transition at T(N) precedes the first-order structural transition at a lower temperature T(s). The structural transition in turn coincides with a change in the character of the magnetic structure. The LTE measurements along the crystallographic c axis display a small distortion close to T(N) due to a lattice striction as a consequence of magnetic ordering, and a much larger change at T(s). The lattice symmetry changes, however, only below T(s) as indicated by powder x-ray diffraction. This behavior is in stark contrast to the sequence in which the phase transitions occur in Fe pnictides.

Anisotropy induced crossover from weakly to strongly first order melting of two dimensional solids

Melting and freezing transitions in two dimensional (2D) systems are known to show highly unusual characteristics. Most of the earlier studies considered atomic systems: the melting of 2D molecular solids is still largely unexplored. In order to understand the role of anisotropy as well as multiple energy and length scales present in molecular systems, here we report computer simulation studies of melting of 2D molecular systems. We computed a limited portion of the solid-liquid phase diagram. We find that the interplay between the strength of isotropic and anisotropic interactions can give rise to rich phase diagram consisting of isotropic liquid and two crystalline phases-honeycomb and oblique. The nature of the transition depends on the relative strength of the anisotropic interaction and a strongly first order melting turns into a weakly first order transition on increasing the strength of the isotropic interaction. This crossover can be attributed to an increase in stiffness of the solid phase free energy minimum on increasing the strength of the anisotropic interaction. The defects involved in melting of molecular systems are quite different from those known for the atomic systems.

Investigation on non-exchange spring behaviour and exchange spring behaviour: A first order reversal curve analysis

The First Order Reversal Curve (FORC) method has been utilised to understand the magnetization reversal and the extent of the irreversible magnetization of the soft CoFe2O4-hard SrFe12O19 nanocomposite in the nonexchange spring and the exchange spring regime. The single peak switching behaviour in the FORC distribution of the exchange spring composite confirms the coherent reversal of the soft and hard phases. The onset of the nucleation field and the magnetization reversal by domain wall movement are also evident from the FORC measurements. (C) 2013 AIP Publishing LLC.

Temperature-Induced Reversible First-Order Single Crystal to Single Crystal Phase Transition in Boc-gamma(4)(R)Val-Val-OH: Interplay of Enthalpy and Entropy

Crystals of Boc-gamma y(4)(R)Val-Val-OH undergo a reversible first-order single crystal to single crystal phase transition at T-c approximate to 205 K from the orthorhombic space group P22(1)2(1) (Z' = 1) to the monoclinic space group P2(1) (Z' = 2) with a hysteresis of similar to 2.1 K. The low-temperature monoclinic form is best described as a nonmerohedral twin with similar to 50% contributions from its two components. The thermal behavior of the dipeptide crystals was characterized by differential scanning calorimetry experiments. Visual changes in birefringence of the sample during heating and cooling cycles on a hot-stage microscope with polarized light supported the phase transition. Variable-temperature unit cell check measurements from 300 to 100 K showed discontinuity in the volume and cell parameters near the transition temperature, supporting the first-order behavior. A detailed comparison of the room-temperature orthorhombic form with the low-temperature (100 K) monoclinic form revealed that the strong hydrogen-bonding motif is retained in both crystal systems, whereas the non-covalent interactions involving side chains of the dipeptide differ significantly, leading to a small change in molecular conformation in the monoclinic form as well as a small reorientation of the molecules along the ac plane. A rigid-body thermal motion analysis (translation, libration, screw; correlation of translation and libration) was performed to study the crystal entropy. The reversible nature of the phase transition is probably the result of an interplay between enthalpy and entropy: the low-temperature monoclinic form is enthalpically favored, whereas the room-temperature orthorhombic form is entropically favored.

Multi-transform based spectral element to include first order shear deformation in plates

For obtaining dynamic response of structure to high frequency shock excitation spectral elements have several advantages over conventional methods. At higher frequencies transverse shear and rotary inertia have a predominant role. These are represented by the First order Shear Deformation Theory (FSDT). But not much work is reported on spectral elements with FSDT. This work presents a new spectral element based on the FSDT/Mindlin Plate Theory which is essential for wave propagation analysis of sandwich plates. Multi-transformation method is used to solve the coupled partial differential equations, i.e., Laplace transforms for temporal approximation and wavelet transforms for spatial approximation. The formulation takes into account the axial-flexure and shear coupling. The ability of the element to represent different modes of wave motion is demonstrated. Impact on the derived wave motion characteristics in the absence of the developed spectral element is discussed. The transient response using the formulated element is validated by the results obtained using Finite Element Method (FEM) which needs significant computational effort. Experimental results are provided which confirms the need to having the developed spectral element for the high frequency response of structures. (C) 2015 Elsevier Ltd. All rights reserved.

