Research Advances and Challenges in One-Dimensional Mathematical Modeling of Secondary Settling Tanks—A Critical Review

2013 ◽  
Vol 2013 (13) ◽  
pp. 3934-3952
Author(s):  
Ben Li ◽  
M.K. Stenstrom
Author(s):  
Matthew Pope ◽  
Bradley Martin ◽  
David Lambert ◽  
Stanley E. Jones ◽  
Jonathan Muse

A “soft catch” is a device with which an explosively formed projectile can be decelerated to zero velocity without sustaining significant damage. The recovered projectile provides data, via metallurgical analysis, on the deformation conditions found within the explosively formed projectile. At Eglin AFB, FL, the soft catch consists of a sequence of sections (Figures 1–3), each roughly one meter long, filled with various soft media. Velocity screens are placed at the entrance and exit of each section. This enables investigators to experimentally determine the time at which the projectile passes each station in the catch. Based on these experimental measurements, average velocity estimates for each section of the soft catch can be made. The purpose of this paper is to support the soft catch design process with a one-dimensional analysis. The mathematical modeling is based on observations presented in studies by Allen, Mayfield, and Morrison [1,2]. Their work addresses the penetration of sand, but their modeling is appropriate for materials in the soft catch. The current paper describes application of their model to interpreting three soft catch experiments where Tantalum projectiles with initial velocities of approximately 1400 m/s were successfully recovered.


2015 ◽  
Vol 55 (8) ◽  
pp. 1381-1392 ◽  
Author(s):  
A. Ya. Bunicheva ◽  
S. I. Mukhin ◽  
N. V. Sosnin ◽  
A. B. Khrulenko

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 517
Author(s):  
Mostafa ZAHRI

In this paper, we present a new model for simulating an interesting class of Islamic design. Based on periodic sequences on the one-dimensional manifolds, and from emerging numbers, we construct closed graphs with edges on the unit circle. These graphs build very nice shapes and lead to a symmetrical class of geometric patterns of so-called Islamic design. Moreover, we mathematically characterize and analyze some convergence properties of the used up-down sequences. Finally, four planar type of patterns are simulated.


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