Einstein-Weyl Gravity from a Topological {{\rm SL}(5, \mathbb{R})} Gauge Invariant Action

A topological field theory of gravity in four-dimension is proposed which is finite after quantization. Since such ‘minimal’ BF type models for the high energy limit are physically not quite realistic, a tiny symmetry breaking is needed to recover standard Einsteinian gravity for the macroscopic metrical background.     

The complexes between CH3OH and CF4. Infrared matrix isolation and theoretical studies

The complex formed between methanol and tetrafluoromethane has been identified in argon and neon matrixes by help of FTIR spectroscopy. Three fundamentals (nu(OH), nu(FCF), and nu(CO)) were observed for the complex isolated in the two matrixes, and the OH stretch was red shifted in a neon matrix and blue shifted in an argon matrix with respect to the corresponding vibration of the methanol monomer. The theoretical studies of the structure and spectral characteristics of the complexes formed between CH(3)OH and CF(4) were carried out at the MP2 level of theory with the 6-311+G(2df,2pd) basis set. The calculations resulted in three stationary points from which two (I-1, I-2) corresponded to structures involving the O-H...F hydrogen bond and the third one (I-3) to the non-hydrogen-bonded structure. The topological analysis of the distribution of the charge density (AIM theory) confirmed the existence of the hydrogen bond in I-1, I-2 complexes and indicated weak interaction between the oxygen atom of CH(3)OH and three fluorine atoms of CF(4) in the I-3 complex. The comparison of the experimental and theoretical data suggests that in the matrixes only the non-hydrogen-bonded complex I-3 is trapped. The blue/red shift of the complex OH stretching vibration with respect to the corresponding vibration of CH(3)OH in argon/neon matrixes is explained by the different sensitivity of the complex and monomer vibrations to matrix material. The ab initio calculations performed for the ternary CH(3)OH-CF(4)-Ar systems indicated a negligible effect of an argon atom on the binary complex frequencies.     

Instability and Stability of Rolls in the Swift–Hohenberg Equation

We develop a method for the stability analysis of bifurcating spatially periodic patterns under general nonperiodic perturbations. In particular, it enables us to detect sideband instabilities. We treat in all detail the stability question of roll solutions in the two–dimensional Swift–Hohenberg equation and derive a condition on the amplitude and the wave number of the rolls which is necessary and sufficent for stability. Moreover, we characterize the set of those wave vectors which give rise to unstable perturbations. Dedicated to Professor K. Kirchg?ssner on the occasion of his sixty-fifth birthday Received: 25 October 1996 / Accepted: 24 March 1997     

RETRACTED: The free energy of mixing for n-variant martensitic phase transformations using quasi-convex analysis

This article has been retracted at the request of the author and editor.Reason: The above paper was published without fully incorporating all the required corrections. The corrected paper is published in Journal of the Mechanics and Physics of Solids, 51/4, I-XXVI. An erratum also immediately precedes the corrected article, p. 763.     

Algebra for a BRST Quantization of Metric-Affine Gravity

For a general gauge-theoretical formulation of gravitational interactions, we analyze the first algebraic steps towards a quantization via BRST ghost operators, replacing the Lagrange multipliers of the classical Hamiltonian constraints. From the nilpotency of the BRST charge, we deduce new restrictions on torsion and curvature of Yang-Mills type metric-affine models.     

Similarity renormalization of the electron-phonon coupling

We study the problem of the phonon-induced electron-electron interaction in a solid. Starting with a Hamiltonian that contains an electron-phonon interaction, we perform a similarity renormalization transformation to calculate an effective Hamiltonian. Using this transformation singularities due to degeneracies are avoided explicitly. The effective interactions are calculated to second order in the electronphonon coupling. It is shown that the effective interaction between two electrons forming a Cooper pair is attractive in the whole parameter space. For a simple Einstein model we calculate the renormalization of the electronic energies and the critical temperature of superconductivity.     

