On Levels in Arrangements of Surfaces in Three Dimensions

A favorite open problem in combinatorial geometry is to determine the worst-case complexity of a level in an arrangement. Up to now, nontrivial upper bounds in three dimensions are known only for the linear cases of planes and triangles. We propose the first technique that can deal with more general surfaces in three dimensions. For example, in an arrangement of n ??pseudo-planes?? or ??pseudo-spherical patches?? (where the main criterion is that each triple of surfaces has at most two common intersections), we prove that there are at most O(n ^2.997) vertices at any given level.     

Optimal Partition Trees

We revisit one of the most fundamental classes of data structure problems in computational geometry: range searching. Matoušek (Discrete Comput. Geom. 10:157–182, 1993) gave a partition tree method for d-dimensional simplex range searching achieving O(n) space and O(n ^1−1/d ) query time. Although this method is generally believed to be optimal, it is complicated and requires O(n ^1+ε ) preprocessing time for any fixed ε>0. An earlier method by Matoušek (Discrete Comput. Geom. 8:315–334, 1992) requires O(nlogn) preprocessing time but O(n ^1−1/d log ^O(1) n) query time. We give a new method that achieves simultaneously O(nlogn) preprocessing time, O(n) space, and O(n ^1−1/d ) query time with high probability. Our method has several advantages:

Drop impact characteristics and structure effects of hydrophobic surfaces with micro- and/or nanoscaled structures

We report the drop impact characteristics on four hydrophobic surfaces with different well-scale structures (smooth, nano, micro, and hierarchical micro/nano) and the effects of those structures on the behavior of water drops during impact. The specimens were fabricated using silicon wet etching, black silicon formation, or the combination of these methods. On the surfaces, the microstructures form obstacles to drop spreading and retracting, the nanostructures give extreme water-repellency, and the hierarchical micro/nanostructures facilitate drop fragmentation. The maximum spreading factor (D*(max)) differed among the structures. On the basis of published models of D*(max), we interpret the results of our experiment and suggest reasonable explanations for these differences. Especially, the micro/nanostructures caused instability of the interface between liquid and air at Weber number We > ~80 and impacting drops fragmented at We > ~150.     

Chemical imaging of protein adsorption and crystallization on a wettability gradient surface

The use of self-assembled monolayers is an established method to study the effect of surface properties on proteins and other biological materials. The generation of a monolayer with a gradient of chemical properties allows for the study of multiple surface properties simultaneously in a high throughput manner. Typically, in order to detect the presence of proteins or biological material on a surface, the use of additional dyes or tags is required. Here we present a novel method of studying the effect of gradient surface properties on protein adsorption and crystallization in situ through the use of ATR-FTIR spectroscopic imaging, which removes the need for additional labeling. We describe the successful application of this technique to the measurement of the growth of a gradient monolayer of octyltrichlorosilane across the surface of a silicon ATR element. ATR-FTIR imaging was also used to study the adsorption of lysozyme, as a model protein, onto the modified surface. The sensitivity of measurements obtained with a focal plane array (FPA) detector were improved though the use of pixel averaging which allowed small absorption bands to be detected with minimal effect on the spatial resolution along the gradient. Study of the effect of surface hydrophobicity on both adsorption of lysozyme to the element and lysozyme crystallization revealed that more lysozyme adsorbed to the hydrophobic side of the ATR element and more lysozyme crystals formed in the same region. These findings strongly suggest a correlation exists between surface protein adsorption and protein crystallization. This method could be applied to the study of other proteins and whole cells.     

Mitigation of signal suppression caused by the use of trifluoroacetic acid in liquid chromatography mobile phases during liquid chromatography/mass spectrometry analysis via post-column addition of ammonium hydroxide

A method has been developed to reduce the mass spectrometric ion signal suppression associated with the use of TFA as an additive in LC mobile phases. Through post-column infusion of diluted NH(4)OH solution to LC eluents, the ammonium ion introduced causes the neutral analyte-TFA ion pair to dissociate which consequently releases the protonated analyte as free ions into the gas phase (through regular electrospray ionization mechanisms). An ion signal improvement from 1.2 to 20 times for a variety of compounds had been achieved through the application of this method. The molar ratios of NH(4)OH:TFA which result in a reduction of signal suppression were determined to be between 0.5:1 and 50:1. In addition, it was shown that this NH(4)OH infusion method could reduce the level of doubly-charged species and the product ions formed via in-source collision. The use of diluted NH(4)OH solution is favorable since it is compatible with mass spectrometry analysis, and it is applicable in both positive and negative-ion generation mode.     

