Reflection Arrangement Research Articles

Microwave Time-Domain Reflection Imaging of Steel Fiber Distribution on Reinforced Concrete

This paper presents a time-domain reflection electromagnetic analysis for nondestructive testing of the fiber dosage inside steel-fiber-reinforced concrete (SFRC). With the fibers treated as electrical dipoles, the Maxwell-Garnett mixing rule for dielectric mixtures is used to obtain an estimation of the density of fibers in the composite material from the time-domain measurement of the effective permittivity of the sample. First, a numerical electromagnetic modeling of the fiber polarizability is performed using a Method-of-Moments-based code and a simple frequency-dependent polarizability is obtained. Second, a robust and novel relationship between the mean propagation delay and the total stored energy with the effective permittivity of the medium is obtained. A wideband measurement system based on a time-domain setup in a reflection arrangement is used for the analysis of SFRC test structures. The fiber dosage in the SFRC structures is reconstructed, showing good agreement with the expected dosage figures.

Coxeter and crystallographic arrangements are inductively free

Using the classification of finite Weyl groupoids we prove that crystallographic arrangements, a large subclass of the class of simplicial arrangements which was recently defined, are hereditarily inductively free. In particular, all crystallographic reflection arrangements are hereditarily inductively free, among them the arrangement of type E 8 . With little extra work we prove that also all Coxeter arrangements are inductively free.

Projection Volumes of Hyperplane Arrangements

We prove that for any finite real hyperplane arrangement the average projection volumes of the maximal cones are given by the coefficients of the characteristic polynomial of the arrangement. This settles the conjecture of Drton and Klivans that this held for all finite real reflection arrangements. The methods used are geometric and combinatorial. As a consequence, we determine that the angle sums of a zonotope are given by the characteristic polynomial of the order dual of the intersection lattice of the arrangement.

Geometric combinatorics of Weyl groupoids

We extend properties of the weak order on finite Coxeter groups to Weyl groupoids admitting a finite root system. In particular, we determine the topological structure of intervals with respect to weak order, and show that the set of morphisms with fixed target object forms an ortho-complemented meet semilattice. We define the Coxeter complex of a Weyl groupoid with finite root system and show that it coincides with the triangulation of a sphere cut out by a simplicial hyperplane arrangement. As a consequence, one obtains an algebraic interpretation of many hyperplane arrangements that are not reflection arrangements.

A geometric interpretation of the characteristic polynomial of reflection arrangements

We consider projections of points onto fundamental chambers of finite real reflection groups. Our main result shows that for groups of types $A_n$, $B_n$, and $D_n$, the coefficients of the characteristic polynomial of the reflection arrangement are proportional to the spherical volumes of the sets of points that are projected onto faces of a given dimension. We also provide strong evidence that the same connection holds for the exceptional, and thus all, reflection groups. These results naturally extend those of De Concini and Procesi, Stembridge, and Denham, which establish the relationship for $0$-dimensional projections. This work is also of interest to the field of order-restricted statistical inference, where projections of random points play an important role.

Reflection groups acting on their hyperplanes

After having established elementary results on the relationship between a finite complex (pseudo-)reflection group W ⊂ GL ( V ) and its reflection arrangement A , we prove that the action of W on A is canonically related with other natural representations of W, through a ‘periodic’ family of representations of its braid group. We also prove that, when W is irreducible, then the squares of defining linear forms for A span the quadratic forms on V, which imply | A | ⩾ n ( n + 1 ) / 2 for n = dim V , and relate the W-equivariance of the corresponding map with the period of our family.

Elastic scattering of $\sf{59.54}$ -keV $\sf{\gamma}$ -rays in elements with $\sf{22 \leq {Z} \leq {92}}$ at momentum transfer $\sf{0.4 \leq {x} \leq 4.7~{\AA}^{\sf -1}}$

Differential cross sections for elastic scattering of the 59.54 keV γ-rays in elements with 22 ≤Z ≤92 have been measured over the angular range 10○–160○corresponding to the momentum transfer 0.4 ≤x ≤4.7 A-1. The measurements at forward and backward angles were performed using the 241Am radioactive point-source, target and the Ge detectors in the transmission and reflection arrangements, respectively. The measured differential scattering cross sections are compared with those based on the form-factor (FF) formalism and state-of-the-art S-matrix calculations to differentiate between their relative efficacies and to check angular-dependence of the anomalous scattering factors (ASF) incorporated as correction to the modified form-factor (MF). The S-matrix values exhibit agreement with the measured data at backward angles and differences ∼10% at forward angles. The scattering cross sections based on the MF including ASF’s are in general lower at various angles by up to 20% for medium- and high-Z elements. The observed deviations being higher at the forward angles infer possibility of angular-dependence of ASF’s.

