On a model of phase relaxation for the hyperbolic Stefan problem

In this paper we study a model of phase relaxation for the Stefan problem with the Cattaneo–Maxwell heat flux law. We prove an existence and uniqueness result for the resulting problem and we show that its solution converges to the solution of the Stefan problem as the two relaxation parameters go to zero, provided a relation between these parameters holds.     

Stress Tensor Fluctuations and Passive Quantum Gravity

The quantum fluctuations of the stress tensor of a quantum field are discussed, as are the resulting space-time metric fluctuations. Passive quantum gravity is an approximation in which gravity is not directly quantized, but fluctuations of the space-time geometry are driven by stress tensor fluctuations. We discuss a decomposition of the stress tensor correlation function into three parts, and consider the physical implications of each part. The operational significance of metric fluctuations and the possible limits of validity of semiclassical gravity are discussed.     

Fluorescence Study of Excited-State Relaxation Processes of 2-Pyridyl-5-Aryloxazoles

Anomalously high fluorescence spectrum Stokes' shifts of 2(4-pyridyl)-5-(4-methylphenyl)oxazole, 2(4-pyridyl)-5-(4-methoxyphenyl)oxazole, 2(4-pyridyl)-5-(4-N,N-dimethylaminophenyl)oxazole have been found. The fluorescence spectra of the compounds studied are shifted to longer wavelengths as the solvent dielectric constant increases. The dipole moments of these compounds increase by 3–4 times upon excitation. The fluorescence spectra of the compounds investigated are shifted to shorter wavelengths, and the fluorescence quantum yields increase as the temperature decreases. The fluorescence rate constant of 2(4-pyridyl)-5-(4-N,N-dimethylaminophenyl)oxazole changes slightly as the temperature decreases from 293 K (relaxed state) to 114 K (mainly nonrelaxed state). It was concluded that the anomalously high fluorescence Stokes' shift of 2-pyridyl-5-aryloxazole derivatives is caused by solvent orientation relaxation.     

Convergence analysis of time-point relaxation iterates for linear systems of differential equations

We study convergence properties of time-point relaxation (TR) Runge-Kutta methods for linear systems of ordinary differential equations. TR methods are implemented by decoupling systems in Gauss-Jacobi, Gauss-Seidel and successive overrelaxation modes (continuous-time iterations) and then solving the resulting subsystems by means of continuous extensions of Runge-Kutta (CRK) methods (discretized iterations). By iterating to convergence, these methods tend to the same limit called diagonally split Runge-Kutta (DSRK) method. We prove that TR methods are equivalent to decouple in the same modes the linear algebraic system obtained by applying DSRK limit method. This issue allows us to study the convergence of TR methods by using standard principles of convergence of iterative methods for linear algebraic systems. For a particular problem regions of convergence are plotted.     

RELAXATION TIME LIMITS PROBLEM FOR HYDRODYNAMIC MODELS IN SEMICONDUCTOR SCIENCE

In this article, two relaxation time limits, namely, the momentum relaxation time limit and the energy relaxation time limit are considered. By the compactness argument, it is obtained that the smooth solutions of the multidimensional nonisentropic Euler-Poisson problem converge to the solutions of an energy transport model or a drift diffusion model, respectively, with respect to different time scales.     

A rheological analysis of interactions in phenoxy/organoclay nanocomposites

Novel oscillatory flow results of phenoxy/organoclay nanocomposites are analysed considering the blocking effect of nanostructure on polymer chain mobility. The modification provoked by this hindering effect on loss tangent spectrum is investigated. The study of three different systems, involving a pristine montmorillonite and two montmorillonites modified with one alkyl tail and two alkyl tails, respectively, leads to conclude that polymer-alkyl repulsive interactions play the most important role in the chain mobility obstruction process. Our results suggest that polymer-alkyl interactions increase with temperature.     

Orientation and relaxation of polymer–clay solutions studied by rheology and small-angle neutron scattering

The influence of shear on viscoelastic solutions of poly(ethylene oxide) (PEO) and clay [montmorillonite, i.e., Cloisite NA+ (CNA)] was investigated with rheology and small-angle neutron scattering (SANS). The steady-state viscosity and SANS were used to measure the shear-induced orientation and relaxation of the polymer and clay platelets. Anisotropic scattering patterns developed at much lower shear rates than in pure clay solutions. The scattering anisotropy saturated at low shear rates, and the CNA clay platelets aligned with the flow, with the surface normal parallel to the gradient direction. The cessation of shear led to partial and slow randomization of the CNA platelets, whereas extremely fast relaxation was observed for laponite (LRD) platelets. These PEO–CNA networklike solutions were compared with previously reported PEO–LRD networks, and the differences and similarities, with respect to the shear orientation, relaxation, and polymer–clay interactions, were examined. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3102–3112, 2004     

Anomalies of attenuation and phase velocity of surface acoustic waves in YBa2Cu3O7‒δ thin films in the vicinity of Tc

We present measurements of the attenuation and phase velocity of surface acoustic waves in thin YBa₂Cu₃O films as a function of temperature, in magnetic fields up to 3.6 T applied parallel to the c-axis of the films. We have observed anomalies in both, the attenuation and the phase velocity in the vicinity of the superconducting critical temperature which do not depend on the magnetic field. Possible origins of these anomalies, observed, to our knowledge, for the first time in YBa₂Cu₃O thin films, are discussed and compared to bulk acoustic wave experiments. We present a kind of feedback technique for surface acoustic waves which improves the sensitivity of this type of measurement. The actual sensitivity limits are mentioned. Received: 7 August 1997 / Revised: 7 November 1997 / Accepted: 17 November 1997     

H andH NMR Relaxation in Hydrogen-Bonded Solids Due to a Complex Motion: Classical Jumps over a Barrier and Incoherent Tunneling

Equations for the temperature dependence of proton and deuteron spin–lattice relaxation rates and second moments due to a complex motion consisting of classical jumps over a potential barrier and quantum mechanical tunneling through the barrier have been derived. Asymmetric double and triple potential wells are considered. These equations have been employed to analyze proton spin–lattice relaxation data for solid naphthazarin in the laboratory and rotating frames as a function of temperature. It is shown that tunneling plays an important role in the proton transfer dynamics of this compound.