牛顿弦截法预估校正迭代格式的收敛阶

研究如下形式的牛顿弦截法的预估校正(P.C.)格式:P(预估):~xk+1=xk-(xk-xk-1)f(xk)f(xk)-f(xk-1)C(校正):xk+1=xk-(~xk+1-xk)f(xk)f~(xk+1)-f(xk)证明了它的收敛阶为2.618.     

Long-time dynamics of von Karman semi-flows with non-linear boundary/interior damping

We study von Karman evolution equations with non-linear dissipation and with partially clamped and partially free boundary conditions. Two distinctive mechanisms of dissipation are considered: (i) internal dissipation generated by non-linear operator, and (ii) boundary dissipation generated by shear forces friction acting on a free part of the boundary. The main emphasis is given to the effects of boundary dissipation. Under suitable hypotheses we prove existence of a compact global attractor and finiteness of its fractal dimension. We also show that any solution is stabilized to an equilibrium and estimate the rate of the convergence which, in turn, depends on the behaviour at the origin of the functions describing the dissipation.     

Resolvability properties via independent families

The authors give a consistent affirmative response to a question of Juhász, Soukup and Szentmiklóssy: If GCH fails, there are (many) extraresolvable, not maximally resolvable Tychonoff spaces. They show also in ZFC that for ω<λ?κ, no maximal λ-independent family of λ-partitions of κ is ω-resolvable. In topological language, that theorem translates to this: A dense, ω-resolvable subset of a space of the form (DI(λ)) is λ-resolvable.     

On the pivot structure for the weighing matrix W(12,11)

In the present article we concentrate our study on the growth problem for the weighing matrix W(12,11) and show that the unique W(12,11) has three pivot structures. An improved algorithm for extending a k × k (0,+,-) matrix to a W(n,n-1), if possible, has been developed to simplify the proof. For the implementation of the algorithm special emphasis is given to the notions of data structures and parallel processing.     

Sympathetic cooling rate of gas-phase ions in a radio-frequency-quadrupole ion trap

We theoretically investigated the mass dependence of the sympathetic cooling rate of gas-phase ions trapped in a linear radio-frequency-quadrupole ion trap. Using an a priori molecular dynamical calculation, tracing numerically with Newtonian equations of motion, we found that ions with a mass greater than 0.54±0.04 times that of the laser-cooled ions are sympathetically cooled; otherwise, they are heated. To understand the mass dependence obtained using the molecular-dynamical calculation, we made a heat-exchange model of sympathetic cooling, which shows that the factor of 0.54±0.04 is a consequence of absence of micro-motion along the axis of the linear ion trap. Received: 10 December 2001 / Revised version: 28 January 2002 / Published online: 14 March 2002     

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     

Material tensor parameters of LiNbO3 relevant for electro- and elasto-optics

The complete set of self-consistent parameters of nominally undoped LiNbO₃ crystals of congruent composition that describe the electro-optic, piezoelectric, elasto-optic, elastic, and dielectric response has been determined by numerically evaluating available measurements. The parameters were determined at room temperature and consist of the low-frequency clamped dielectric constants ε^S _ij, elastic stiffness constants at constant electric field C^E _ijkl, piezoelectric stress coefficients e_ijk, elasto-optic constants at constant electric field p^E _ijkl, and clamped electro-optic coefficients r^S _ijk. It is shown that the complete set is required for calculating the effective electro-optic coefficients and dielectric constants in photorefractive applications of LiNbO₃. Received: 4 January 2002 / Revised version: 1 February 2002 / Published online: 14 March 2002     

Magnetic anisotropy of textured CrO2 thin films investigated by X-ray magnetic circular dichroism

Highly a-axis-textured CrO₂ films have been deposited on Al₂O₃ (0001) substrates by chemical vapor deposition. CrO₂ has been found to have highly a-axis (010)-oriented columnar growth on a Cr₂O₃ (0001) initial layer. The six-fold surface symmetry of the Cr₂O₃ initial layer leads to three equivalent in-plane orientations of the a-axis-oriented CrO₂ unit cell. We report Cr L_2,3 X-ray magnetic circular dichroism data along the surface normal and at 60° off-normal sample orientation. For a 60° sample alignment, a strong increase of the projected orbital moment could be observed for unoccupied majority t_2g states using moment analysis. Therefore, the c axis is identified as the intrinsic magnetic easy axis of CrO₂. In addition, a small spin moment and a very strong magnetic dipole term T_z have been found. Received: 8 January 2002 / Accepted: 8 January 2002     

The time recovery of the spectroscopic properties of heavily irradiated CdZnTe and CdTe detectors

The time recovery of the spectroscopic capabilities of CdZnTe and CdTe detectors, irradiated with increasing doses of high- and low-energy neutrons, as well as electrons, has been investigated by studying their spectroscopic behavior at different photon energies using leakage current measurements and PICTS (photo-induced current transient spectroscopy) analysis. The detectors were stored at room temperature for up to one year to study the time evolution of their spectroscopic performance and to correlate it with the presence of defective states in the material. We have observed a clear improvement in the material’s detection properties with time, though only in those detectors which have not been severely degraded by the irradiation. The recovery can be associated with a decrease in the concentration of some defective states, thus allowing the assessment of the crucial role these play in determining the charge collection processes in the material and its spectroscopic capabilities. Received: 1 August 2001 / Accepted: 3 August 2001 / Published online: 20 December 2001     

The treatment of nonhomogeneous Dirichlet boundary conditions by thep-version of the finite element method

Summary The paper addresses the problem of the implementation of nonhomogeneous essential Dirichlet type boundary conditions in thep-version of the finite element method.Partially supported by the Office of Naval Research under Grant N-00014-85-K-0169Research partially supported by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant Number AFOSR 85-0322