scholarly journals Reflectionless wave propagation on shallow water with variable bathymetry and current

2021 ◽  
Vol 931 ◽  
Author(s):  
Semyon M. Churilov ◽  
Yury A. Stepanyants
Keyword(s):  
Wave Propagation ◽  
Water Depth ◽  
Arbitrary Shape ◽  
Dimensional Problem ◽  
Coastal Zones ◽  
One Dimensional ◽  
Marine Engineering ◽  
The One ◽  
Spatially Varying ◽  
Propagation Velocities

In the linear approximation, we study the one-dimensional problem of reflectionless wave propagation on the surface of a shallow duct with spatially varying water depth, duct width and current. We show that both global and bounded exact solutions describing the reflectionless propagation in opposite directions of long waves of arbitrary shape exist for the particular variations of these parameters. A general analysis of the problem is illustrated by a few solutions constructed for the specific cases of spatial profiles of the flow and wave propagation velocities. The results obtained can be of interest to mitigate the possible impact of waves on ships, marine engineering constructions and human activity in coastal zones.

scholarly journals Algorithms for Necklace Maps

2015 ◽  
Vol 25 (01) ◽  
pp. 15-36 ◽  
Author(s):  
Bettina Speckmann ◽  
Kevin Verbeek
Keyword(s):  
Exact Algorithm ◽  
Dimensional Problem ◽  
Order Problem ◽  
Fixed Parameter Tractable ◽  
One Dimensional ◽  
Algorithmic Question ◽  
Fixed Parameter ◽  
Fixed Order ◽  
The One ◽  
Decision Version

Necklace maps visualize quantitative data associated with regions by placing scaled symbols, usually disks, without overlap on a closed curve (the necklace) surrounding the map regions. Each region is projected onto an interval on the necklace that contains its symbol. In this paper we address the algorithmic question how to maximize symbol sizes while keeping symbols disjoint and inside their intervals. For that we reduce the problem to a one-dimensional problem which we solve efficiently. Solutions to the one-dimensional problem provide a very good approximation for the original necklace map problem. We consider two variants: Fixed-Order, where an order for the symbols on the necklace is given, and Any-Order where any symbol order is possible. The Fixed-Order problem can be solved in O(n log n) time. We show that the Any-Order problem is NP-hard for certain types of intervals and give an exact algorithm for the decision version. This algorithm is fixed-parameter tractable in the thickness K of the input. Our algorithm runs in O(n log n + n2K4K) time which can be improved to O(n log n + nK2K) time using a heuristic. We implemented our algorithm and evaluated it experimentally.

Oscillating flames: multiple-scale analysis

2009 ◽  
Vol 465 (2107) ◽  
pp. 2089-2110 ◽  
Author(s):  
Luc Bauwens ◽  
C. Regis L. Bauwens ◽  
Ida Wierzba
Keyword(s):  
Approximate Solution ◽  
Reaction Front ◽  
Burning Velocity ◽  
Propagation Speed ◽  
Multiple Scale ◽  
Expansion Ratio ◽  
Scale Analysis ◽  
Dimensional Problem ◽  
One Dimensional ◽  
The One

A complete multiple-scale solution is constructed for the one-dimensional problem of an oscillating flame in a tube, ignited at a closed end, with the second end open. The flame front moves into the unburnt mixture at a constant burning velocity relative to the mixture ahead, and the heat release is constant. The solution is based upon the assumption that the propagation speed multiplied by the expansion ratio is small compared with the speed of sound. This approximate solution is compared with a numerical solution for the same physical model, assuming a propagation speed of arbitrary magnitude, and the results are close enough to confirm the validity of the approximate solution. Because ignition takes place at the closed end, the effect of thermal expansion is to push the column of fluid in the tube towards the open end. Acoustics set in motion by the impulsive start of the column of fluid play a crucial role in the oscillation. The analytical solution also captures the subsequent interaction between acoustics and the reaction front, the effect of which does not appear to be as significant as that of the impulsive start, however.

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