Vanadium valency charge state in solid solutions ScNb2−2xTa2xVO9

Phase equilibria in the Sc₂O₃-V₂O₅-Nb₂O₅-Ta₂O₅ system and properties of ScNb_2−2xTa_2xVO₉ phases were studied by X-ray phase analysis, optical and radio spectroscopy. A continuous series of solid solutions was shown to exist at 0≤x≤1. V(IV) centers with different crystallographic surrounding were detected for all the considered compositions. A correlation between the number of V(IV) ions and the width of the forbidden gap in the solid solutions was found.     

Likelihood Ratio Processes for Markovian Particle Systems with Killing and Jumps

We consider Markov processes built from pasting together pieces of strong Markov processes which are killed at a position dependent rate and connected via a transition kernel. We give necessary and sufficient conditions for local absolute continuity of probability laws for such processes on a suitable path space and derive an explicit formula for the corresponding likelihood ratio process. The main tool is the consideration of the process between successive jumps – what we call ‘elementary experiments’ – and criteria for absolute continuity of laws of the process there. We apply our results to systems of branching diffusions with interactions and immigrations. This revised version was published online in June 2006 with corrections to the Cover Date.     

Relativistic Notion of Mass and a Resolution of a Conflict Between Schopenhauer and Hegel

We discuss a mass change that has its origin in the action of forces on an object. This phenomenon, well-known in the context of quantum field theory (mass renormalization), can be discussed systematically in both classical and quantum mechanics in a framework given by Stückelberg. We employ this framework to resolve an interesting conflict of opinions between Schopenhauer and Hegel in the mid-19th century. We show that Hegel, Kant, and Schopenhauer demonstrated remarkable prescience in their views as seen from a modern perspective.     

Changes in the kurtosis parameter of super-Gaussian beams passing through a spherically aberrated lens

Based on the Collins formula and irradiance moments definition, the propagation of the kurtosis parameter of super-Gaussian beams through a spherically aberrated lens is studied. Detailed numerical results are given. It is shown that, as compared with aberration-free super-Gaussian beams, the profile of spherically aberrated super-Gaussian beams can be leptokurtic, mesokurtic or platykurtic, depending on the aberration and propagation distance. The results for the spherically aberrated Gaussian beams can be dealt with as a special case treated in this paper. Finally, the advantage of our method is pointed out.     

Equilibrium point damage prognosis models for structural health monitoring

Most structural dynamic systems are of high order; however, they often exhibit phenomena that can be dealt with effectively using low order models. This paper presents a method for describing certain kinds of damage evolution in mechanical systems. The method relies on a simple principle that as damage evolves in a structural dynamic system, the damage indicator (i.e., diagnostic feature) behaves like a stable quasi-stationary equilibrium point in a subsidiary non-linear bifurcating system within the so-called damage center manifold. It is shown that just as linear normal modes govern the behavior of linear structures with idealized damping, so too do non-linear normal forms govern the evolution of damage within structures in many instances. The method is justified with citations from the literature on certain types of mechanical failure and then applied in an experimental case involving reversible damage in a bolted fastener. Off-line experiments on a rotorcraft fuselage show that the evolution of damage is sensitive to both temporal and spatial bifurcation parameters. A diagnostic sensing strategy whereby output-only transmissibility features are used to decrease the order of high order structural dynamic measurements is also described.     

Conformational analysis of dipeptide‐derived polyisocyanides

The conformational properties of polymers derived from isocyanodipeptides have been investigated with a combination of model calculations, X‐ray diffraction, and circular dichroism spectroscopy. Depending on the configuration of the side chains, defined arrays of hydrogen bonds along the polymeric backbone are formed. This leads to a well‐defined conformation as, for example, expressed in the formation of lyotropic liquid‐crystalline phases and increased helical stability. Upon the disruption of the hydrogen bonds by a strong acid, a less well‐defined macromolecular conformation is observed. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1725–1736, 2003     

Quantum chaos and fractals with atoms in cavities

We study the coupled translational, electronic, and field dynamics of the combined system “a two-level atom + a single-mode quantized field + a standing-wave ideal cavity”. In the semiclassical approximation with a point-like atom, interacting with the classical field, the dynamics is described by the Heisenberg equations for the atomic and field expectation values which are known to produce semiclassical chaos under appropriate conditions. We derive Hamilton–Schrödinger equations for probability amplitudes and averaged position and momentum of a point-like atom interacting with the quantized field in a standing-wave cavity. They constitute, in general, an infinite-dimensional set of equations with an infinite number of integrals of motion which may be reduced to a dynamical system with four degrees of freedom if the quantized field is supposed to be initially prepared in a Fock state. This system is found to produce semiquantum chaos with positive values of the maximal Lyapunov exponent. At exact resonance, the semiquantum dynamics is regular. At large values of detuning |δ|1, the Rabi atomic oscillations are usually shallow, and the dynamics is found to be almost regular. The Doppler–Rabi resonance, deep Rabi oscillations that may occur at any large value of |δ| to be equal to |αp₀|, is found numerically and described analytically (with α to be the normalized recoil frequency and p₀ the initial atomic momentum). Two gedanken experiments are proposed to detect manifestations of semiquantum chaos in real experiments. It is shown that in the chaotic regime values of the population inversion z_out, measured with atoms after transversing a cavity, are so sensitive to small changes in the initial inversion z_in that the probability of detecting any value of z_out in the admissible interval [−1,1] becomes almost unity in a short time. Chaotic wandering of a two-level atom in a quantized Fock field is shown to be fractal. Fractal-like structures, typical with chaotic scattering, are numerically found in the dependence of the time of exit of atoms from the cavity on their initial momenta.     

Nonequilibrium Ionization by Vibrationally Excited Molecules in Supersonic Flows

The results of experimental investigations on thermal nonequilibrium ionization in CO₂: N₂: He mixtures are presented. Measurements of electron density, n_e, in vibrationally excited nitrogen were made in a supersonic flow with different CO₂ contents as well as in a CO₂: N₂: He = 1 : 5 : 4 mixture laser gas. The mixtures were heated in a shock tube and expanded through a supersonic nozzle. Furthermore, supersonic mixing of N₂ and CO₂ + He was used in some experiments. The measured values of n_e in the plenum chamber and in the supersonic nozzle are reported, and the processes responsible for nonequilibrium ionization in a laser-active medium are discussed.