scholarly journals Allee optimal control of a system in ecology

2018 ◽  
Vol 28 (09) ◽  
pp. 1665-1697 ◽  
Author(s):  
Emmanuel Trélat ◽  
Jiamin Zhu ◽  
Enrique Zuazua
Keyword(s):  
Optimal Control ◽  
Numerical Simulations ◽  
Travelling Waves ◽  
Travelling Wave ◽  
Computational Method ◽  
Diffusion Reaction ◽  
Macroscopic Model ◽  
Future Research ◽  
Optimal Controls ◽  
Open Problems

The Allee threshold of an ecological system distinguishes the sign of population growth either towards extinction or to carrying capacity. In practice, human interventions can tune the Allee threshold for instance thanks to the sterile male technique and the mating disruption. In this paper, we address various control problems for a system described by a diffusion–reaction equation regulating the Allee threshold, viewed as a real parameter determining the unstable equilibrium of the bistable nonlinear reaction term. We prove that this system is the mean field limit of an interacting system of particles in which the individual behaviour is driven by stochastic laws. Numerical simulations of the stochastic process show that the propagation of population is governed by travelling wave solutions of the macroscopic reaction–diffusion system, which model the fact that solutions, in bounded space domains, reach asymptotically an equilibrium configuration.An optimal control problem for the macroscopic model is then introduced with the objective of steering the system to a target travelling wave. Using well-known analytical results and stability properties of travelling waves, we show that well-chosen piecewise constant controls allow to reach the target approximately in sufficiently long time. We then develop a direct computational method and show its efficiency for computing such controls in various numerical simulations. Finally, we show the effectiveness of the obtained macroscopic optimal controls in the microscopic system of interacting particles and we discuss their advantage when addressing situations that are out of reach for the analytical methods. We conclude the paper with some open problems and directions for future research.

scholarly journals On the generation of nonlinear travelling waves in confined geometries using electric fields

2014 ◽  
Vol 372 (2020) ◽  
pp. 20140066 ◽  
Author(s):  
R Cimpeanu ◽  
D. T Papageorgiou
Keyword(s):  
Numerical Simulations ◽  
Electric Fields ◽  
Travelling Waves ◽  
Travelling Wave ◽  
Direct Numerical Simulations ◽  
Small Scale ◽  
Interfacial Instabilities ◽  
Lower Electrode ◽  
Nonlinear Deformations ◽  
Moving Parts

We investigate electrostatically induced interfacial instabilities and subsequent generation of nonlinear coherent structures in immiscible, viscous, dielectric multi-layer stratified flows confined in small-scale channels. Vertical electric fields are imposed across the channel to produce interfacial instabilities that would normally be absent in such flows. In situations when the imposed vertical fields are constant, interfacial instabilities emerge due to the presence of electrostatic forces, and we follow the nonlinear dynamics via direct numerical simulations. We also propose and illustrate a novel pumping mechanism in microfluidic devices that does not use moving parts. This is achieved by first inducing interfacial instabilities using constant background electric fields to obtain fully nonlinear deformations. The second step involves the manipulation of the imposed voltage on the lower electrode (channel wall) to produce a spatio-temporally varying voltage there, in the form of a travelling wave with pre-determined properties. Such travelling wave dielectrophoresis methods are shown to generate intricate fluid–surface–structure interactions that can be of practical value since they produce net mass flux along the channel and thus are candidates for microfluidic pumps without moving parts. We show via extensive direct numerical simulations that this pumping phenomenon is a result of an externally induced nonlinear travelling wave that forms at the fluid–fluid interface and study the characteristics of the generated velocity field inside the channel.

scholarly journals Frictional hysteresis and particle deposition in granular free-surface flows

2019 ◽  
Vol 875 ◽  
pp. 1058-1095 ◽  
Author(s):  
A. N. Edwards ◽  
A. S. Russell ◽  
C. G. Johnson ◽  
J. M. N. T. Gray
Keyword(s):  
Numerical Simulations ◽  
Particle Deposition ◽  
Initial Conditions ◽  
Travelling Waves ◽  
Travelling Wave ◽  
Free Surface Flows ◽  
Uniform Flow ◽  
Glass Beads ◽  
Deposit Thickness ◽  
Frictional Hysteresis