A homodyne Michelson interferometer with sub-picometer resolution

A homodyne interferometer which exploits a multiple reflection arrangement between two quasi parallel mirrors to deliver a multiplication factor is presented. The relative displacement of the two mirrors causes a more than 100-fold increment of the optical path, which is measured by the optoelectronic circuitry. This leads to a proportional reduction of the errors associated with the subdivision of the optical fringes, with the effect of fringe nonlinearities, and with the opto-electronic noise. In particular the reduction of the electronic noise limit to the level of 20 fm Hz−1/2 has been demonstrated. The exact formula of the gain has been calculated and confirmed experimentally.

The Loewy Length of the Descent Algebra of Type D

In this article the Loewy length of the descent algebra of D2m + 1 is shown to be m + 2, for m ≥ 2, by providing an upper bound that agrees with the lower bound in Bonnafe and Pfeiffer (2006). The bound is obtained by showing that the length of the longest path in the quiver of the descent algebra of D2m + 1 is at most m + 1. To achieve this bound, the geometric approach to the descent algebra is used, in which the descent algebra of a finite Coxeter group W is identified with an algebra associated to the reflection arrangement of W.

Cohomology of Pure Braid Groups of exceptional cases

Consider the ring R : = Q [ τ , τ − 1 ] of Laurent polynomials in the variable τ. The Artin's Pure Braid Groups (or Generalized Pure Braid Groups) act over R, where the action of every standard generator is the multiplication by τ. In this paper we consider the cohomology of these groups with coefficients in the module R (it is well known that such cohomology is strictly related to the untwisted integral cohomology of the Milnor fibration naturally associated to the reflection arrangement). We compute this cohomology for the cases I 2 ( m ) , H 3 , H 4 , F 4 and A n with 1 ⩽ n ⩽ 7 .

On the quiver of the descent algebra

We study the quiver of the descent algebra of a finite Coxeter group W. The results include a derivation of the quiver of the descent algebra of types A and B. Our approach is to study the descent algebra as an algebra constructed from the reflection arrangement associated to W.

Three Counter-Examples on Semi-Graphoids

Semi-graphoids are combinatorial structures that arise in statistical learning theory. They are equivalent to convex rank tests and to polyhedral fans that coarsen the reflection arrangement of the symmetric group Sn. In this paper we resolve two problems on semi-graphoids posed in Studený's book (2005), and we answer a related question of Postnikov, Reiner and Williams on generalized permutohedra. We also study the semigroup and the toric ideal associated with semi-graphoids.

Active particle control through silicon using conventional optical trapping techniques

Functional integration of optical trapping techniques with silicon surfaces and environments can be realized with minimal modification of conventional optical trapping instruments offering a method to manipulate, track and position cells or non-biological particles over silicon substrates. This technique supports control and measurement advances including the optical control of silicon-based microfluidic devices and precision single molecule measurement of biological interactions at the semiconductor interface. Using a trapping laser in the near infra-red and a reflective imaging arrangement enables object control and measurement capabilities comparable to trapping through a classical glass substrate. The transmission efficiency of the silicon substrate affords the only reduction in trap stiffness. We implement conventional trap calibration, positioning, and object tracking over silicon surfaces. We demonstrate control of multiple objects including cells and complex non-spherical objects on silicon wafers and fabricated surfaces.

Surface plasmon resonance spectroscopy on rotated sub-micrometer polymer gratings generated by UV-laser based two-beam interference

Abstract Two-beam interference method was applied to generate gratings having periods of 416 nm and 833 nm by the forth harmonic of a Nd:Yag laser on thin poly-carbonate films spin-coated onto silver layer-covered substrates. The dependence of the modulation depth on the fluence and number of laser pulses was investigated by atomic force microscopy. A secondary pattern appeared on very thin polymer layers thanks to the “p” polarized laser beam illumination induced self-organized processes. The conditions of the emergence of grating-coupling caused additional plasmon resonance peak were determined for the sub-micrometer periodic polymer gratings. Surface plasmon resonance measurements were performed in attenuated total reflection arrangement to determine the effect of the angle between the plasmon propagation direction and the polymer groves on the grating-coupling. The effect of the modulation depth on the grating-coupling caused additional resonance minimum was also analyzed. We found coupling phenomena according to our calculations, the differences between the measured and theoretically predicted resonance curves were explained by the scattering on the complex surface structure.

Surface Plasmon Sensor Based on the Enhanced Light Transmission through Arrays of Nanoholes in Gold Films

Arrays of nanoholes in a gold film were used to monitor the binding of organic and biological molecules to the metallic surface. This technique is particularly sensitive to surface binding events because it is based upon the resonant surface plasmon enhanced transmission through the array of nanoholes. The sensitivity was found to be 400 nm per refractive index unit, which is comparable to other grating-based surface plasmon resonance (SPR) devices. The array of nanoholes is well suited for dense integration in a sensor chip. Furthermore, the optical geometry is collinear, which simplifies the alignment with respect to the traditional Kretschmann (reflection) arrangement for SPR sensing.