Stability analysis of thick piezoelectric metal based FGM plate using first order and higher order shear deformation theory

This paper presents the stability analysis of functionally graded plate integrated with piezoelectric actuator and sensor at the top and bottom face, subjected to electrical and mechanical loading. The finite element formulation is based on first order and higher order shear deformation theory, degenerated shell element, von-Karman hypothesis and piezoelectric effect. The equation for static analysis is derived by using the minimum energy principle and solutions for critical buckling load is obtained by solving eigenvalue problem. The material properties of the functionally graded plate are assumed to be graded along the thickness direction according to simple power law function. Two types of boundary conditions are used, such as SSSS (simply supported) and CSCS (simply supported along two opposite side perpendicular to the direction of compression and clamped along the other two sides). Sensor voltage is calculated using present analysis for various power law indices and FG (functionally graded) material gradations. The stability analysis of piezoelectric FG plate is carried out to present the effects of power law index, material variations, applied mechanical pressure and piezo effect on buckling and stability characteristics of FG plate.

Ortho-positronium annihilation: steps toward computing the first order radiative corrections

The 0.2% experimental accuracy of the 1968 Beers and Hughes measurement of the annihilation lifetime of ortho-positronium motivates the attempt to compute the first order quantum electrodynamic corrections to this lifetime. The theoretical problems arising in this computation are here studied in detail up to the point of preparing the necessary computer programs and using them to carry out some of the less demanding steps -- but the computation has not yet been completed. Analytic evaluation of the contributing Feynman diagrams is superior to numerical evaluation, and for this process can be carried out with the aid of the Reduce algebra manipulation computer program.

The relation of the positronium decay rate to the electronpositron annihilation-in-flight amplitude is derived in detail, and it is shown that at threshold annihilation-in-flight, Coulomb divergences appear while infrared divergences vanish. The threshold Coulomb divergences in the amplitude cancel against like divergences in the modulating continuum wave function.

Using the lowest order diagrams of electron-positron annihilation into three photons as a test case, various pitfalls of computer algebraic manipulation are discussed along with ways of avoiding them. The computer manipulation of artificial polynomial expressions is preferable to the direct treatment of rational expressions, even though redundant variables may have to be introduced.

Special properties of the contributing Feynman diagrams are discussed, including the need to restore gauge invariance to the sum of the virtual photon-photon scattering box diagrams by means of a finite subtraction.

A systematic approach to the Feynman-Brown method of Decomposition of single loop diagram integrals with spin-related tensor numerators is developed in detail. This approach allows the Feynman-Brown method to be straightforwardly programmed in the Reduce algebra manipulation language.

The fundamental integrals needed in the wake of the application of the Feynman-Brown decomposition are exhibited and the methods which were used to evaluate them -- primarily dis persion techniques are briefly discussed.

Finally, it is pointed out that while the techniques discussed have permitted the computation of a fair number of the simpler integrals and diagrams contributing to the first order correction of the ortho-positronium annihilation rate, further progress with the more complicated diagrams and with the evaluation of traces is heavily contingent on obtaining access to adequate computer time and core capacity.

I. Numerical solution of exact pair equations. II. Numerical solution of first-order pair equations

Part I

Numerical solutions to the S-limit equations for the helium ground state and excited triplet state and the hydride ion ground state are obtained with the second and fourth difference approximations. The results for the ground states are superior to previously reported values. The coupled equations resulting from the partial wave expansion of the exact helium atom wavefunction were solved giving accurate S-, P-, D-, F-, and G-limits. The G-limit is -2.90351 a.u. compared to the exact value of the energy of -2.90372 a.u.

Part II

The pair functions which determine the exact first-order wavefunction for the ground state of the three-electron atom are found with the matrix finite difference method. The second- and third-order energies for the (1s1s)¹S, (1s2s)³S, and (1s2s)¹S states of the two-electron atom are presented along with contour and perspective plots of the pair functions. The total energy for the three-electron atom with a nuclear charge Z is found to be E(Z) = -1.125•Z² +1.022805•Z-0.408138-0.025515•(1/Z)+O(1/Z²)a.u.