16 research outputs found
Exact soliton solutions of coupled nonlinear Schr\"odinger equations: Shape changing collisions, logic gates and partially coherent solitons
The novel dynamical features underlying soliton interactions in coupled
nonlinear Schr{\"o}dinger equations, which model multimode wave propagation
under varied physical situations in nonlinear optics, are studied. In this
paper, by explicitly constructing multisoliton solutions (upto four-soliton
solutions) for two coupled and arbitrary -coupled nonlinear Schr{\"o}dinger
equations using the Hirota bilinearization method, we bring out clearly the
various features underlying the fascinating shape changing (intensity
redistribution) collisions of solitons, including changes in amplitudes, phases
and relative separation distances, and the very many possibilities of energy
redistributions among the modes of solitons. However in this multisoliton
collision process the pair-wise collision nature is shown to be preserved in
spite of the changes in the amplitudes and phases of the solitons. Detailed
asymptotic analysis also shows that when solitons undergo multiple collisions,
there exists the exciting possibility of shape restoration of atleast one
soliton during interactions of more than two solitons represented by three and
higher order soliton solutions. From application point of view, we have shown
from the asymptotic expressions how the amplitude (intensity) redistribution
can be written as a generalized linear fractional transformation for the
-component case. Also we indicate how the multisolitons can be reinterpreted
as various logic gates for suitable choices of the soliton parameters, leading
to possible multistate logic. In addition, we point out that the various
recently studied partially coherent solitons are just special cases of the
bright soliton solutions exhibiting shape changing collisions, thereby
explaining their variable profile and shape variation in collision process.Comment: 50 Pages, 13 .jpg figures. To appear in PR
A framework for the local information dynamics of distributed computation in complex systems
The nature of distributed computation has often been described in terms of
the component operations of universal computation: information storage,
transfer and modification. We review the first complete framework that
quantifies each of these individual information dynamics on a local scale
within a system, and describes the manner in which they interact to create
non-trivial computation where "the whole is greater than the sum of the parts".
We describe the application of the framework to cellular automata, a simple yet
powerful model of distributed computation. This is an important application,
because the framework is the first to provide quantitative evidence for several
important conjectures about distributed computation in cellular automata: that
blinkers embody information storage, particles are information transfer agents,
and particle collisions are information modification events. The framework is
also shown to contrast the computations conducted by several well-known
cellular automata, highlighting the importance of information coherence in
complex computation. The results reviewed here provide important quantitative
insights into the fundamental nature of distributed computation and the
dynamics of complex systems, as well as impetus for the framework to be applied
to the analysis and design of other systems.Comment: 44 pages, 8 figure
Cryptanalysis of a message authentication code due to Cary and
We present a cryptanalysis of a MAC proposal at CRYPTO 2003 due to Cary and Venkatesan. Our attacks find collisions for the MAC and yield MAC forgeries, both faster than a straightforward application of the birthday paradox would suggest.
A message authentication code based on unimodular matrix groups
Abstract. We present a new construction based on modular groups. A novel element of our construction is to embed each input into a sequence of matrices with determinant ±1, the product of which yields the desired mac. We analyze using the invertibility and the arithmetic properties of the determinants of certain types of matrices; this may be of interest in other applications. Performance results on our preliminary implementations show the speed of our mac is competitive with recent fast mac algorithms, achieving 0.5 Gigabytes per second on a 1.06 GHz Celeron