Accession Number:

ADA199988

Title:

Collective Properties of Neural Systems and Their Relation to Other Physical Models

Descriptive Note:

Final rept. 1 Jul 1987-31 Aug 1988

Corporate Author:

CLARKSON UNIV POTSDAM NY DIV OF RESEARCH

Personal Author(s):

Report Date:

1988-08-05

Pagination or Media Count:

172.0

Abstract:

During the tenure of this contract progress was accomplished on three fronts 1 The recursion operator of the Landau-Lifshitz equation has been completed explicitly. This has been achieved algorithmically by utilizing methods introduced earlier. It should be emphasized that in addition to the important implications of these results to general lattice theories and neural networks, the answers obtained are novel on their own merit since textbooks referred to constructing the above recursion operation as an outstanding open problem. 2 We have continued our study of nonlinear optics. We have introduced a new system of nonlinear PDEs that governs the development path of photoresist fabrication. We have employed a proof given in collaboration with Araki concerning an iteration scheme, used throughout the analysis. We have reported this work in various publications and in a number of international conferences. 3 Substantial progress has been made towards solving the nonlinear Schrodinger NLS equation on the half-time. Finite boundedness in conjunction with nonlinear evolution equations have alluded investigators for years. Since nonlinear optics is to be employed on finite boundaries, a major thrust was needed to achieve viable results. A new method has been introduced and tested on the NLS on the half-line. For the first time concrete analytical results have been obtained, and the entire problem has been reduced to linearizing a certain equation satisfied by the scattering data. This linearization and the application of the above method to other important evolution equations is under investigation.

Subject Categories:

  • Electrooptical and Optoelectronic Devices
  • Operations Research
  • Optics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE