Mathematics and fiber arts

Mathematics can be found all over the world, even in what could be considered an unrelated area, like fiber arts. In knitting, crochet, and counted-thread embroidery, we can find concepts of algebra, graph theory, number theory, geometry of transformations, and symmetry, as well as computer science. For example, many fiber art pieces embody notions related with groups of symmetry. In this work, we focus on two areas of Mathematics associated with knitting, crochet, and cross-stitch works – number theory and geometry of transformations.

POLAR ACTIONS ON CERTAIN PRINCIPAL BUNDLES OVER SYMMETRIC SPACES OF COMPACT TYPE

We study polar actions with horizontal sections on the total space of certain principal bundles G/K -> G/H with base a symmetric space of compact type. We classify such actions up to orbit equivalence in many cases. In particular, we exhibit examples of hyperpolar actions with cohomogeneity greater than one on locally irreducible homogeneous spaces with nonnegative curvature which are not homeomorphic to symmetric spaces.

(Non-)ergodicity of a degenerate diffusion modeling the fiber lay down process

We analyze the large time behavior of a stochastic model for the lay down of fibers on a moving conveyor belt in the production process of nonwovens. It is shown that under weak conditions this degenerate diffusion process has a unique invariant distribution and is even geometrically ergodic. This generalizes results from previous works [M. Grothaus and A. Klar, SIAM J. Math. Anal., 40 (2008), pp. 968–983; J. Dolbeault et al., arXiv:1201.2156] concerning the case of a stationary conveyor belt, in which the situation of a moving conveyor belt has been left open.

Homotopy type of gauge groups of quaternionic line bundles over spheres

Let P be a principal S(3)-bundle over a sphere S(n), with n >= 4. Let G(p) be the gauge group of P. The homotopy type of G(p) when n - 4 was studied by A. Kono in [A. Kono, A note on the homotopy type of certain gauge groups, Proc. Roy. Soc. Edinburgh Sect. A 117 (1991) 295-297]. In this paper we extend his result anti we study the homotopy type of the gauge group of these bundles for all n <= 25. (C) 2008 Elsevier B.V. All rights reserved.

Design of laminated piezocomposite shell transducers with arbitrary fiber orientation using topology optimization approach

Sensor and actuator based on laminated piezocomposite shells have shown increasing demand in the field of smart structures. The distribution of piezoelectric material within material layers affects the performance of these structures; therefore, its amount, shape, size, placement, and polarization should be simultaneously considered in an optimization problem. In addition, previous works suggest the concept of laminated piezocomposite structure that includes fiber-reinforced composite layer can increase the performance of these piezoelectric transducers; however, the design optimization of these devices has not been fully explored yet. Thus, this work aims the development of a methodology using topology optimization techniques for static design of laminated piezocomposite shell structures by considering the optimization of piezoelectric material and polarization distributions together with the optimization of the fiber angle of the composite orthotropic layers, which is free to assume different values along the same composite layer. The finite element model is based on the laminated piezoelectric shell theory, using the degenerate three-dimensional solid approach and first-order shell theory kinematics that accounts for the transverse shear deformation and rotary inertia effects. The topology optimization formulation is implemented by combining the piezoelectric material with penalization and polarization model and the discrete material optimization, where the design variables describe the amount of piezoelectric material and polarization sign at each finite element, with the fiber angles, respectively. Three different objective functions are formulated for the design of actuators, sensors, and energy harvesters. Results of laminated piezocomposite shell transducers are presented to illustrate the method. Copyright (C) 2012 John Wiley & Sons, Ltd.

Isolation and Contraction of the Stress Fiber

Stress fibers were isolated from cultured human foreskin fibroblasts and bovine endothelial cells, and their contraction was demonstrated in vitro. Cells in culture dishes were first treated with a low-ionic-strength extraction solution and then further extracted using detergents. With gentle washes by pipetting, the nucleus and the apical part of cells were removed. The material on the culture dish was scraped, and the freed material was forced through a hypodermic needle and fractionated by sucrose gradient centrifugation. Isolated, free-floating stress fibers stained brightly with fluorescently labeled phalloidin. When stained with anti-α-actinin or anti-myosin, isolated stress fibers showed banded staining patterns. By electron microscopy, they consisted of bundles of microfilaments, and electron-dense areas were associated with them in a semiperiodic manner. By negative staining, isolated stress fibers often exhibited gentle twisting of microfilament bundles. Focal adhesion–associated proteins were also detected in the isolated stress fiber by both immunocytochemical and biochemical means. In the presence of Mg-ATP, isolated stress fibers shortened, on the average, to 23% of the initial length. The maximum velocity of shortening was several micrometers per second. Polystyrene beads on shortening isolated stress fibers rotated, indicating spiral contraction of stress fibers. Myosin regulatory light chain phosphorylation was detected in contracting stress fibers, and a myosin light chain kinase inhibitor, KT5926, inhibited isolated stress fiber contraction. Our study demonstrates that stress fibers can be isolated with no apparent loss of morphological features and that they are truly contractile organelle.

