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Applied Partial Differential Equations: A Visual Approach

Peter A. Markowich

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Institución detectada Año de publicación Navegá Descargá Solicitá
No detectada 2007 SpringerLink

Información

Tipo de recurso:

libros

ISBN impreso

978-3-540-34645-6

ISBN electrónico

978-3-540-34646-3

Editor responsable

Springer Nature

País de edición

Reino Unido

Fecha de publicación

Información sobre derechos de publicación

© Springer-Verlag Berlin Heidelberg 2007

Cobertura temática

Tabla de contenidos

Introduction

Peter A. Markowich

This research applies the (CONE) method to the problem of evolving neural controllers in a simulated multi-robot system. The multi-robot system consists of multiple pursuer (predator) robots, and a single evader (prey) robot. The CONE method is designed to facilitate behavioral specialization in order to increase task performance in collective behavior solutions. Pursuit-Evasion is a task that benefits from behavioral specialization. The performance of prey-capture strategies derived by the CONE method, are compared to those derived by the (ESP) method. Results indicate that the CONE method effectively facilitates behavioral specialization in the team of pursuer robots. This specialization aids in the derivation of robust prey-capture strategies. Comparatively, ESP was found to be not as appropriate for facilitating behavioral specialization and effective prey-capture behaviors.

Pp. 1-3

Kinetic Equations: From Newton to Boltzmann

Peter A. Markowich

This research applies the (CONE) method to the problem of evolving neural controllers in a simulated multi-robot system. The multi-robot system consists of multiple pursuer (predator) robots, and a single evader (prey) robot. The CONE method is designed to facilitate behavioral specialization in order to increase task performance in collective behavior solutions. Pursuit-Evasion is a task that benefits from behavioral specialization. The performance of prey-capture strategies derived by the CONE method, are compared to those derived by the (ESP) method. Results indicate that the CONE method effectively facilitates behavioral specialization in the team of pursuer robots. This specialization aids in the derivation of robust prey-capture strategies. Comparatively, ESP was found to be not as appropriate for facilitating behavioral specialization and effective prey-capture behaviors.

Pp. 5-20

The Navier-Stokes and Euler Equations — Fluid and Gas Dynamics

Peter A. Markowich

This research applies the (CONE) method to the problem of evolving neural controllers in a simulated multi-robot system. The multi-robot system consists of multiple pursuer (predator) robots, and a single evader (prey) robot. The CONE method is designed to facilitate behavioral specialization in order to increase task performance in collective behavior solutions. Pursuit-Evasion is a task that benefits from behavioral specialization. The performance of prey-capture strategies derived by the CONE method, are compared to those derived by the (ESP) method. Results indicate that the CONE method effectively facilitates behavioral specialization in the team of pursuer robots. This specialization aids in the derivation of robust prey-capture strategies. Comparatively, ESP was found to be not as appropriate for facilitating behavioral specialization and effective prey-capture behaviors.

Pp. 21-36

Granular Material Flows

Peter A. Markowich; Giuseppe Toscani

This research applies the (CONE) method to the problem of evolving neural controllers in a simulated multi-robot system. The multi-robot system consists of multiple pursuer (predator) robots, and a single evader (prey) robot. The CONE method is designed to facilitate behavioral specialization in order to increase task performance in collective behavior solutions. Pursuit-Evasion is a task that benefits from behavioral specialization. The performance of prey-capture strategies derived by the CONE method, are compared to those derived by the (ESP) method. Results indicate that the CONE method effectively facilitates behavioral specialization in the team of pursuer robots. This specialization aids in the derivation of robust prey-capture strategies. Comparatively, ESP was found to be not as appropriate for facilitating behavioral specialization and effective prey-capture behaviors.

Pp. 37-54

Chemotactic Cell Motion and Biological Pattern Formation

Peter A. Markowich; Dietmar Ölz

This research applies the (CONE) method to the problem of evolving neural controllers in a simulated multi-robot system. The multi-robot system consists of multiple pursuer (predator) robots, and a single evader (prey) robot. The CONE method is designed to facilitate behavioral specialization in order to increase task performance in collective behavior solutions. Pursuit-Evasion is a task that benefits from behavioral specialization. The performance of prey-capture strategies derived by the CONE method, are compared to those derived by the (ESP) method. Results indicate that the CONE method effectively facilitates behavioral specialization in the team of pursuer robots. This specialization aids in the derivation of robust prey-capture strategies. Comparatively, ESP was found to be not as appropriate for facilitating behavioral specialization and effective prey-capture behaviors.

