Gratings in novel fibre geometry for applications in shape sensing

A long period grating (LPG) fabricated in progressive three-layered (PTL) fibre is described. The grating with a period of 391µm, had dual attenuation bands associated with a particular cladding mode. The dual attenuation bands have been experimentally characterised for their spectral sensitivity to bending, which resulted in the highest sensitivity to bending seen for this particular fibre and temperature. The spectral characteristics of the fibre have been modelled giving good agreement to the experimental data as well as showing that the attenuation bands are both associated with the second order HE/EH2,n cladding mode.

One Application of the Informatics in the Descriptive Geometry

This work acquaints with a program for interactive computer training to students on the subject "Mutual intersecting of pyramids in axonometry ”. Our software is a set of three modules, which we call "student", "teacher" and "autopilot". It gives the final solution of the problem, the traceability of various significant moments in its solution and 3D-image of the finished composition of the two intersecting polyhedra, stripped of the working lines and subjected to rotation and translation.

Two Remarkable Points of the Triangle Geometry

It is shown in the paper the discovery of two remarkable points of the triangle by means of “THE GEOMETER’S SKETCHPAD” software. Some properties of the points are considered too.

Geometry over two Arbitrary Arithmetic Progressions

We consider quadrate matrices with elements of the first row members of an arithmetic progression and of the second row members of other arithmetic progression. We prove the set of these matrices is a group. Then we give a parameterization of this group and investigate about some invariants of the corresponding geometry. We find an invariant of any two points and an invariant of any sixth points. All calculations are made by Maple.

An Improvement to the Achievement of the Griesmer Bound

We denoted by nq(k, d), the smallest value of n for which an [n, k, d]q code exists for given q, k, d. Since nq(k, d) = gq(k, d) for all d ≥ dk + 1 for q ≥ k ≥ 3, it is a natural question whether the Griesmer bound is attained or not for d = dk , where gq(k, d) = ∑[d/q^i], i=0,...,k-1, dk = (k − 2)q^(k−1) − (k − 1)q^(k−2). It was shown by Dodunekov [2] and Maruta [9], [10] that there is no [gq(k, dk ), k, dk ]q code for q ≥ k, k = 3, 4, 5 and for q ≥ 2k − 3, k ≥ 6. The purpose of this paper is to determine nq(k, d) for d = dk as nq(k, d) = gq(k, d) + 1 for q ≥ k with 3 ≤ k ≤ 8 except for (k, q) = (7, 7), (8, 8), (8, 9).

The Nonexistence of [132, 6, 86]3 Codes and [135, 6, 88]3 Codes

We prove the nonexistence of [g3(6, d), 6, d]3 codes for d = 86, 87, 88, where g3(k, d) = ∑⌈d/3i⌉ and i=0 ... k−1. This determines n3(6, d) for d = 86, 87, 88, where nq(k, d) is the minimum length n for which an [n, k, d]q code exists.

Recursive Methods for Construction of Balanced N-ary Block Designs

2000 Mathematics Subject Classification: Primary 05B05; secondary 62K10.

Construction of Optimal Linear Codes by Geometric Puncturing

Dedicated to the memory of S.M. Dodunekov (1945–2012)Abstract. Geometric puncturing is a method to construct new codes. ACM Computing Classification System (1998): E.4.

Compositional Geometry and Programming

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2014

Predegree Polynomials of Plane Configurations in Projective Space

2000 Mathematics Subject Classification: 14N10, 14C17.

Geometry of Warped Product Semi-Invariant Submanifolds of a Locally Riemannian Product Manifold

2000 Mathematics Subject Classification: 53C42, 53C15.

Formation and precise geometry control of SNAP microresonators by external electrostatic fields

In SNAP (Surface nanoscale axial photonics) resonators propagation of a slow whispering gallery mode along an optical fiber is controlled by nanoscale variation of the effective radius of the fiber [1]. Similar behavior can be realized in so - called nanobump microresonators in which the introduced variation of the effective radius is asymmetric, i.e. depends on the axial coordinate [2]. The possibilities of realization of such structures “on the fly” in an optical fiber by applying external electrostatic fields to it is discussed in this work. It is shown that local variations in effective radius of the fiber and in its refractive index caused by external electric fields can be large enough to observe SNAP structure - like behavior in an originally flat optical fiber. Theoretical estimations of the introduced refractive index and effective radius changes and results of finite element calculations are presented. Various effects are taken into account: electromechanical (piezoelectricity and electrostriction), electro-optical (Pockels and Kerr effects) and elasto-optical effect. Different initial fibre cross-sections are studied. The aspects of use of linear isotropic (such as silica) and non-linear anisotropic (such as lithium niobate) materials of the fiber are discussed. REFERENCES [1] M. Sumetsky, J. M. Fini, Opt. Exp. 19, 26470 (2011). [2] L. A. Kochkurov, M. Sumetsky, Opt. Lett. 40, 1430 (2015).

Improved sampling, pre-concentration, and detection of hidden explosives and illicit drugs by a novel solid phase microextraction geometry coupled to ion mobility spectrometry

The 9/11 Act mandates the inspection of 100% of cargo shipments entering the U.S. by 2012 and 100% inspection of air cargo by March 2010. So far, only 5% of inbound shipping containers are inspected thoroughly while air cargo inspections have fared better at 50%. Government officials have admitted that these milestones cannot be met since the appropriate technology does not exist. This research presents a novel planar solid phase microextraction (PSPME) device with enhanced surface area and capacity for collection of the volatile chemical signatures in air that are emitted from illicit compounds for direct introduction into ion mobility spectrometers (IMS) for detection. These IMS detectors are widely used to detect particles of illicit substances and do not have to be adapted specifically to this technology. For static extractions, PDMS and sol-gel PDMS PSPME devices provide significant increases in sensitivity over conventional fiber SPME. Results show a 50–400 times increase in mass detected of piperonal and a 2–4 times increase for TNT. In a blind study of 6 cases suspected to contain varying amounts of MDMA, PSPME-IMS correctly detected 5 positive cases with no false positives or negatives. One of these cases had minimal amounts of MDMA resulting in a false negative response for fiber SPME-IMS. A La (dihed) phase chemistry has shown an increase in the extraction efficiency of TNT and 2,4-DNT and enhanced retention over time. An alternative PSPME device was also developed for the rapid (seconds) dynamic sampling and preconcentration of large volumes of air for direct thermal desorption into an IMS. This device affords high extraction efficiencies due to strong retention properties under ambient conditions resulting in ppt detection limits when 3.5 L of air are sampled over the course of 10 seconds. Dynamic PSPME was used to sample the headspace over the following: MDMA tablets (12–40 ng detected of piperonal), high explosives (Pentolite) (0.6 ng detected of TNT), and several smokeless powders (26–35 ng of 2,4-DNT and 11–74 ng DPA detected). PSPME-IMS technology is flexible to end-user needs, is low-cost, rapid, sensitive, easy to use, easy to implement, and effective. ^

Inspection of parts with complex geometry and welds with structural health monitoring techniques

Structural Health Monitoring (SHM) systems were developed to evaluate the integrity of a system during operation, and to quickly identify the maintenance problems. They will be used in future aerospace vehicles to improve safety, reduce cost and minimize the maintenance time of a system. Many SHM systems were already developed to evaluate the integrity of plates and used in marine structures. Their implementation in manufacturing processes is still expected. The application of SHM methods for complex geometries and welds are two important challenges in this area of research. This research work started by studying the characteristics of piezoelectric actuators, and a small energy harvester was designed. The output voltages at different frequencies of vibration were acquired to determine the nonlinear characteristics of the piezoelectric stripe actuators. The frequency response was evaluated experimentally. AA battery size energy harvesting devices were developed by using these actuators. When the round and square cross section devices were excited at 50 Hz frequency, they generated 16 V and 25 V respectively. The Surface Response to Excitation (SuRE) and Lamb wave methods were used to estimate the condition of parts with complex geometries. Cutting tools and welded plates were considered. Both approaches used piezoelectric elements that were attached to the surfaces of considered parts. The variation of the magnitude of the frequency response was evaluated when the SuRE method was used. The sum of the square of the differences was calculated. The envelope of the received signal was used for the analysis of wave propagation. Bi-orthogonal wavelet (Binlet) analysis was also used for the evaluation of the data obtained during Lamb wave technique. Both the Lamb wave and SuRE approaches along with the three methods for data analysis worked effectively to detect increasing tool wear. Similarly, they detected defects on the plate, on the weld, and on a separate plate without any sensor as long as it was welded to the test plate.

Aspects of Motives: Finite-dimensionality, Chow-Kunneth Decompositions and Intersections of Cycles

This thesis analyzes the Chow motives of 3 types of smooth projective varieties: the desingularized elliptic self fiber product, the Fano surface of lines on a cubic threefold and an ample hypersurface of an Abelian variety. For the desingularized elliptic self fiber product, we use an isotypic decomposition of the motive to deduce the Murre conjectures. We also prove a result about the intersection product. For the Fano surface of lines, we prove the finite-dimensionality of the Chow motive. Finally, we prove that an ample hypersurface on an Abelian variety possesses a Chow-Kunneth decomposition for which a motivic version of the Lefschetz hyperplane theorem holds.