Nonplanar distortions and strain energies of polycyclic aromatic hydrocarbons

On the basis of HF/6-31G(d) optimized structures, the nonplanar distortions of 135 polycyclic aromatic hydrocarbons (PAHs) have been classified as splitting (S-) and arching (A-) distortions. Three bay structures are proposed as the structural origin of S-distortion. Due to the limitation of sample molecules, a set of universal motifs for molecules containing A-distortions is not available; however, a set of motifs and parameters are developed for the semiquantitative estimation of the nonplanar strain energies of PAHs containing the corannulene structure, and the differences between the E, values from quantum calculations and those from these estimations vary from -5.60 to 5.51 kcal/mol. The above results are fundamentally important for the understanding of nonplanar distortion of PAHs and fullerenes, and this method can also be employed to semiquantitatively estimate strain energies of such molecules containing hundreds of carbon atoms.

Explicit derivation of the relativistic mass-energy relation for internal kinetic and potential energies of a composite system

A straightforward derivation of relativistic expressions for the mechanical momentum, kinetic and total energies, and mass-energy equivalence (including potential energy) which does not require any knowledge of the energy-momentum relation for electromagnetic waves or consideration of elastic collisions, but is directly based on Newton's second law and Lorentz's transformations, is presented in this paper. The existence of an invariant force is shown to be important for the validity of the relativistic mechanics.

Strain energies due to nonplanar distortion of fullerenes and their dependence on structural motifs

Accurate strain energies due to nonplanar distortion of 114 isolated pentagon rule (IPR) fullerenes with 60-102 carbon atoms have been calculated based on B3LYP/6-31G(d) optimized structures. The calculated values of strain energy due to nonplanar distortion (E-np) are reproduced by three simple schemes based upon counts of 8, 16, and 30 distinct structural motifs composed of hexagons and pentagons. Using C-180 (I-h) and CN (I-h) (N is very large) as test molecules, the intrinsic limitations of the motif model based on six-membered rings (6-MRs) as the central unit have been discussed. On the basis of the relationship between the contributions of motifs to E-np and the number of five-membered rings (5-MRs) in motifs, we found that IPR fullerenes with dispersed 5-MRs present smaller nonplanar distortions.

Oxidation mechanism of Si3N4-bonded SiC ceramics by CO, CO2 and steam

This paper presents a theoretical and experimental investigation into the oxidation reactions of Si3N4-bonded SiC ceramics. Such ceramics which contain a small amount of silicon offer increased oxidation and wear resistance and are widely used as lining refractories in blast furnaces. The thermodynamics of oxidation reactions were studied using the JANAF tables. The weight gain was measured using a thermogravimetric analysis technique to study the kinetics. The temperature range of oxidation measurements is from 1073 to 1573 K and the oxidation atmosphere is water vapour, pure CO and CO-CO2 gas mixtures with various CO-to-CO2 ratios. Thermodynamic simulations showed that the oxidation mechanism of Si3N4-bonded SiC ceramics is passive oxidation and all components contribute to the formation of a silica film. The activated energies of the reactions follow the sequence Si3N4>SiC>Si. The kinetic study revealed that the oxidation of Si3N4-bonded SiC ceramics occurred in a mixed regime controlled by both interface reaction and diffusion through the silica film. Under the atmosphere conditions prevailing in the blast furnace, this ceramic is predicted to be passively oxidized with the chemical reaction rate becoming more dominant as the CO concentration increases. (C) 1998 Chapman & Hall.

Quantum integrability and exact solution of the supersymmetric U model with boundary terms

Quantum integrability is established for the one-dimensional supersymmetric U model with boundary terms by means of the quantum inverse-scattering method. The boundary supersymmetric U chain is solved by using the coordinate-space Bethe-ansatz technique and Bethe-ansatz equations are derived. This provides us with a basis for computing the finite-size corrections to the low-lying energies in the system. [S0163-1829(98)00425-1].

Thermochromism and structure of piperazinium tetrachlorocuprate(II) complexes

The tetrachlorocuprate(II) ion can crystallize in two different structures with the piperazinium dication (pipzH(2)). Both structures contain discrete CuCl42- species. A yellow compound (pipzH(2))[CuCl4]. 2H(2)O (1) is monoclinic (C2/c, Z = 4, a = 10.538(3) Angstrom, b = 7.4312(5) Angstrom, c = 17.281(4) Angstrom, beta = 111.900(10)degrees) and contains the CuCl42- ion as a distorted tetrahedron. A green compound (pipzH(2))(2)[CuCl4]. Cl-2. 3H(2)O (2) is triclinic (P (1) over bar, Z = 2, a = 9.264(3) Angstrom, b = 10.447(2) Angstrom, c = 11.366(2) Angstrom, alpha = 68.38 degrees, beta = 82.86(2)degrees, gamma = 83.05(2)degrees) and contains the CuCl42- ion with a square planar geometry. This latter compound shows thermo/photochromism, changing from green to yellow upon heating or laser irradiation.

Multiphoton ac Stark effect in a bichromatically driven two-level atom

We study the interaction of a two-level atom with two lasers of different frequencies and amplitudes: a strong laser of Rabi frequency 2 Ohm(1) on resonance with the atomic transition, and a weaker laser detuned by subharmonics (2 Ohm(1)/n) of the Rabi frequency of the first. We find that under these conditions the second laser couples the dressed states created by the first in an n-photon process, resulting in doubly dressed states and in a ''multiphoton ac Stark'' effect. We calculate the eigenstates of the doubly dressed atom and their energies, and illustrate the role of this multiphoton ac Stark effect in its fluorescence, absorption, and Autler-Townes spectra. [S1050-2947(98)07607-0].

