Transmission of a Gaussian beam after incidenting nonnormally on a Fabry–Perot etalon: a nonresonant case

Under the nonresonant case where the carrier frequency of a Gaussian beam deviates from the resonant frequency of a Fabry–Perot etalon, the transmission of a Gaussian beam after incidenting nonnormally on a Fabry–Perot etalon has been investigated. The results show that under the nonresonant case, variations of the peak intensity, the position of the peak intensity and the spot size of the transmitted beam with the input angle behave differently and even with a reversed tendency compared with those obtained under the resonant case.     

The epitaxial sexiphenyl (0 0 1) monolayer on TiO2(1 1 0): A grazing incidence X-ray diffraction study

A para-sexiphenyl monolayer of near up-right standing molecules (nominal thickness of 30 Å) is investigated in-situ by X-ray diffraction using synchrotron radiation and ex-situ by atomic force microscopy. A terrace like morphology is observed, the step height between the terraces is approximately one molecular length. The monolayer terraces, larger than 20 μm in size, are extended along the [0 0 1] direction of the TiO₂(1 1 0) substrate i.e. along the Ti-O rows of the reconstructed substrate surface. The structure of the monolayer and its epitaxial relationship to the substrate is determined by grazing incidence X-ray diffraction. Extremely sharp diffraction peaks reveal high crystalline order within the monolayer, which was found to have the bulk structure of sexiphenyl. The monolayer terraces are epitaxially oriented with the (0 0 1) plane parallel to the substrate surface (out-of-plane order). Four epitaxial relationships are observed. This in-plane alignment is determined by the arrangement of the terminal phenyl rings of the sexiphenyl molecules parallel to the oxygen rows of the substrate.     

Design and fabrication of 2 kHz nematic liquid crystal variable retarder with reflection mode

ABSTRACT

This study proposes a simple method of designing a high-speed liquid crystal variable retarder (LCVR) with reflection mode. First, a series of simple formulas is provided for analysing the effects of tilt incidence and birefringence of the liquid crystal on the phase retardation and response time of the LCVR. Then, a reflective LCVR is fabricated to validate the theoretical analysis. Measured results show that the response speed can reach 2.7 kHz with a phase retardation of 1 λ. Furthermore, the theoretical curve is close to the measured curve while the incident angle is less than 10°. However, the theoretical and measured values show a considerable difference under a large incident angle. This problem is discussed, and a modified method is given. This work is helpful for the design and fabrication of high-speed LCVR.     

Traveling waves for a four-compartment lattice epidemic system with exposed class and standard incidence

This paper is considering the problem of traveling wave solutions (TWS) for a susceptible-exposed-infectious-recovered (SEIR) epidemic model with discrete diffusion. The threshold condition for the existence and nonexistence of TWS is obtained. More specifically, such kind of solutions are governed by the threshold number ?₀. We can find a critical wave speed c^? if ?₀ > 1, by employing the Schauder's fixed point theorem, limiting argument and two-sided Laplace transform, we confirm that there exists TWS for c > c^?, while there exists no TWS for c < c^?. We also obtain the nonexistence of TWS for ?₀ ≤ 1. At last, we give some biological explanations from the epidemiological perspective.     

?*-extensions of tori, higher chow groups and applications to incidence equivalence relations for algebraic cycles

LetX be a smooth projective variety over an algebraically closed fieldk. We repeat Bloch's construction of aG _m -biextension (torseur)E over CH _hom ^p (X)×CH _hom ^q (X) forp+q=dim(X)+1. First we show that in characteristic zeroE comes via pullback from the Poincaré biextension over the corresponding product of intermediate Jacobians which has been conjectured by Bloch and Murre. Then the relations betweenE and various equivalence relations for algebraic cycles are studied. In particular we reprove Murre's theorem stating that Griffiths' conjecture holds for codimension 2 cycles, i.e. every 2-codimensional cycle which is algebraically and incidence equivalent to zero has torsion Abel-Jacobi invariant.     

Residual stress/strain analysis in thin films by X-ray diffraction

Residual stresses are found in the majority of multilayer thin film structures used in modem technology. The measurement and modeling of such stress fields and the elucidation of their effects on structural reliability and device operation have been a “growth area” in the literature, with contributions from authors in various scientific and engineering disciplines.

In this article the measurement of the residual stresses in thin film structures with X-ray diffraction techniques is reviewed and the interpretation of such data and their relationship to mechanical reliability concerns are discussed.     

An Arithmetic Reduction of Finite Rank 3 Geometries with Linear Spaces as Plane Residues and with Dual Linear Spaces as Point Residues

Let be a rank three incidence geometry of points, lines and planes whose planes are linear spaces and whose point residues are dual linear spaces (notice that we do not require anything on the line residues). We assume that the residual linear spaces of belong to a natural class of finite linear spaces, namely those linear spaces whose full automorphism group acts flag-transitively and whose orders are polynomial functions of some prime number. This class consists of six families of linear spaces. In the amalgamation of two such linear spaces imposes an equality on their orders leading, in particular, to a series of diophantine equations, the solutions of which provide a reduction theorem on the possible amalgams of linear spaces that can occur in .We prove that one of the following holds (up to a permutation of the words point and plane):A) the planes of and the dual of the point residues belong to the same family and have the same orders,B) the diagram of is in one of six families,C) the diagram of belongs to a list of seven sporadic cases.Finally, we consider the particular case where the line residues of are generalized digons.     

In Situ Study of the Surface Oxidation of FeCr Alloys Using Grazing Incidence X‐ray Absorption Spectroscopy (GIXAS)

The surface oxidation of FeCr alloys with 18, 28, and 43 mass‐% Cr was investigated in situ using grazing‐incidence X‐ray absorption spectroscopy (GIXAS) at the chromium and iron K‐edges. Oxidation in air was monitored in situ in the temperature range from 290 K to 680 K. The standard GIXAS data analysis is extended for the treatment of a single layer model in order to estimate the chromium concentrations of the oxide layer and of the near‐interface substrate as well as the oxide layer thickness. XANES analysis shows transitions from b.c.c. Fe to corundum type Fe₂O₃ and from b.c.c. Cr to corundum type Cr₂O₃. The initial oxide layers are 1.1‐1.4 nm thick and contain 60‐90 mass‐% chromium, while the near‐interface substrate is depleted in Cr. During heating, iron oxide growth dominates up to 560‐600 K. Then the chromium oxide layer loses its passivation effect and Cr oxidation sets in.     

Comparisons of the vector method and tensor method for simulating liquid crystal devices

In calculating the director configuration in a liquid crystal device, two methods are commonly employed: a vector model and a tensor model. In this paper, we compare and contrast these methods for liquid crystal devices consisting of a layer of liquid crystal sandwiched between two plates. We compare the reliability and accuracy of the results, the speed of computation and the complexity of implementations of each method.