Ergodic theory and the Strong Law of Large Numbers on Riesz spaces

In [W.-C. Kuo, C.C.A. Labuschagne, B.A. Watson, Discrete-time stochastic processes on Riesz spaces, Indag. Math. (N.S.) 15 (3) (2004) 435-451], we introduced the concepts of conditional expectations, martingales and stopping times on Riesz spaces. Here we formulate and prove order theoretic analogues of the Birkhoff, Hopf and Wiener ergodic theorems and the Strong Law of Large Numbers on Riesz spaces (vector lattices).     

Artificial time integration

Many recent algorithmic approaches involve the construction of a differential equation model for computational purposes, typically by introducing an artificial time variable. The actual computational model involves a discretization of the now time-dependent differential system, usually employing forward Euler. The resulting dynamics of such an algorithm is then a discrete dynamics, and it is expected to be “close enough” to the dynamics of the continuous system (which is typically easier to analyze) provided that small – hence many – time steps, or iterations, are taken. Indeed, recent papers in inverse problems and image processing routinely report results requiring thousands of iterations to converge. This makes one wonder if and how the computational modeling process can be improved to better reflect the actual properties sought. In this article we elaborate on several problem instances that illustrate the above observations. Algorithms may often lend themselves to a dual interpretation, in terms of a simply discretized differential equation with artificial time and in terms of a simple optimization algorithm; such a dual interpretation can be advantageous. We show how a broader computational modeling approach may possibly lead to algorithms with improved efficiency. AMS subject classification (2000)  65L05, 65M32, 65N21, 65N22, 65D18     

Existence Results for Semilinear Neutral Functional Differential Inclusions via Analytic Semigroups

In this paper we prove existence results for semilinear neutral functional differential inclusions with finite or infinite delay in Banach spaces. Our theory makes use of analytic semigroups and fractional powers of closed operators, integrated semigroups and cosine families.      

Stored energy release behaviour of disordered carbon

The use of graphite as a moderator in a low temperature thermal nuclear reactor is restricted due to accumulation of energy caused by displacement of atoms by neutrons and high energetic particles. Thermal transients may lead to a release of stored energy that may raise the temperature of the fuel clad above the design limit. Disordered carbon is thought to be an alternative choice for this purpose. Two types of disordered carbon composites, namely, CB (made up of 15 wt. % carbon black dispersed in carbonized phenolic resin) and PAN (made up of 20 vol. % chopped polyacrylonitrile carbon fibre dispersed in carbonized phenolic resin matrix) have been irradiated with 145 MeV Ne⁶⁺ ions at three fluence levels of 1.0×10¹³, 5.0×10¹³ and 1.5×10¹⁴ Ne⁶⁺/cm², respectively. The XRD patterns revealed that both the samples remained disordered even after irradiation. The maximum release of stored energy for CB was 212 J/g and that of PAN was 906 J/g. For CB, the release of stored energy was a first order reaction with activation energy of 2.79 eV and a frequency factor of 3.72×10²⁸ per second. 13% of the defects got annealed by heating up to 700 °C. PAN showed a third-order release rate with activation energy of 1.69 eV and a frequency factor of 1.77×10¹⁴ per second. 56% of the total defects got annealed by heating it up to 700 °C. CB seems to be the better choice than PAN as it showed less energy release with a slower rate. PACS 61.80.Jh; 61.80.-x; 61.43Er; 61.43.-j; 68.43.Vx     

Giant shot-like voltage noise in high current density Nb–AlOx–Nb superconducting tunnel junctions

The flat voltage noise component of current biased, high-transparency Nb/AlO_x/Nb superconducting tunnel junctions has been investigated at frequencies up to 70 kHz. Several aspects of the analyzed phenomena suggest the presence of current noise effects induced by the discreteness of the charge carriers. At subgap voltages, where excess currents occur, a behavior coherent with a multiple Andreev reflection-assisted transport through the tunnel barrier has been found. However, the measured charge values exceed any theoretical prediction.     

Mode beating in spot-size converter lasers

An anomalous modulation in the wavelength spectrum has been observed in lasers with spot-size converters. This intensity modulation is shown to be caused by beating between the fundamental lasing mode and radiation modes in the taper. This results in a periodic modulation in the net gain spectrum, which causes wavelength jumps between adjacent net gain maxima, and a drive current dependent spectral width that is expected to affect system performance. The amplitude of this spectral modulation is reduced significantly by either using an angled rear-facet which reflects the beating radiation modes away from the laser axis, or by using a nonlinear, adiabatic taper.     

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     

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     

Method of linear prediction in the ultrasonic spectroscopy of rock

The possibility of using the resonant acoustic spectroscopy method for testing the internal state of rock is considered. This method can be used for the determination of the concentration of defects and their spatial distribution. A rock specimen with defects is characterized by a high loss of vibrational energy, which leads to the overlapping of the resonant responses. In this case, the complex resonant frequencies are determined as the parameters of a model that describes the measured transfer function of the response of the mechanical system. The linearity of the vibratory system is used as the a priori information for presetting the functional dependences of the model. An algorithm is developed for the determination of the parameters of the resonances in conditions of their partial overlapping. Examples are presented to demonstrate the possibility of analyzing the complex elastic constant tensor of rock by the acoustic spectroscopy method. The proposed method of experimental data processing provides the possibility for the determination of the weak anisotropy that occurs in the velocity of sound because of a partial fracture of rock.     

Antimagnons in ferrimagnets

Purely antiferromagnetic intrinsic oscillations of magnetic ions in a tetragonal ferrimagnet are considered. The magnetic ions occupy two double positions (forming four magnetic sublattices) so that the center of symmetry for each position is not a closed element. Not involving the total magnetization vector, the oscillations are not excited by the magnetic field; however, the oscillations can be excited by an alternating electric field or by a combination of a constant electric field and the alternating magnetic field of a certain frequency. This phenomenon is a dynamic manifestation of the magnetoelectric interaction. These oscillations, representing a new special type of spin waves (magnons), were called antimagnons. The intrinsic frequencies of antimagnons, as well as the corresponding susceptibilities, were determined. Quantitative estimates were obtained for a Mn₂Sb-based ferrimagnetic phase in both easy-axis and easy-plane orientation states.