Completeness of unbounded convergences

Taylor, Mitchell A.

doi:10.1090/proc/14007

Cited by 16 publications

(21 citation statements)

References 16 publications

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“…Following Einstein's work on suspended solid sphere in Newtonian medium, it was proposed that droplet deformation is controlled by Capillary number (

normalC normala = \frac{{\overset{γ}{true} η}_{m} r_{0}}{α}

) which is indicative of coincidence of hydrodynamic force (

\dot{γ} η_{m}

) versus interfacial force (

\frac{true}{α}

), where

\dot{γ}

η_{m}

r_{0}

, and α are shear rate, matrix viscosity, radius of droplet, and interfacial tension, respectively . Decreasing the droplet diameter decreases the Ca number and consequently, the less the diameter, the less the droplet deformation.…”

Section: Resultsmentioning

confidence: 99%

Investigation of rheology and morphology to follow physical fibrillar network evolution through fiber spinning of PP/PA6 blend fiber

Hajiraissi

Jahani

Hallmann

2017

Polymer Engineering & Sci

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This work is aimed at investigating the influence of fibrillar morphology of deformed Polyamide 6 (PA6) droplets dispersed in Polypropylene (PP) matrix on the melt viscoelastic behavior of their blends. The blends of PP with various amounts of PA6 (1%, 6%, 10%, and 20%) were prepared by melt mixing in a co‐rotating twin screw extruder and fibrillated by fiber spinning process. Scanning Electron Microscopy revealed that the PA6 spherical droplets form fibrillar inclusions after fiber spinning. The steady and transient shear rheological responses of samples were evaluated in both linear and nonlinear ranges of deformation. Non‐terminal behavior of storage modulus at low frequency appeared as a typical characteristic of fibrillar morphology whose width and value depend on fibril growth. Storage modulus and complex viscosity of the blends containing PA6 fibrillated structure were remarkably enhanced compared to as‐extruded samples. The fibrillar‐induced elasticity of the fibers is a distinguishable behavior which was revealed by conducting transient stress and creep‐recovery measurements and upon appearing mature fibrils, elasticity of the polymer blend fibers increased significantly. POLYM. ENG. SCI., 58:1251–1260, 2018. © 2017 Society of Plastics Engineers

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“…Following Einstein's work on suspended solid sphere in Newtonian medium, it was proposed that droplet deformation is controlled by Capillary number (

normalC normala = \frac{{\overset{γ}{true} η}_{m} r_{0}}{α}

) which is indicative of coincidence of hydrodynamic force (

\dot{γ} η_{m}

) versus interfacial force (

\frac{true}{α}

), where

\dot{γ}

η_{m}

r_{0}

Section: Resultsmentioning

confidence: 99%

Investigation of rheology and morphology to follow physical fibrillar network evolution through fiber spinning of PP/PA6 blend fiber

Hajiraissi

Jahani

Hallmann

2017

Polymer Engineering & Sci

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“…Within six months of submitting this paper, I submitted the sequel papers [16] and [19]. Since those papers were accepted earlier than this, there are some minor misalignments of the references.…”

mentioning

confidence: 99%

Unbounded topologies and uo-convergence in locally solid vector lattices

Taylor

2019

Journal of Mathematical Analysis and Applications

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Suppose X is a vector lattice and there is a notion of convergence x α σ − → x in X. Then we can speak of an "unbounded" version of this convergence by saying thatIn the literature, the unbounded versions of the norm, order and absolute weak convergence have been studied. Here we create a general theory of unbounded convergence but with a focus on uo-convergence and those convergences deriving from locally solid topologies. We will see that, not only do the majority of recent results on unbounded norm convergence generalize, but they do so effortlessly. Not only that, but the stucture of unbounded topologies is clearer without a norm. We demonstrate this by removing metrizability, completeness, and local convexity from nearly all arguments, while at the same time making the proofs simpler and more general. We also give characterizations of minimal topologies in terms of unbounded topologies and uo-convergence.

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“…In general, the mechanical properties of the blends can be optimized by controlling its morphology . What is more, the stability of microscopic appearance such as droplet size and shape was affected by rheological properties . If the matrix viscosities of the two phases match, the minimum droplet size can be obtained and, generally, the best microscopic appearance can be achieved .…”

Section: Introductionmentioning

confidence: 99%

Microscopic morphology, rheological behavior, and mechanical properties of polymers: Recycled acrylonitrile‐butadiene‐styrene/polybutylene terephthalate blends

Zhan

Zhu

et al. 2019

J of Applied Polymer Sci

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In this study, styrene‐acrylonitrile‐glycidyl methacrylate (SAG) series copolymers were specially designed for producing the recycled acrylonitrile‐butadiene‐styrene (rABS)/poly(butylene terephthalate) (PBT)/SAG blends, which were prepared through the process of continuous melt blending and batch feeding. The effects of viscosity composition, SAG chemical composition, and SAG content on the morphology, and rheological and mechanical properties of the blends have been investigated. As demonstrated by morphological observation, the variety of viscosity composition of the blends affects the size of dispersed PBT droplets. Moreover, high viscosity of rABS matrix seems to facilitate the formation of smaller dispersed phase size of blends. Various SAG chemical compositions have different stabilities on the morphology of the blends, which affects the deformation, fragmentation, and coalescence of dispersed phase droplets. In addition, a finer phase morphology can be achieved when the density distribution of epoxy group is optimal in SAG copolymer. Rheological characterization manifested that the rheological properties of the blends depends strongly on its composition and structure, while the crosslinking degree is associated with the concentration of reactive groups and extent of reaction. Thereby, the rheological behavior of the blends during processing can be controlled by changing the reactive sequence and adding the quantity of epoxy group. The test on mechanical properties verified that a recycled product with excellent performance can be obtained by altering processing methods and the blends formula, which may be further applied to the 3D printing materials required by fused deposition modeling technology. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019, 136, 48310.

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Completeness of unbounded convergences

Cited by 16 publications

References 16 publications

Investigation of rheology and morphology to follow physical fibrillar network evolution through fiber spinning of PP/PA6 blend fiber

Investigation of rheology and morphology to follow physical fibrillar network evolution through fiber spinning of PP/PA6 blend fiber

Unbounded topologies and uo-convergence in locally solid vector lattices

Microscopic morphology, rheological behavior, and mechanical properties of polymers: Recycled acrylonitrile‐butadiene‐styrene/polybutylene terephthalate blends

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