On the Existence of a Convex Polygon with a Specified Number of Interior Points

2003 ◽  
pp. 351-358 ◽  
Author(s):  
Kiyoshi Hosono ◽  
Masatsugu Urabe ◽  
Gyula Karolyi
Keyword(s):  
Convex Polygon ◽  
Interior Points

Flow Pattern Analysis of Constructed Wetlands Treating Landfill Leachate

1999 ◽  
Vol 40 (3) ◽  
pp. 309-315 ◽  
Author(s):  
Jonathan K. Rash ◽  
Sarah K. Liehr
Keyword(s):  
Constructed Wetlands ◽  
Vertical Mixing ◽  
Subsurface Flow ◽  
Free Water ◽  
Chemical Reactor ◽  
Operating Conditions ◽  
Conservative Tracer ◽  
Residence Time Distributions ◽  
Physical Barriers ◽  
Interior Points

Three series of tracer studies were performed on three constructed wetlands at the New Hanover County Landfill near Wilmington, North Carolina, USA. One vegetated free water surface wetland (FWS-R), one vegetated subsurface flow wetland (SSF-R), and one unvegetated control subsurface flow wetland (SSF-C) were studied. A conservative tracer, lithium chloride, was used to study the chemical reactor behavior of these wetlands under normal operating conditions. Results indicated that short-circuiting is quite common in SSF wetlands, while FWS wetlands are well-mixed and not as subject to short-circuiting. These results were obtained from and reinforced with tracer measurements at interior points in these wetlands, analysis of residence time distributions from two different formulations, and the construction of residence volume distributions. The short-circuiting in the SSF wetlands can be attributed to the following: (1) Vertical mixing is inhibited by a combination of physical barriers and density gradients caused by rainfall and runoff dilution of the upper layer; and (2) Leachate is drawn from the bottom of the wetland, causing it to further prefer a flow path along the bottom.

scholarly journals Nonlinear Compartment Models with Time-Dependent Parameters

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1657
Author(s):  
Jochen Merker ◽  
Benjamin Kunsch ◽  
Gregor Schuldt
Keyword(s):  
Stable Equilibrium ◽  
Compartment Model ◽  
Basins Of Attraction ◽  
Dynamical Behaviour ◽  
Time Dependent ◽  
Compartment Models ◽  
Autonomous Case ◽  
Hyperbolic Equilibrium ◽  
Interior Points ◽  
Two Parameter

A nonlinear compartment model generates a semi-process on a simplex and may have an arbitrarily complex dynamical behaviour in the interior of the simplex. Nonetheless, in applications nonlinear compartment models often have a unique asymptotically stable equilibrium attracting all interior points. Further, the convergence to this equilibrium is often wave-like and related to slow dynamics near a second hyperbolic equilibrium on the boundary. We discuss a generic two-parameter bifurcation of this equilibrium at a corner of the simplex, which leads to such dynamics, and explain the wave-like convergence as an artifact of a non-smooth nearby system in C0-topology, where the second equilibrium on the boundary attracts an open interior set of the simplex. As such nearby idealized systems have two disjoint basins of attraction, they are able to show rate-induced tipping in the non-autonomous case of time-dependent parameters, and induce phenomena in the original systems like, e.g., avoiding a wave by quickly varying parameters. Thus, this article reports a quite unexpected path, how rate-induced tipping can occur in nonlinear compartment models.

scholarly journals Markov chain approximation of one-dimensional sticky diffusions

2021 ◽  
Vol 53 (2) ◽  
pp. 335-369
Author(s):  
Christian Meier ◽  
Lingfei Li ◽  
Gongqiu Zhang
Keyword(s):  
Markov Chain ◽  
Approximate Solutions ◽  
Price Model ◽  
One Dimensional ◽  
Markov Chain Approximation ◽  
Alternative Approaches ◽  
Second Order Convergence ◽  
Chain Approximation ◽  
Matrix Exponentials ◽  
Interior Points

AbstractWe develop a continuous-time Markov chain (CTMC) approximation of one-dimensional diffusions with sticky boundary or interior points. Approximate solutions to the action of the Feynman–Kac operator associated with a sticky diffusion and first passage probabilities are obtained using matrix exponentials. We show how to compute matrix exponentials efficiently and prove that a carefully designed scheme achieves second-order convergence. We also propose a scheme based on CTMC approximation for the simulation of sticky diffusions, for which the Euler scheme may completely fail. The efficiency of our method and its advantages over alternative approaches are illustrated in the context of bond pricing in a sticky short-rate model for a low-interest environment and option pricing under a geometric Brownian motion price model with a sticky interior point.

Learning gradual rules to model convex polygon-shaped classes

2010 ◽  
Author(s):  
Lavinia Darlea ◽  
Sylvie Galichet ◽  
Lionel Valet ◽  
Gabriel Vasile ◽  
Emmanuel Trouve
Keyword(s):  
Convex Polygon

Elastic Fields in a Polygon-Shaped Inclusion With Uniform Eigenstrains

1997 ◽  
Vol 64 (3) ◽  
pp. 495-502 ◽  
Author(s):  
H. Nozaki ◽  
M. Taya
Keyword(s):  
Composite Materials ◽  
Closed Form ◽  
Strain Field ◽  
Strain Energy ◽  
Convex Polygon ◽  
Numerical Examples ◽  
Elastic Fields ◽  
Closed Form Solutions ◽  
Arbitrary Convex ◽  
Shaped Inclusion

In this paper the elastic fields in an arbitrary, convex polygon-shaped inclusion with uniform eigenstrains are investigated under the condition of plane strain. Closed-form solutions are obtained for the elastic fields in a polygon-shaped inclusion. The applications to the evaluation of the effective elastic properties of composite materials with polygon-shaped reinforcements are also investigated for both dilute and dense systems. Numerical examples are presented for the strain field, strain energy, and stiffness of the composites with polygon shaped fibers. The results are also compared with some existing solutions.

AN APPROXIMATION ALGORITHM FOR LOCATING MAXIMAL DISKS WITHIN CONVEX POLYGONS

2011 ◽  
Vol 21 (06) ◽  
pp. 661-684
Author(s):  
HIROFUMI AOTA ◽  
TAKURO FUKUNAGA ◽  
HIROSHI NAGAMOCHI
Keyword(s):  
Approximation Algorithm ◽  
Convex Polygon ◽  
Computation Time ◽  
Approximation Ratio ◽  
Convex Polygons ◽  
The Given

This paper considers a problem of locating the given number of disks into a container so that the area covered by the disks is maximized. In the problem, the radii of the disks can be changed arbitrarily unless they overlap outside of the container, and the disks are allowed to overlap with each other. We present an approximation algorithm for this problem assuming that the container is a convex polygon. Our algorithm achieves approximation ratio (0.78 - ϵ) for any small ϵ > 0. Since the computation time of our algorithm depends on the number of corners of the convex polygon exponentially, we also give a heuristic to reduce the number of corners.

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