A stability-like theorem for cohomology of pure braid groups of the series A, B and D

Consider the ring R:= Q[τ,τ −1] of Laurent polynomials in the variable τ. The Artin's pure braid groups (or generalized pure braid groups) act over R, where the action of every standard generator is the multiplication by τ. In this paper we consider the cohomology of such groups with coefficients in the module R (it is well known that such cohomology is strictly related to the untwisted integral cohomology of the Milnor fibration naturally associated to the reflection arrangement). We give a sort of stability theorem for the cohomologies of the infinite series A, B and D, finding that these cohomologies stabilize, with respect to the natural inclusion, at some number of copies of the trivial R-module Q . We also give a formula which computes this number of copies.

The dual braid monoid

We study a new monoid structure for Artin groups associated with finite Coxeter systems. Like the classical positive braid monoid, the new monoid is a Garside monoid. We give several equivalent constructions: algebraically, the new monoid arises when studying Coxeter systems in a “dual” way, replacing the pair ( W, S) by ( W, T), with T the set of all reflections; geometrically, it arises when looking at the reflection arrangement from a certain basepoint. In the type A case, we recover the monoid constructed by Birman, Ko and Lee.

Fourier Transform Infrared Spectroscopy Using Polarization Modulation and Polarization Selective Techniques for Internal and External Reflection Geometries: Investigation of Self-Assembled Octadecylmercaptan on a Thin Gold Film

By combining the polarization modulation (PM) technique with Fourier transform infrared reflection−absorption spectroscopy (FT-IRRAS), one can substantially improve the detection sensitivity and data collection efficiency. Using PM, the step of “background subtraction” can be eliminated for quantifying adsorbed species or covalently attached monolayers, and the IR spectra can be taken in situ in aqueous solutions. We demonstrate here that such a combination of PM and FT-IRRAS is possible, not only for external reflection measurements, but also for the attenuated total internal reflection (ATR) arrangement. The unique advantage of this second combination is that it couples the surface sensitivity of ATR with the experimental convenience and rapid data collection capability of polarization modulated FT-IRRAS. In the present work, we combine numerical calculations with experiments to study octadecylmercaptan (ODM) monolayers, self-assembled onto a gold-coated calcium fluoride prism. Results, including IR spectra (2800−3000 cm-1) of ODM on Au are presented for PM as well as for parallel (p) and perpendicular (s) polarization selective detection schemes and for both external reflection and ATR experimental geometries.

Real-time detection of nucleic acid interactions by total internal reflection fluorescence.

This paper describes the development of an optical readout system for the real-time analysis of fluorescent-labeled DNA microarrays is described. The system is targeted toward research applications in genomics, agriculture, and life sciences, where the end-point detection of state-of-the-art readout systems does not provide sufficient information on the hybridization process. The hybridization progress of molecules from the liquid phase in a flow cell to immobilized oligonucleotides on a transducer surface can be observed. The excitation of fluorochromes is realized by a semiconductor laser, and the fluorescence emission is collected by a cooled CCD camera. Quantitative data can be extracted from the images for analysis of the microarray. For the signal transduction, the principle of total internal reflection is used. With a multiple internal reflection arrangement, the sensor chip was adapted to the standard microscope slide format and a homogeneous evanescent illumination of the active area of the sensor surface was achieved. An application measurement was carried out with this readout system. The hybridization of Cy5-labeled 30-mer single-stranded oligonucleotides to fully complementary immobilized strands was observed in real time. A kinetic analysis was demonstrated with the recorded data. Melting curves of a 140-mer PCR product from a hemochromatosis patient sample hybridized to immobilized wild-type mutant 15- and 17-mer oligonucleotides were recorded and single-point mutations could be detected.

Study of Si Surface Reactions by Infrared Reflection Absorption Spectroscopy Using Buried Metal Layer Substrates

In order to obtain the infrared reflection absorption spectroscopy (IRRAS) on semiconductor or insulator surfaces, IRRAS using a buried metal layer substrate (BML) was proposed. Compared with attenuated total reflection (ATR) arrangement, sensitivity is low, but it is a favorable point that sensitivity exists at wide frequency ranges including the finger print regions. The transmission (TR) arrangement is also applicable for wide frequency ranges, but its sensitivity is slightly lower than that of the BML-IRRAS. The important difference between TR and BML-IRRAS is in the selection rule. TR is sensitive for parallel components, but on the other hand, BML-IRRAS is for perpendicular components. Some recent results about the reaction of hydrogen on the Si(100) surfaces and the IR spectra of self assembled alkyl monolayers (SAMs) investigated by BML-IRRAS are introduced.