Helmholtz-Manakov solitons

A novel spatial soliton-bearing wave equation is introduced, the Helmholtz-Manakov (H-M) equation, for describing the evolution of broad multi-component self-trapped beams in Kerr-type media. By omitting the slowly-varying envelope approximation, the H-M equation can describe accurately vector solitons propagating and interacting at arbitrarily large angles with respect to the reference direction. The H-M equation is solved using Hirota’s method, yielding four new classes of Helmholtz soliton that are vector generalizations of their scalar counterparts. General and particular forms of the three invariants of the H-M system are also reported

Bistable Helmholtz bright solitons in saturable materials

We present, to the best of our knowledge, the first exact analytical solitons of a nonlinear Helmholtz equation with a saturable refractive-index model. These new two-dimensional spatial solitons have a bistable characteristic in some parameter regimes, and they capture oblique (arbitrary-angle) beam propagation in both the forward and backward directions. New conservation laws are reported, and the classic paraxial solution is recovered in an appropriate multiple limit. Analysis and simulations examine the stability of both solution branches, and stationary Helmholtz solitons are found to emerge from a range of perturbed input beams

A Computation in a Cellular Automaton Collider Rule 110

A cellular automaton collider is a finite state machine build of rings of one-dimensional cellular automata. We show how a computation can be performed on the collider by exploiting interactions between gliders (particles, localisations). The constructions proposed are based on universality of elementary cellular automaton rule 110, cyclic tag systems, supercolliders, and computing on rings.Comment: 39 pages, 32 figures, 3 table

Neural network design of multilayer metamaterial for temporal differentiation

Controlling wave-matter interactions with metamaterials (MTMs) for the calculation of mathematical operations has become an important paradigm for analogue computing given their ability to dramatically increase computational processing speeds. Here, motivated by the importance of performing mathematical operations on temporal signals, we propose, design and study multilayer MTMs with the ability to calculate the derivative of incident modulated temporal signals, as an example of a significant computing process for signal processing. To do this, we make use of a neural network (NN) based algorithm to design the multilayer structures (alternating layers of indium tin oxide (ITO) and titanium dioxide (TiO2)) that can calculate the first temporal derivative of the envelope of an impinging electromagnetic signal at telecom wavelengths (modulated wavelength of 1550 nm). Different designs are presented using multiple incident temporal signals including a modulated Gaussian as well as modulated arbitrary functions, demonstrating an excellent agreement between the predicted results (NN results) and the theoretical (ideal) values. It is shown how, for all the designs, the proposed NN-based algorithm can complete its search of design space for the layer thicknesses of the multilayer MTM after just a few seconds, with a low mean square error in the order of (or below) 10^-4 when comparing the predicted results with the theoretical spectrum of the ideal temporal derivative.Comment: 4 Figures, 17 page

An all-optical soliton FFT computational arrangement in the 3NLSE-domain

In this paper an all-optical soliton method for calculating the Fast Fourier Transform (FFT) algorithm is presented. The method comes as an extension of the calculation methods (soliton gates) as they become possible in the cubic non-linear Schrödinger equation (3NLSE) domain, and provides a further proof of the computational abilities of the scheme. The method involves collisions entirely between first order solitons in optical fibers whose propagation evolution is described by the 3NLSE. The main building block of the arrangement is the half-adder processor. Expanding around the half-adder processor, the “butterfly” calculation process is demonstrated using first order solitons, leading eventually to the realisation of an equivalent to a full Radix-2 FFT calculation algorithm

Towards Soliton Computer Based on Solitary Wave Solution of Maxwell Dirac equation: A Plausible Alternative to Manakov System

In recent years, there are a number of proposals to consider collision-based soliton computer based on certain chemical reactions, namely Belousov-Zhabotinsky reaction, which leads to soliton solutions of coupled Nonlinear Schroedinger equations. They are called Manakov System. But it seems to us that such a soliton computer model can also be based on solitary wave solution of Maxwell-Dirac equation, which reduces to Choquard equation. And soliton solution of Choquard equation has been investigated by many researchers, therefore it seems more profound from physics perspective. However, we consider both schemes of soliton computer are equally possible. More researches are needed to verify our proposition

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

Simple networks on complex cellular automata: From de Bruijn diagrams to jump-graphs

We overview networks which characterise dynamics in cellular automata. These networks are derived from one-dimensional cellular automaton rules and global states of the automaton evolution: de Bruijn diagrams, subsystem diagrams, basins of attraction, and jump-graphs. These networks are used to understand properties of spatially-extended dynamical systems: emergence of non-trivial patterns, self-organisation, reversibility and chaos. Particular attention is paid to networks determined by travelling self-localisations, or gliders.Comment: 25 pages, 14 figure