Etsushi Nakaguchi

Reaction-diffusion based autonomous control of wireless sensor networks

Taking into account requirements of sensor networks, we need fully-distributed and self-organising control mechanisms which are scalable to the size of a network, robust to failures of sensor nodes, and adaptive to different and dynamically changing topology and changes in wireless communication environment. To accomplish this goal, our research group focuses on behaviour of biological systems, which inherently are scalable, adaptive and robust. In this paper, we first verify the practicality of control mechanisms adopting a reaction-diffusion equation, which explains emergence of patterns on the surface of body of fishes and mammals, and then propose two methods for faster pattern generation to save energy consumption. Prom simulation and practical experiments on a prototype, it was shown that a stable pattern could be generated in a wireless sensor network in several minutes, even when packets were lost for collisions in wireless communication.

On a new dimension estimate of the global attractor for chemotaxis-growth systems

In this paper we continue systematic study of the dimension e stimate of the global attractor for the chemotaxis-growth system. Using n onnegativity of solutions we manage significantly to improve dimension estimate s with respect to the chemotactic parameter.

Experiments and considerations on Reaction-Diffusion based Pattern Generation in a Wireless Sensor Network

Taking into account requirements of sensor networks, we need fully-distributed and self-organizing control mechanisms which are scalable to the size of a network, robust to failures of sensor nodes, and adaptive to different and dynamically changing topology and changes in wireless communication environment. To accomplish this goal, our research group focuses on behavior of biological systems, which inherently are scalable, adaptive, and robust. In this paper, we first verify the practicality of control mechanisms adopting a reaction diffusion equation, which explains emergence of patterns on the surface of body of fishes and mammals, and then propose two methods for faster pattern generation to save energy consumption. From simulation and practical experiments on a prototype, it was shown that a stable pattern could be generated in a wireless sensor network in several minutes, even when packets were lost for collisions in wireless communication.

An algebraic reconstruction of a moving point source for a scalar wave equation

We discuss an identification problem of a single point source for a three-dimensional scalar wave equation. In this problem, the location and magnitude of the point source are assumed to be unknown. The location moves in a compact region, and the magnitude changes with time. As given data, we use the observed values of the retarded potential and its derivatives obtained at a single observation point and time. For this problem, we propose a direct identification method for the location and magnitude of the source. Our method consists only of the methods of linear algebra, though the problem is formulated by a partial differential equation. Numerical examples are also given to illustrate the effectiveness of our method.

DIMENSION ESTIMATE OF THE EXPONENTIAL ATTRACTOR FOR THE CHEMOTAXIS–GROWTH SYSTEM

In this paper, we study an upper bound of the fractal dimension of the exponential attractor for the chemotaxis–growth system in a two-dimensional domain. We apply the technique given by Eden, Foias, Nicolaenko and Temam. Our results show that the bound is estimated by polynomial order with respect to the chemotactic coefficient in the equation similar to our preceding papers. 2000 Mathematics Subject Classification. 35K15, 35K57, 37L30.

Global existence of solutions to an

We study the global existence of solutions to an n-dimensional parabolic-parabolic system for chemotaxis with logistic-type growth. We introduce superlinear production of a chemoattractant. We then show the global existence of solutions in Lp space (p > n) under certain relations between the degradation and production orders.

n

We study the Galerkin Euler approximations of semilinear evolution equations of parabolic: type. We utilize both the semigroup method and the variational method to construct approximate solutions and estimate errors.