Three-dimensional quantum solitons with parametric coupling

We consider the quantum field theory of two bosonic fields interacting via both parametric (cubic) and quartic couplings. In the case of photonic fields in a nonlinear optical medium, this corresponds to the process of second-harmonic generation (via chi((2)) nonlinearity) modified by the chi((3)) nonlinearity. The quantum solitons or energy eigenstates (bound-state solutions) are obtained exactly in the simplest case of two-particle binding, in one, two, and three space dimensions. We also investigate three-particle binding in one space dimension. The results indicate that the exact quantum solitons of this field theory have a singular, pointlike structure in two and three dimensions-even though the corresponding classical theory is nonsingular. To estimate the physically accessible radii and binding energies of the bound states, we impose a momentum cutoff on the nonlinear couplings. In the case of nonlinear optical interactions, the resulting radii and binding energies of these photonic particlelike excitations in highly nonlinear parametric media appear to be close to physically observable values.

Multidimensional parametric quantum solitons

We consider the parametric quantum field theory involving cubic and quartic couplings of two bosonic fields. This is exactly soluble for the two-particle energy eigenstates (or quantum solitons) in one, two, and three space dimensions. We estimate the binding energies and corresponding radii in the case of photonic fields in nonlinear optical materials, and Bose-Einstein condensates. [S1050-2947(98)51110-9].

Thermogravimetric analysis of carbon deposition over Ni/gamma-Al2O3 catalysts in carbon dioxide reforming of methane

Carbon formation on Ni/gamma-Al2O3 catalysts and its kinetics during methane reforming with carbon dioxide was studied in the temperature range of 500-700 degrees C using a thermogravimetric analysis technique. The activation energies of methane cracking, carbon gasification in CO2, as well as carbon deposition in CO2-CH4 reforming were obtained. The results show that the activation energy for carbon gasification is larger than that of carbon formation in methane cracking and that the activation energy of coking in CO2-CH4 reforming is also larger than that of methane decomposition to carbon. The dependencies of coking rate on partial pressures of CH4 and CO2 indicate that methane decomposition is the main route for carbon deposition. A mechanism and kinetic model for carbon deposition is proposed.

Extended integrability regime for the supersymmetric U model

An extension of the supersymmetric U model for correlated electrons is given and integrability is established by demonstrating that the model can he constructed through the quantum inverse scattering method using an R-matrix without the difference property. Some general symmetry properties of the model are discussed and from the Bethe ansatz solution an expression for the energies is presented.

Protein fold recognition score functions: Unusual construction strategies

We describe two ways of optimizing score functions for protein sequence to structure threading. The first method adjusts parameters to improve sequence to structure alignment. The second adjusts parameters so as to improve a score function's ability to rank alignments calculated in the first score function. Unlike those functions known as knowledge-based force fields, the resulting parameter sets do not rely on Boltzmann statistics, have no claim to representing free energies and are purely constructions for recognizing protein folds. The methods give a small improvement, but suggest that functions can be profitably optimized for very specific aspects of protein fold recognition, Proteins 1999;36:454-461. (C) 1999 Wiley-Liss, Inc.

Multidimensional quantum solitons with nondegenerate parametric interactions: Photonic and Bose-Einstein condensate environments

We consider the quantum theory of three fields interacting via parametric and repulsive quartic couplings. This can be applied to treat photonic chi((2)) and chi((3)) interactions, and interactions in atomic Bose-Einstein condensates or quantum Fermi gases, describing coherent molecule formation together with a-wave scattering. The simplest two-particle quantum solitons or bound-state solutions of the idealized Hamiltonian, without a momentum cutoff, are obtained exactly. They have a pointlike structure in two and three dimensions-even though the corresponding classical theory is nonsingular. We show that the solutions can be regularized with a momentum cutoff. The parametric quantum solitons have much more realistic length scales and binding energies than chi((3)) quantum solitons, and the resulting effects could potentially be experimentally tested in highly nonlinear optical parametric media or interacting matter-wave systems. N-particle quantum solitons and the ground state energy are analyzed using a variational approach. Applications to atomic/molecular Bose-Einstein condensates (BEC's) are given, where we predict the possibility of forming coupled BEC solitons in three space dimensions, and analyze superchemistry dynamics.

Free energy approximations in simple lattice proteins

This work addresses the question of whether it is possible to define simple pairwise interaction terms to approximate free energies of proteins or polymers. Rather than ask how reliable a potential of mean force is, one can ask how reliable it could possibly be. In a two-dimensional, infinite lattice model system one can calculate exact free energies by exhaustive enumeration. A series of approximations were fitted to exact results to assess the feasibility and utility of pairwise free energy terms. Approximating the true free energy with pairwise interactions gives a poor fit with little transferability between systems of different size. Adding extra artificial terms to the approximation yields better fits, but does not improve the ability to generalize from one system size to another. Furthermore, one cannot distinguish folding from nonfolding sequences via the approximated free energies. Most usefully, the methodology shows how one can assess the utility of various terms in lattice protein/polymer models. (C) 2001 American Institute of Physics.

Energy and averages in the mechanics of granular materials

We derive a general thermo-mechanical theory for particulate materials consisting of granules of arbitrary whose material points possess three translational and three independent rotational degrees of freedom. Additional field variables are the translational and rotational granular temperatures, the kinetic energies shape and size. The kinematics of granulate is described within the framework of a polar continuum theory of the velocity and spin fluctuations respectively and the usual thermodynamic temperature. We distinguish between averages over particle categories (averages in mass/velocity and moment of inertia/spin space, respectively) and particle phases where the average extends over distinct subsets of particle categories (multi phase flows). The relationship between the thermal energy in the granular system and phonon energy in a molecular system is briefly discussed in the main body of the paper and discussed in detail in the Appendix A. (C) 2001 Elsevier Science B.V. All rights reserved.