Shallow granular avalanches on slopes close to repose exhibit hysteretic behaviour. For instance, when a steady-uniform granular flow is brought to rest it leaves a deposit of thickness $h_{stop}(\unicode[STIX]{x1D701})$ on a rough slope inclined at an angle $\unicode[STIX]{x1D701}$ to the horizontal. However, this layer will not spontaneously start to flow again until it is inclined to a higher angle $\unicode[STIX]{x1D701}_{start}$, or the thickness is increased to $h_{start}(\unicode[STIX]{x1D701})>h_{stop}(\unicode[STIX]{x1D701})$. This simple phenomenology leads to a rich variety of flows with co-existing regions of solid-like and fluid-like granular behaviour that evolve in space and time. In particular, frictional hysteresis is directly responsible for the spontaneous formation of self-channelized flows with static levees, retrogressive failures as well as erosion–deposition waves that travel through the material. This paper is motivated by the experimental observation that a travelling-wave develops, when a steady uniform flow of carborundum particles on a bed of larger glass beads, runs out to leave a deposit that is approximately equal to $h_{stop}$. Numerical simulations using the friction law originally proposed by Edwards et al. (J. Fluid Mech., vol. 823, 2017, pp. 278–315) and modified here, demonstrate that there are in fact two travelling waves. One that marks the trailing edge of the steady-uniform flow and another that rapidly deposits the particles, directly connecting the point of minimum dynamic friction (at thickness $h_{\ast }$) with the deposited layer. The first wave moves slightly faster than the second wave, and so there is a slowly expanding region between them in which the flow thins and the particles slow down. An exact inviscid solution for the second travelling wave is derived and it is shown that for a steady-uniform flow of thickness $h_{\ast }$ it produces a deposit close to $h_{stop}$ for all inclination angles. Numerical simulations show that the two-wave structure deposits layers that are approximately equal to $h_{stop}$ for all initial thicknesses. This insensitivity to the initial conditions implies that $h_{stop}$ is a universal quantity, at least for carborundum particles on a bed of larger glass beads. Numerical simulations are therefore able to capture the complete experimental staircase procedure, which is commonly used to determine the $h_{stop}$ and $h_{start}$ curves by progressively increasing the inclination of the chute. In general, however, the deposit thickness may depend on the depth of the flowing layer that generated it, so the most robust way to determine $h_{stop}$ is to measure the deposit thickness from a flow that was moving at the minimum steady-uniform velocity. Finally, some of the pathologies in earlier non-monotonic friction laws are discussed and it is explicitly shown that with these models either steadily travelling deposition waves do not form or they do not leave the correct deposit depth $h_{stop}$.

scholarly journals The COVID-19 Model with Partially Recovered Carriers

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
T. S. Faniran ◽  
E. A. Bakare ◽  
A. O. Falade
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Numerical Simulations ◽  
Pontryagin’S Maximum Principle ◽  
Optimality System ◽  
World Health ◽  
Control Analysis ◽  
Optimal Controls ◽  
Pontryagin's Maximum Principle ◽  
Social Distancing

Novel coronavirus (COVID-19) has been spreading and wreaking havoc globally, despite massive efforts by the government and World Health Organization (WHO). Consideration of partially recovered carriers is hypothesized to play a leading role in the persistence of the disease and its introduction to new areas. A model for transmission of COVID-19 by symptomless partially recovered carriers is proposed and analysed. It is shown that key parameters can be identified such that below a threshold level, built on these parameters, the epidemic tends towards extinction, while above another threshold, it tends towards a nontrivial epidemic state. Moreover, optimal control analysis of the model, using Pontryagin’s maximum principle, is performed. The optimal controls are characterized in terms of the optimality system and solved numerically for several scenarios. Numerical simulations and sensitivity analysis of the basic reproduction number, R c , indicate that the disease is mainly driven by parameters involving the partially recovered carriers rather than symptomatic ones. Moreover, optimal control analysis of the model, using Pontryagin’s maximum principle, is performed. The optimal controls were characterized in terms of the optimality system and solved numerically for several scenarios. Numerical simulations were explored to illustrate our theoretical findings, scenarios were built, and the model predicted that social distancing and treatment of the symptomatic will slow down the epidemic curve and reduce mortality of COVID-19 given that there is an average adherence to social distancing and effective treatment are administered.

