A Verified Optimization Technique to Locate Chaotic Regions of Hénon Systems

We present a new verified optimization method to find regions for Hénon systems where the conditions of chaotic behaviour hold. The present paper provides a methodology to verify chaos for certain mappings and regions. We discuss first how to check the set theoretical conditions of a respective theorem in a reliable way by computer programs. Then we introduce optimization problems that provide a model to locate chaotic regions. We prove the correctness of the underlying checking algorithms and the optimization model. We have verified an earlier published chaotic region, and we also give new chaotic places located by the new technique.     

A systematic elimination procedure for Ito stochastic differential equations and the adiabatic approximation

We study a class of nonlinear Ito stochastic differential equations (with possibly state dependent diffusion coefficients), in which the variables can be divided into linearly damped (slaved) variables s and linearly undamped variablesu (order parameters). We devise a systematic and constructive procedure to eliminate the slaved variables. We take explicit time and chance dependence of the slaved variables into account, the latter via a family of diffusion processesZ _t ^(v) . These act as fluctuating coefficients of the Center Manifolds _t=s(u _t, t,Z _t ^(v) (v=2, 3, ...)) and appear explicitly in the elimination procedure. We show how in the Ito calculus fluctuating and deterministic coefficients of the Center Manifold are more completely separated than in the previously treated Stratonovich case [1]. The adiabatic approximation is defined as a partial summation of the elimination expansion and the stochastic generalization ofs=0 is derived. We show how thus ambiguity of stochastic calculi is removed. Closed form summations are given in two examples. We briefly indicate the potential use of perturbation theory techniques in the systematic elimination procedure.     

Potential for micromachined actuation of ultra-wide continuously tunable optoelectronic devices

Tailored scaling represents a principle of success that, both in nature and in technology, allows the effectiveness of physical effects to be enhanced. Mutation and selection in nature are imitated in technology, e.g. by model calculation and design. Proper scaling of dimensions in natural photonic crystals and our fabricated artificial 1D photonic crystals (DBRs, distributed Bragg reflectors) enable efficient diffractive interaction in a specific spectral range. For our optical microsystems we illustrate that tailored miniaturization may also increase the mechanical stability and the effectiveness of spectral tuning by thermal and electrostatic actuation, since the relative significance of the fundamental physical forces involved considerably changes with scaling. These basic physical principles are rigorously applied in micromachined 1.55-μm vertical-resonator-based devices. We modeled, implemented and characterized 1.55-μm micromachined optical filters and vertical-cavity surface-emitting laser devices capable of wide, monotonic and kink-free tuning by a single control parameter. Tuning is achieved by mechanical actuation of one or several air-gaps that are part of the vertical resonator including two ultra-highly reflective DBR mirrors of strong refractive index contrast: (i) Δn=2.17 for InP/air-gap DBRs (3.5 periods) using GaInAs sacrificial layers and (ii) Δn=0.5 for Si₃N₄/SiO₂ DBRs (12 periods) with a polymer sacrificial layer to implement the air-cavity. In semiconductor multiple air-gap filters, a continuous tuning of >8% of the absolute wavelength is obtained. Varying the reverse voltage (U=0–5 V) between the membranes (electrostatic actuation), a tuning range of >110 nm was obtained for a large number of devices. The correlation of the wavelength and the applied voltage is accurately reproducible without any hysteresis. In two filters, tuning of 127 and 130 nm was observed for about ΔU=7 V. The extremely wide tuning range and the very small voltage required are record values to the best of our knowledge. For thermally actuated dielectric filters based on polymer sacrificial layers, Δλ/ΔU=-7 nm/V is found. Received: 10 May 2002 / Published online: 8 August 2002     

Electronic properties of model quantum-dot structures in zero and finite magnetic fields

