scholarly journals Radial expansion preserves hyperbolic convexity and radial contraction preserves spherical convexity

2019 ◽  
Vol 110 (2) ◽  
Author(s):  
Dhruv Kohli ◽  
Jeffrey M. Rabin
2020 ◽  
Vol 14 (3) ◽  
pp. 7235-7243
Author(s):  
N.M. Ali ◽  
F. Dzaharudin ◽  
E.A. Alias

Microbubbles have the potential to be used for diagnostic imaging and therapeutic delivery. However, the transition from microbubbles currently being used as ultrasound contrast agents to achieve its’ potentials in the biomedical field requires more in depth understanding. Of particular importance is the influence of microbubble encapsulation of a microbubble near a vessel wall on the dynamical behaviour as it stabilizes the bubble. However, many bubble studies do not consider shell encapsulation in their studies. In this work, the dynamics of an encapsulated microbubble near a boundary was studied by numerically solving the governing equations for microbubble oscillation. In order to elucidate the effects of a boundary to the non-linear microbubble oscillation the separation distances between microbubble will be varied along with the acoustic driving. The complex nonlinear vibration response was studied in terms of bifurcation diagrams and the maximum radial expansion. It was found that the increase in distance between the boundary and the encapsulated bubble will increase the oscillation amplitude. When the value of pressure amplitude increased the single bubble is more likely to exhibit the chaotic behaviour and maximum radius also increase as the inter wall-bubble distance is gradually increased. While, with higher driving frequency the maximum radial expansion decreases and suppress the chaotic behaviour.


2021 ◽  
Vol 153 ◽  
pp. 108072
Author(s):  
Sunghwan Yun ◽  
Gennadii Mikhailov ◽  
Sang Ji Kim ◽  
Jae-Yong Lim

CORROSION ◽  
2012 ◽  
Vol 68 (6) ◽  
pp. 489-498 ◽  
Author(s):  
G. Williams ◽  
K. Gusieva ◽  
N. Birbilis

The influence of neodymium (Nd) alloying additions in the 0.47 wt% to 3.53 wt% range on the localized corrosion behavior of Mg, when freely corroding in aqueous sodium chloride (NaCl) electrolyte, is investigated using an in situ scanning vibrating electrode technique (SVET). For all samples, the point of surface breakdown is an intense focal anode that expands radially with respect to time, revealing a cathodically activated interior, which is galvanically coupled with the local anode at the perimeter. However, for Nd compositions of ≤0.74%, radial expansion ceases within ca. 2 h of initiation, whereupon dark filiform-like corrosion features are observed, which traverse over the exposed Mg surface. For Nd additions of ≥1.25%, the radial expansion continues with time up to a point where the entire intact surface becomes consumed. The intensity of the local anode ring of circular corroded regions is seen to increase as more cathodically activated corroded surface becomes exposed. Mean current density values measured within these corroded areas increase progressively with Nd content, leading to a progressive rise in localized corrosion rates. The cathodic activation of corroded regions is proposed to derive from an enrichment of noble, Nd-rich intermetallic grains caused as the alpha-Mg phase becomes attacked at local anode sites.


2017 ◽  
Vol 840 (2) ◽  
pp. L13 ◽  
Author(s):  
Sarah E. Gibson ◽  
Kevin Dalmasse ◽  
Laurel A. Rachmeler ◽  
Marc L. De Rosa ◽  
Steven Tomczyk ◽  
...  

2018 ◽  
Vol 47 (2) ◽  
pp. 392-402 ◽  
Author(s):  
Eric L. Pierce ◽  
Keshav Kohli ◽  
Beatrice Ncho ◽  
Vahid Sadri ◽  
Charles H. Bloodworth ◽  
...  

RSC Advances ◽  
2017 ◽  
Vol 7 (68) ◽  
pp. 43047-43051 ◽  
Author(s):  
Jiangbin Su ◽  
Xianfang Zhu

In contrast to straight NWs, curved NWs quickly become straight accompanied by uniform axial shrinkage and radial expansion.


2014 ◽  
Vol 70 (3) ◽  
pp. 187-198
Author(s):  
Ewa Kupidłowska

The ultrastructure and morphology of roots treated with coumarin and umbelliferone as well as the reversibility of the coumarins effects caused by exogenous GA, were studied in <em>Arabidopsis thaliana</em>. Both coumarins suppressed root elongation and appreciably stimulated radial expansion of epidermal and cortical cells in the upper part of the meristem and in the elongation zone. The gibberellic acid applied simultaneously with coumarins decreased their inhibitory effect on root elongation and reduced cells swelling.Microscopic observation showed intensive vacuolization of cells and abnormalities in the structure of the Golgi stacks and the nuclear envelope. The detection of active acid phosphatase in the cytosol of swollen cells indicated increased membrane permeability. Significant abnormalities of newly formed cell walls, e.g. the discontinuity of cellulose layer, uncorrect position of walls and the lack of their bonds with the mother cell wall suggest that coumarins affected the cytoskeleton.


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