Characterization of an In Vitro Model of Elastic Fiber Assembly

Elastic fibers consist of two morphologically distinct components: elastin and 10-nm fibrillin-containing microfibrils. During development, the microfibrils form bundles that appear to act as a scaffold for the deposition, orientation, and assembly of tropoelastin monomers into an insoluble elastic fiber. Although microfibrils can assemble independent of elastin, tropoelastin monomers do not assemble without the presence of microfibrils. In the present study, immortalized ciliary body pigmented epithelial (PE) cells were investigated for their potential to serve as a cell culture model for elastic fiber assembly. Northern analysis showed that the PE cells express microfibril proteins but do not express tropoelastin. Immunofluorescence staining and electron microscopy confirmed that the microfibril proteins produced by the PE cells assemble into intact microfibrils. When the PE cells were transfected with a mammalian expression vector containing a bovine tropoelastin cDNA, the cells were found to express and secrete tropoelastin. Immunofluorescence and electron microscopic examination of the transfected PE cells showed the presence of elastic fibers in the matrix. Biochemical analysis of this matrix showed the presence of cross-links that are unique to mature insoluble elastin. Together, these results indicate that the PE cells provide a unique, stable in vitro system in which to study elastic fiber assembly.

Physics and mathematics of dispersion-managed optical solitons

We review the main physical and mathematical properties of dispersion-managed (DM) optical solitons. Theory of DM solitons can be presented at two levels of accuracy: first, simple, but nevertheless, quantitative models based on ordinary differential equations governing evolution of the soliton width and phase parameter (the so-called chirp); and second, a comprehensive path-average theory that is capable of describing in detail both the fine structure of DM soliton form and its evolution along the fiber line. An analogy between DM soliton and a macroscopic nonlinear quantum oscillator model is also discussed. © 2003 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS. All rights reserved.

On The Brill-noether Theory of Spanned Vector Bundles on Smooth Curves

Here we study the integers (d, g, r) such that on a smooth projective curve of genus g there exists a rank r stable vector bundle with degree d and spanned by its global sections.

Projectively Normal Line Bundles on K-Gonal Curves and Rational Surfaces

2000 Mathematics Subject Classification: 14H50.

Granulocyte Colony-stimulating Factor (g-csf) Positive Effects On Muscle Fiber Degeneration And Gait Recovery After Nerve Lesion In Mdx Mice.

G-CSF has been shown to decrease inflammatory processes and to act positively on the process of peripheral nerve regeneration during the course of muscular dystrophy. The aims of this study were to investigate the effects of treatment of G-CSF during sciatic nerve regeneration and histological analysis in the soleus muscle in MDX mice. Six-week-old male MDX mice underwent left sciatic nerve crush and were G-CSF treated at 7 days prior to and 21 days after crush. Ten and twenty-one days after surgery, the mice were euthanized, and the sciatic nerves were processed for immunohistochemistry (anti-p75(NTR) and anti-neurofilament) and transmission electron microscopy. The soleus muscles were dissected out and processed for H&E staining and subsequent morphologic analysis. Motor function analyses were performed at 7 days prior to and 21 days after sciatic crush using the CatWalk system and the sciatic nerve index. Both groups treated with G-CSF showed increased p75(NTR) and neurofilament expression after sciatic crush. G-CSF treatment decreased the number of degenerated and regenerated muscle fibers, thereby increasing the number of normal muscle fibers. The reduction in p75(NTR) and neurofilament indicates a decreased regenerative capacity in MDX mice following a lesion to a peripheral nerve. The reduction in motor function in the crushed group compared with the control groups may reflect the cycles of muscle degeneration/regeneration that occur postnatally. Thus, G-CSF treatment increases motor function in MDX mice. Nevertheless, the decrease in baseline motor function in these mice is not reversed completely by G-CSF.

Effects Of Misalignments In The Retinal Nerve Fiber Layer Thickness Measurements With Spectral Domain Optical Coherence Tomography.

Purpose. To investigate misalignments (MAs) on retinal nerve fiber layer thickness (RNFLT) measurements obtained with Cirrus(©) SD-OCT. Methods. This was a retrospective, observational, cross-sectional study. Twenty-seven healthy and 29 glaucomatous eyes of 56 individuals with one normal exam and another showing MA were included. MAs were defined as an improper alignment of vertical vessels in the en face image. MAs were classified in complete MA (CMA) and partial MA (PMA), according to their site: 1 (superior, outside the measurement ring (MR)), 2 (superior, within MR), 3 (inferior, within MR), and 4 (inferior, outside MR). We compared RNFLT measurements of aligned versus misaligned exams in all 4 sectors, in the superior area (sectors 1 + 2), inferior area (sectors 3 + 4), and within the measurement ring (sectors 2 + 3). Results. RNFLT measurements at 12 clock-hour of eyes with MAs in the superior area (sectors 1 + 2) were significantly lower than those obtained in the same eyes without MAs (P = 0.043). No significant difference was found in other areas (sectors 1 + 2 + 3 + 4, sectors 3 + 4, and sectors 2 + 3). Conclusion. SD-OCT scans with superior MAs may present lower superior RNFLT measurements compared to aligned exams.

Brazilian Natural Fiber (jute) As Raw Material For Activated Carbon Production.

Jute fiber is the second most common natural cellulose fiber worldwide, especially in recent years, due to its excellent physical, chemical and structural properties. The objective of this paper was to investigate: the thermal degradation of in natura jute fiber, and the production and characterization of the generated activated carbon. The production consisted of carbonization of the jute fiber and activation with steam. During the activation step the amorphous carbon produced in the initial carbonization step reacted with oxidizing gas, forming new pores and opening closed pores, which enhanced the adsorptive capacity of the activated carbon. N2 gas adsorption at 77K was used in order to evaluate the effect of the carbonization and activation steps. The results of the adsorption indicate the possibility of producing a porous material with a combination of microporous and mesoporous structure, depending on the parameters used in the processes, with resulting specific surface area around 470 m2.g-1. The thermal analysis indicates that above 600°C there is no significant mass loss.

Processos adaptativos do tecido muscular esqueletico e tecido conjuntivo : repercussões sobre a flexibilidade

Universidade Estadual de Campinas. Faculdade de Educação Física