CO oxidation of bare and TiO2-coated NiO-Ni(OH)2 nanoparticles

CO oxidation reactivity of bare and TiO₂-coated nanoparticles consisting of both NiO and Ni(OH)₂ surfaces was studied. For the deposition of TiO₂, atomic layer deposition was used, and formation of three-dimensional domains of TiO₂ on NiO-Ni(OH)₂ could be identified. Based on the data of X-ray Photoelectron Spectroscopy, we suggest that upon TiO₂ deposition only Ni(OH)₂ was remained on the surface, whereas NiO surface disappeared. Both CO adsorption and CO oxidation took place on NiO-Ni(OH)₂ surfaces under our experimental conditions. CO adsorption was almost completely suppressed after TiO₂ deposition, whereas CO oxidation activity was maintained to large extent. It is proposed that bare NiO cannot be active for CO oxidation, and can only uptake CO under our experimental condition, whereas hydroxylated surface of NiO can be active for CO oxidation.     

Simultaneous strain and temperature measurement based on a photonic crystal fiber modal-interference interacting with a long period fiber grating

An alternative all-fiber sensor for simultaneous strain and temperature measurement based on a photonic crystal fiber (PCF) spliced between single-mode fibers cascaded with a long period grating (LPG) is proposed. By collapsing the air holes at two splicing regions along the PCF, a simple but effective modal-interference (MI) is occurred between the core and cladding modes of the PCF. Due to the different responses on the changes of strain and temperature on the MI and the cascaded LPG, the strain and temperature can be measured simultaneously. Experimental results show that the sensing resolution of 9.1 με in strain measurement is experimentally achieved over a range of 2640 με, while the temperature sensing resolution is 0.27 °C within a range of 30-100 °C.     

Roughness measurement of metals using a modified binary speckle image and adaptive optics

This paper proposes an integrated roughness measurement system that is based on adaptive optics (AO) and binary analysis of speckle pattern images. The aim of this study was to demonstrate the necessity for AO compensation in regions containing both heat and fluid flow turbulences. A speckle image was obtained by projecting a laser beam onto the specimen surface, and the laser pattern image reflected from the surface was binarized to experimentally correlate the intensity with the surface roughness. In the absence of the AO correction scheme, induced turbulences can severely increase the residual rms error from 0.14 to 1.4 μm. After a real-time closed-loop AO correction, we can reduce the wavefront root mean square (rms) error to 0.12 μm, which not only compensates for the aberration error from induced disturbances but also improves the overall performance of the optical system. In addition, an AO system having different gains was investigated, and a threshold gain value was found to be able to steadily compensate for the wavefront errors in less than 2 s. Measurement results of five steel samples having roughness ranging from 0.2 to 3.125 μm (0.3λ and 5λ, where λ is the diode laser wavelength) demonstrate an excellent correlation between the intensity distribution of binary images and average roughness with a correlation coefficient of 0.9982. Furthermore, the proposed AO-assisted system is in good agreement with the stylus method and less than 9.73% error values can be consistently obtained.     

Compact optical function generator

We demonstrate the use of a nonlinear photonic crystal to generate a harmonic comb and an ultrabroad-band acousto-optic modulator for the field amplitudes and phases of the comb to succeed in synthesizing femtosecond and subfemtosecond optical field waveforms. Nonsinusoidal fields of various shapes are synthesized and verified using shaper-assisted linear cross-correlation. The compact all-solid-state system could lead to the realization of a portable arbitrary optical waveform synthesizer that is analogous in many aspects to an RF function generator.     

Role of photon statistics of light source in ghost imaging

The theory of ghost imaging is examined by taking into account the quantum state of the light source explicitly. It is proved that ghost images can be obtained by any light source that is non-Poissonian. It is also shown that ghost images with unity visibility can be achieved with either quantum or classical correlation.