Lower bounds for boundary roughness for droplets in Bernoulli percolation

We consider boundary roughness for the ``droplet' created when supercritical two-dimensional Bernoulli percolation is conditioned to have an open dual circuit surrounding the origin and enclosing an area at least l², for large l. The maximum local roughness is the maximum inward deviation of the droplet boundary from the boundary of its own convex hull; we show that for large l this maximum is at least of order l^1/3(logl)^–2/3. This complements the upper bound of order l^1/3(logl)^–2/3 proved in [Al3] for the average local roughness. The exponent 1/3 on l here is in keeping with predictions from the physics literature for interfaces in two dimensions. The research of the first author was supported by NSF grant DMS-9802368. The research of the second author was supported by NSF grants DMS-9802368 and DMS-0103790.Mathematics Subject Classification (2000): Primary 60K35; Secondary 82B20, 82B43     

Initial data truncation for multivariate output of discrete-event simulations using the Kalman filter

Data truncation is a commonly accepted method of dealing with initialization bias in discrete-event simulation. An algorithm for determining the appropriate initial-data truncation point for multivariate output is proposed. The technique entails averaging across independent replications and estimating a steady-state output model in a state-space framework. A Bayesian technique called Multiple Model Adaptive Estimation (MMAE) is applied to compute a time varying estimate of the output's steady-state mean vector. This MMAE implementation features the use, in paralle, of a bank of Kalman filters. Each filter is constructed under a different assumption concerning the output's steady-state mean vector. One of the filters assumes that the steady-state mean vector is accurately reflected by an estimate, called the assumed steady-state mean vector, taken from the last half of the simulation data. As the filters process the output through the effective transient, this particular filter becomes more likely (in a Bayesian sense) to be the best filter to represent the data and the MMAE mean estimator is influenced increasingly towards the assumed steady-state mean vector. The estimated truncation point is selected when a norm of the MMAE mean vector estimate is within a small tolerance of the assumed steady-state mean vector. A Monte Carlo analysis using data from simulations of open and closed queueing models is used to evaluate the technique. The evaluation criteria include the ability to construct accurate and reliable confidence regions for the mean response vector based on the truncated sequences.     

Valence state and magnetic interactions in magnetically ordered Eu(Pd1−x Au x )2Si2

X-ray diffraction,¹⁵¹Eu Mössbauer effect (ME) and magnetic susceptibility measurements have been performed to investigate the valence behavior and the magnetic interactions of the Eu ions in the intermetallic series Eu(Pd_1–x Au _x )₂Si₂ (0x1) as a Forx>0.4 all experimental techniques are in agreement with each other and suggest a divalent 4f ⁷ ground state of the Eu ion. Belowx=0.4 the different methods lead to different results: while the lattice parameters and the ME isomer shift suggest an instable behavior of the valence the magnetic susceptibility proves a pure divalent 4f ⁷ ground state. These differences can be explained by assuming a partial extension of the 4f-shell radius such that the localized character of the 4f-electrons is preserved.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday     

Finite element modal solutions of planar photonic crystal fibers with rectangular air-holes

Modal solutions of planar photonic crystal waveguides with rectangular air-holes are presented by using a rigorous full-vectorial finite element-based approach. The effective indices, mode field profiles, spot-sizes, power confinements, modal hybridness, beat lengths and group velocity dispersions are shown for the fundamental and higher order modes of the quasi-TE and TM polarizations.     

Delay-coordinates embeddings as a data mining tool for denoising speech signals

In this paper, we utilize techniques from the theory of nonlinear dynamical systems to define a notion of embedding estimators. More specifically, we use delay-coordinates embeddings of sets of coefficients of the measured signal (in some chosen frame) as a data mining tool to separate structures that are likely to be generated by signals belonging to some predetermined data set. We implement the embedding estimator in a windowed Fourier frame, and we apply it to speech signals heavily corrupted by white noise. Our experimental work suggests that, after training on the data sets of interest, these estimators perform well for a variety of white noise processes and noise intensity levels.     

Nanoscale laser-induced forward transfer through patterned Cr films

The resolution enhancement of laser-induced forward transfer (LIFT) is investigated through the pre-patterning of Cr on the donor substrate. 85 nm dots are first patterned on a microscope slide, and an 800 nm wavelength and 130 fs pulse laser with a beam waist of ～9 μm is used to transfer the Cr dots to an acceptor substrate. The threshold fluence is found to be ～0.15 the threshold fluence of a similar continuous film, which is thought to be due to the fact that no force is needed to tear away Cr from the film itself, unlike in a continuous film experiment. Since the volume of the material limits the transfer feature sizes instead of the laser parameters, as in a continuous film system, minimum transferable feature diameters are significantly lower compared to the continuous film case. Also, the transferred feature diameters are not dependent on the laser parameters, so the diameters are consistent across a wide range of fluences. The force per unit area generated by the laser at threshold fluence is estimated to be ～3 GPa, which is consistent with previous results in the literature. The simplified model that our pre-patterned Cr LIFT experiment represents would make it an ideal case for benchmarking molecular dynamics simulations of femtosecond laser ablation.     

Manipulating supercontinuum generation by minute continuous wave

We report a simple triggering mechanism that greatly enhances and stabilizes supercontinuum generation by using an extremely weak cw light (~200,000 times weaker than the pump light). Such an active manipulation scheme can be enabled by a wide range of input conditions and circumvents complex techniques such as precise time delay tuning and dedicated feedback control. It thus offers a handy and versatile approach to control and optimize supercontinuum generation, expanding its range of applications, including ultrafast all-optical signal processing, spectroscopy, and imaging. The utility of the present technique for improving signal integrity in chirped pump optical parametric amplification is also demonstrated.