Solitary and Travelling Wave Solutions of Certain Nonlinear Diffusion-Reaction Equations

2020 ◽  
Author(s):  
Miftachul Hadi
Keyword(s):  
Nonlinear Diffusion ◽  
Travelling Wave ◽  
Diffusion Reaction ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Reaction Equations

We review the work of Ranjit Kumar, R S Kaushal, Awadhesh Prasad. The work is still in progress.

scholarly journals Climate Change Sustainability: From Bargaining to Cooperative Balanced Approach

Games ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 45
Author(s):  
Tiziana Ciano ◽  
Massimiliano Ferrara ◽  
Mariangela Gangemi ◽  
Domenica Stefania Merenda ◽  
Bruno Antonio Pansera
Keyword(s):  
Climate Change ◽  
Cooperative Game Theory ◽  
Research Field ◽  
Future Research ◽  
Open Problems ◽  
Cooperative Approach ◽  
Change Dynamics ◽  
Bargaining Solutions ◽  
Balanced Approach ◽  
Competitive Bargaining

This work aims to provide different perspectives on the relationships between cooperative game theory and the research field concerning climate change dynamics. New results are obtained in the framework of competitive bargaining solutions and related issues, moving from a cooperative approach to a competitive one. Furthermore, the dynamics of balanced and super-balanced games are exposed, with particular reference to coalitions. Some open problems are presented to aid future research in this area.

Hierarchical Reinforcement Learning

2021 ◽  
Vol 54 (5) ◽  
pp. 1-35
Author(s):  
Shubham Pateria ◽  
Budhitama Subagdja ◽  
Ah-hwee Tan ◽  
Chai Quek
Keyword(s):  
Reinforcement Learning ◽  
Future Research ◽  
Comprehensive Overview ◽  
Open Problems ◽  
Practical Applications ◽  
Hierarchical Reinforcement Learning ◽  
The Past ◽  
Agent Learning ◽  
Multi Agent ◽  
Supplementary Material

Hierarchical Reinforcement Learning (HRL) enables autonomous decomposition of challenging long-horizon decision-making tasks into simpler subtasks. During the past years, the landscape of HRL research has grown profoundly, resulting in copious approaches. A comprehensive overview of this vast landscape is necessary to study HRL in an organized manner. We provide a survey of the diverse HRL approaches concerning the challenges of learning hierarchical policies, subtask discovery, transfer learning, and multi-agent learning using HRL. The survey is presented according to a novel taxonomy of the approaches. Based on the survey, a set of important open problems is proposed to motivate the future research in HRL. Furthermore, we outline a few suitable task domains for evaluating the HRL approaches and a few interesting examples of the practical applications of HRL in the Supplementary Material.

Travelling Wave Control of Rotating Discs and Analysis of its Spillover Effect

1988 ◽  
Vol 202 (2) ◽  
pp. 119-127 ◽  
Author(s):  
C-S Kim ◽  
C-W Lee
Keyword(s):  
Travelling Waves ◽  
Spillover Effect ◽  
Polynomial Equation ◽  
Travelling Wave ◽  
Rotating Disc ◽  
System A ◽  
Finite Dimensional ◽  
Control Scheme ◽  
Actuator System ◽  
Wave Control

A modal control scheme for rotating disc systems is developed based upon the finite-dimensional sub-system model including a few lower backward travelling waves important to the disc response. For the single discrete sensor and actuator system, a polynomial equation, which determines the closed-loop system poles, is derived and the spillover effect is analysed, providing a sufficient condition for stability. Finally, simulation studies are performed to show the effectiveness of the travelling wave control scheme proposed.

TRAVELLING WAVES AND OSCILLATIONS IN SAL’NIKOV’S COMBUSTION REACTION IN A COMPRESSIBLE GAS

2015 ◽  
Vol 56 (3) ◽  
pp. 233-247 ◽  
Author(s):  
RHYS A. PAUL ◽  
LAWRENCE K. FORBES
Keyword(s):  
Asymptotic Solution ◽  
Multiple Scales ◽  
Travelling Waves ◽  
Method Of Lines ◽  
Travelling Wave ◽  
Reaction Scheme ◽  
Compressible Viscous Gas ◽  
The Method Of Lines ◽  
Temperature Waves ◽  
Parameter Values

We consider a two-step Sal’nikov reaction scheme occurring within a compressible viscous gas. The first step of the reaction may be either endothermic or exothermic, while the second step is strictly exothermic. Energy may also be lost from the system due to Newtonian cooling. An asymptotic solution for temperature perturbations of small amplitude is presented using the methods of strained coordinates and multiple scales, and a travelling wave solution with a sech-squared profile is derived. The method of lines is then used to approximate the full system with a set of ordinary differential equations, which are integrated numerically to track accurately the evolution of the reaction front. This numerical method is used to verify the asymptotic solution and investigate behaviours under different conditions. Using this method, temperature waves progressing as pulsatile fronts are detected at appropriate parameter values.

Sign in / Sign up

Export Citation Format

Share Document