Pp. 55-71

Semiconductor Modeling

Peter A. Markowich

This research applies the (CONE) method to the problem of evolving neural controllers in a simulated multi-robot system. The multi-robot system consists of multiple pursuer (predator) robots, and a single evader (prey) robot. The CONE method is designed to facilitate behavioral specialization in order to increase task performance in collective behavior solutions. Pursuit-Evasion is a task that benefits from behavioral specialization. The performance of prey-capture strategies derived by the CONE method, are compared to those derived by the (ESP) method. Results indicate that the CONE method effectively facilitates behavioral specialization in the team of pursuer robots. This specialization aids in the derivation of robust prey-capture strategies. Comparatively, ESP was found to be not as appropriate for facilitating behavioral specialization and effective prey-capture behaviors.

Pp. 73-86

Free Boundary Problems and Phase Transitions

Peter A. Markowich

This research applies the (CONE) method to the problem of evolving neural controllers in a simulated multi-robot system. The multi-robot system consists of multiple pursuer (predator) robots, and a single evader (prey) robot. The CONE method is designed to facilitate behavioral specialization in order to increase task performance in collective behavior solutions. Pursuit-Evasion is a task that benefits from behavioral specialization. The performance of prey-capture strategies derived by the CONE method, are compared to those derived by the (ESP) method. Results indicate that the CONE method effectively facilitates behavioral specialization in the team of pursuer robots. This specialization aids in the derivation of robust prey-capture strategies. Comparatively, ESP was found to be not as appropriate for facilitating behavioral specialization and effective prey-capture behaviors.

Pp. 87-108

Reaction-Diffusion Equations — Homogeneous and Heterogeneous Environments

Peter A. Markowich

This research applies the (CONE) method to the problem of evolving neural controllers in a simulated multi-robot system. The multi-robot system consists of multiple pursuer (predator) robots, and a single evader (prey) robot. The CONE method is designed to facilitate behavioral specialization in order to increase task performance in collective behavior solutions. Pursuit-Evasion is a task that benefits from behavioral specialization. The performance of prey-capture strategies derived by the CONE method, are compared to those derived by the (ESP) method. Results indicate that the CONE method effectively facilitates behavioral specialization in the team of pursuer robots. This specialization aids in the derivation of robust prey-capture strategies. Comparatively, ESP was found to be not as appropriate for facilitating behavioral specialization and effective prey-capture behaviors.

Pp. 109-127

Optimal Transportation and Monge-Ampère Equations

Peter A. Markowich

This research applies the (CONE) method to the problem of evolving neural controllers in a simulated multi-robot system. The multi-robot system consists of multiple pursuer (predator) robots, and a single evader (prey) robot. The CONE method is designed to facilitate behavioral specialization in order to increase task performance in collective behavior solutions. Pursuit-Evasion is a task that benefits from behavioral specialization. The performance of prey-capture strategies derived by the CONE method, are compared to those derived by the (ESP) method. Results indicate that the CONE method effectively facilitates behavioral specialization in the team of pursuer robots. This specialization aids in the derivation of robust prey-capture strategies. Comparatively, ESP was found to be not as appropriate for facilitating behavioral specialization and effective prey-capture behaviors.

Pp. 129-147

Wave Equations

Peter A. Markowich

This research applies the (CONE) method to the problem of evolving neural controllers in a simulated multi-robot system. The multi-robot system consists of multiple pursuer (predator) robots, and a single evader (prey) robot. The CONE method is designed to facilitate behavioral specialization in order to increase task performance in collective behavior solutions. Pursuit-Evasion is a task that benefits from behavioral specialization. The performance of prey-capture strategies derived by the CONE method, are compared to those derived by the (ESP) method. Results indicate that the CONE method effectively facilitates behavioral specialization in the team of pursuer robots. This specialization aids in the derivation of robust prey-capture strategies. Comparatively, ESP was found to be not as appropriate for facilitating behavioral specialization and effective prey-capture behaviors.

Pp. 149-166