We have computed electronic structures and total energies of circularly confined two-dimensional quantum dots and their lateral dimers in zero and finite uniform external magnetic fields using different theoretical schemes: the spin-density-functional theory (SDFT), the current-and-spin-density-functional theory (CSDFT), and the variational quantum Monte Carlo (VMC) method. The SDFT and CSDFT calculations employ a recently-developed, symmetry-unrestricted real-space algorithm allowing solutions which break the spin symmetry. Results obtained for a six-electron dot in the weak confinement limit and in zero magnetic field as well as in a moderate confinement and in finite magnetic fields enable us to draw conclusions about the reliability of the more approximative SDFT and CSDFT schemes in comparison with the VMC method. The same is true for results obtained for the two-electron quantum dot dimer as a function of inter-dot distance. The structure and role of the symmetry-breaking solutions appearing in the SDFT and CSDFT calculations for the above systems are discussed. Received 16 October 2001 and Received in final form 17 January 2002     

Tracing Possible Structural Asymmetry of Silica Gel Used for Precoating Thin-Layer Chromatography Plates

JPC – Journal of Planar Chromatography – Modern TLC - We have previously described unexpected two-dimensionality in the thin-layer chromatographic separation of pairs of enantiomers of...     

Ultrasonic evaluation of anisotropic damage in multiaxially textile-reinforced thermoplastic composites made from hybrid yarns

The basic damage and failure models of multiaxially reinforced composites with a thermoplastic matrix are presented and verified. Within the framework of continuum damage mechanics, a phenomenological model is introduced, where the damage is defined as a change in the elasticity tensor. For damage identification, a specific ultrasonic device was developed. A combination of an immersion set-up and a contact coupling device formed a system for an efficient determination of stiffness-tensor components from convenient sets of velocity measurements. Linked to a tensile machine, it allowed us to measure the anisotropic damage of the new materials group caused by tensile loading. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 2, pp. 221–234, March–April, 2006.     

A note on the Σ1 spectrum of a theory

Let T be a suitable system of classical set theory. We will show, that the Σ₁ spectrum of T, i.e. the set of ordinals having good Σ₁ definition in T is an initial segment of the ordinals. Received: 11 October 1999 / Published online: 12 December 2001     

Orderings of uniquely colorable hypergraphs

For a mixed hypergraph H=(X,C,D), where C and D are set systems over the vertex set X, a coloring is a partition of X into ‘color classes’ such that every C∈C meets some class in more than one vertex, and every D∈D has a nonempty intersection with at least two classes. A vertex-orderx₁,x₂,…,x_n on X (n=|X|) is uniquely colorable if the subhypergraph induced by {x_j:1?j?i} has precisely one coloring, for each i (1?i?n). We prove that it is NP-complete to decide whether a mixed hypergraph admits a uniquely colorable vertex-order, even if the input is restricted to have just one coloring. On the other hand, via a characterization theorem it can be decided in linear time whether a given color-sequence belongs to a mixed hypergraph in which the uniquely colorable vertex-order is unique.     

Optical properties of in situ doped and undoped titania nanocatalysts and doped titania sol-gel nanofilms

In this paper we present spectroscopic properties of doped and undoped titanium dioxide (TiO₂) as nanofilms prepared by the sol-gel process with rhodamine 6G doping and studied by photoacoustic absorption, excitation and emission spectroscopy. The absorption spectra of TiO₂ thin films doped with rhodamine 6G at very low concentration during their preparation show two absorption bands, one at 2.3 eV attributed to molecular dimmer formation, which is responsible for the fluorescence quenching of the sample and the other at 3.0 eV attributed to TiO₂ absorption, which subsequently yields a strong emission band at 600 nm. The electronic band structure and optical properties of the rutile phase of TiO₂ are calculated employing a fully relativistic, full-potential, linearized, augmented plane-wave (FPLAPW) method within the local density approximation (LDA). Comparison of this calculation with experimental data for TiO₂ films prepared for undoped sol-gels and by sputtering is performed.