scholarly journals Short-time existence of solutions to the cross curvature flow on 3-manifolds

2005 ◽  
Vol 134 (6) ◽  
pp. 1803-1807 ◽  
Author(s):  
John A. Buckland
Keyword(s):  
Existence Of Solutions ◽  
Curvature Flow ◽  
The Cross ◽  
Short Time ◽  
Cross Curvature Flow ◽  
Time Existence

scholarly journals A local regularity theorem for mean curvature flow with triple edges

2020 ◽  
Vol 2020 (758) ◽  
pp. 281-305 ◽  
Author(s):  
Felix Schulze ◽  
Brian White
Keyword(s):  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Natural Extension ◽  
Regularity Result ◽  
Curvature Flow ◽  
Higher Order ◽  
Local Regularity ◽  
Initial Surface ◽  
Short Time ◽  
Time Existence

AbstractMean curvature flow of clusters of n-dimensional surfaces in {\mathbb{R}^{n+k}} that meet in triples at equal angles along smooth edges and higher order junctions on lower-dimensional faces is a natural extension of classical mean curvature flow. We call such a flow a mean curvature flow with triple edges. We show that if a smooth mean curvature flow with triple edges is weakly close to a static union of three n-dimensional unit density half-planes, then it is smoothly close. Extending the regularity result to a class of integral Brakke flows, we show that this implies smooth short-time existence of the flow starting from an initial surface cluster that has triple edges, but no higher order junctions.

On the cross curvature flow

2020 ◽  
Vol 71 ◽  
pp. 101636
Author(s):  
Pak Tung Ho ◽  
Jinwoo Shin
Keyword(s):  
Curvature Flow ◽  
The Cross ◽  
Cross Curvature Flow

scholarly journals On short time existence of Lagrangian mean curvature flow

2016 ◽  
Vol 367 (3-4) ◽  
pp. 1473-1515 ◽  
Author(s):  
Tom Begley ◽  
Kim Moore
Keyword(s):  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Short Time ◽  
Time Existence

Effect of operational modes on the removal of a synthetic organic chemical by powdered activated carbon during ultrafiltration

2001 ◽  
Vol 1 (5-6) ◽  
pp. 39-47
Author(s):  
Y. Matsui ◽  
A. Yuasa ◽  
F. Colas
Keyword(s):  
Activated Carbon ◽  
Cross Flow ◽  
Powdered Activated Carbon ◽  
Organic Chemical ◽  
Filtration Cycle ◽  
Dead End ◽  
Synthetic Organic Chemical ◽  
The Cross ◽  
Short Time ◽  
Operational Modes

The effects of operational modes on the removal of a synthetic organic chemical (SOC) in natural water by powdered activated carbon (PAC) during ultrafiltration (UF) were studied, through model simulations and experiments. The removal percentage of the trace SOC was independent of its influent concentration for a given PAC dose. The minimum PAC dosage required to achieve a desired effluent concentration could quickly be optimized from the C/C0 plot as a function of the PAC dosage. The cross-flow operation was not advantageous over the dead-end regarding the SOC removal. Added PAC was re-circulated as a suspension in the UF loop for only a short time even under the cross-flow velocity of gt; 1.0 m/s. The cross-flow condition did not contribute much to the suspending of PAC. The pulse PAC addition at the beginning of a filtration cycle resulted in somewhat better SOC removal than the continuous PAC addition. The increased NOM loading on PAC which was dosed in a pulse and stayed longer in the UF loop could possibly further decrease the adsorption rate.

Sign in / Sign up

Export Citation Format

Share Document