CH stretching vibration of N-methylformamide as a sensitive probe of its complexation: infrared matrix isolation and computational study

The complexes between trans-N-methylformamide (t-NMF) and Ar, N(2), CO, H(2)O have been studied by infrared matrix isolation spectroscopy and/or ab initio calculations. The infrared spectra of NMF/Ne, NMF/Ar and NMF/N(2)(CO,H(2)O)/Ar matrices have been measured and the effect of the complexation on the perturbation of t-NMF frequencies was analyzed. The geometries of the complexes formed between t-NMF and Ar, N(2), CO and H(2)O were optimized in two steps at the MP2/6-311++G(2d,2p) level of theory. The four structures, found for every system at this level, were reoptimized on the CP-corrected potential energy surface; both normal and CP corrected harmonic frequencies and intensities were calculated. For every optimized structure the interaction energy was partitioned according to the SAPT scheme and the topological distribution of the charge density (AIM theory) was performed. The analysis of the experimental and theoretical results indicates that the t-NMF-N(2) and CO complexes present in the matrices are stabilized by very weak N-H···N and N-H···C hydrogen bonds in which the N-H group of t-NMF serves as a proton donor. In turn, the t-NMF-H(2)O complex present in the matrix is stabilized by O-H···O(C) hydrogen bonding in which the carbonyl group of t-NMF acts as a proton acceptor. Both, the theoretical and experimental results indicate that involvement of the NH group of t-NMF in formation of very weak hydrogen bonds with the N(2) or CO molecules leads to a clearly noticeable red shift of the CH stretching wavenumber whereas engagement of the CO group as a proton acceptor triggers a blue shift of this wavenumber.     

The photoinduced isomerization and its implication in the photo-dynamical processes in two simple Schiff bases isolated in solid argon

Two Schiff bases: 2-(1-(methylimino)methyl)-phenol (SMA) and its chlorosubstituted derivative 2-(1-(methylimino)methyl)-6-chlorophenol (SMAC), and SMA complexes with water were studied by infrared matrix isolation spectroscopy and DFT/B3LYP/6-311G++(2d,2p) quantum chemical calculations. SMA and SMAC bases trapped in an argon matrix from the vapor above the liquid and solid samples have the most stable enol conformation with intramolecular O-H···N bonding. Irradiation (λ > 320 nm) leads in both bases to a rotational isomerization reaction in which the scission of the O-H···N bond occurs and the C(H)NCH(3) and OH groups are turned by 180° around the C-C and C-O bonds, respectively. In SMAC a competitive photoreaction channel yields the trans-keto tautomer. The identification of the two SMAC photoproducts evidences that in the excited enol form of this compound two processes compete with each other: the rotational isomerization and intramolecular proton transfer (ESIPT). In the argon matrices doped with SMA and H(2)O the SMA-water complexes were identified and characterized spectroscopically. Interaction of SMA with one or two water molecules does not affect the photochemistry of SMA.     

Formulation of thermoelastic dissipative material behavior using GENERIC

We show that the coupled balance equations for a large class of dissipative materials can be cast in the form of GENERIC (General Equations for Non-Equilibrium Reversible Irreversible Coupling). In dissipative solids (generalized standard materials), the state of a material point is described by dissipative internal variables in addition to the elastic deformation and the temperature. The framework GENERIC allows for an efficient derivation of thermodynamically consistent coupled field equations, while revealing additional underlying physical structures, like the role of the free energy as the driving potential for reversible effects and the role of the free entropy (Massieu potential) as the driving potential for dissipative effects. Applications to large and small-strain thermoplasticity are given. Moreover, for the quasistatic case, where the deformation can be statically eliminated, we derive a generalized gradient structure for the internal variable and the temperature with a reduced entropy as driving functional.     

A gradient structure for systems coupling reaction–diffusion effects in bulk and interfaces

We derive gradient-flow formulations for systems describing drift-diffusion processes of a finite number of species which undergo mass-action type reversible reactions. Our investigations cover heterostructures, where material parameter may depend in a nonsmooth way on the space variable. The main results concern a gradient-flow formulation for electro-reaction–diffusion systems with active interfaces permitting drift-diffusion processes and reactions of species living on the interface and transfer mechanisms allowing bulk species to jump into an interface or to pass through interfaces. The gradient flows are formulated in terms of two functionals: the free energy and the dissipation potential. Both functionals consist of a bulk and an interface integral. The interface integrals determine the interface dynamics as well as the self-consistent coupling to the model in the bulk. The advantage of the gradient structure is that it automatically generates thermodynamically consistent models.