1,207 research outputs found
Nonlinear Propagation of Light in One Dimensional Periodic Structures
We consider the nonlinear propagation of light in an optical fiber waveguide
as modeled by the anharmonic Maxwell-Lorentz equations (AMLE). The waveguide is
assumed to have an index of refraction which varies periodically along its
length. The wavelength of light is selected to be in resonance with the
periodic structure (Bragg resonance). The AMLE system considered incorporates
the effects non-instantaneous response of the medium to the electromagnetic
field (chromatic or material dispersion), the periodic structure (photonic band
dispersion) and nonlinearity. We present a detailed discussion of the role of
these effects individually and in concert. We derive the nonlinear coupled mode
equations (NLCME) which govern the envelope of the coupled backward and forward
components of the electromagnetic field. We prove the validity of the NLCME
description and give explicit estimates for the deviation of the approximation
given by NLCME from the {\it exact} dynamics, governed by AMLE. NLCME is known
to have gap soliton states. A consequence of our results is the existence of
very long-lived {\it gap soliton} states of AMLE. We present numerical
simulations which validate as well as illustrate the limits of the theory.
Finally, we verify that the assumptions of our model apply to the parameter
regimes explored in recent physical experiments in which gap solitons were
observed.Comment: To appear in The Journal of Nonlinear Science; 55 pages, 13 figure
Brainlab: A Python Toolkit to Aid in the Design, Simulation, and Analysis of Spiking Neural Networks with the NeoCortical Simulator
Neuroscience modeling experiments often involve multiple complex neural network and cell model variants, complex input stimuli and input protocols, followed by complex data analysis. Coordinating all this complexity becomes a central difficulty for the experimenter. The Python programming language, along with its extensive library packages, has emerged as a leading āglueā tool for managing all sorts of complex programmatic tasks. This paper describes a toolkit called Brainlab, written in Python, that leverages Python's strengths for the task of managing the general complexity of neuroscience modeling experiments. Brainlab was also designed to overcome the major difficulties of working with the NCS (NeoCortical Simulator) environment in particular. Brainlab is an integrated model-building, experimentation, and data analysis environment for the powerful parallel spiking neural network simulator system NCS
Framework and Implications of Virtual Neurorobotics
Despite decades of societal investment in artificial learning systems, truly āintelligentā systems have yet to be realized. These traditional models are based on input-output pattern optimization and/or cognitive production rule modeling. One response has been social robotics, using the interaction of human and robot to capture important cognitive dynamics such as cooperation and emotion; to date, these systems still incorporate traditional learning algorithms. More recently, investigators are focusing on the core assumptions of the brain āalgorithmā itselfātrying to replicate uniquely āneuromorphicā dynamics such as action potential spiking and synaptic learning. Only now are large-scale neuromorphic models becoming feasible, due to the availability of powerful supercomputers and an expanding supply of parameters derived from research into the brain's interdependent electrophysiological, metabolomic and genomic networks. Personal computer technology has also led to the acceptance of computer-generated humanoid images, or āavatarsā, to represent intelligent actors in virtual realities. In a recent paper, we proposed a method of virtual neurorobotics (VNR) in which the approaches above (social-emotional robotics, neuromorphic brain architectures, and virtual reality projection) are hybridized to rapidly forward-engineer and develop increasingly complex, intrinsically intelligent systems. In this paper, we synthesize our research and related work in the field and provide a framework for VNR, with wider implications for research and practical applications
Chaos and Stability in The Crucible
The script of The Crucible is built on a structure of binary oppositions, particularly good vs. evil and stability vs. chaos. Revealing the structure deconstructs the binary oppositions and explains how the play challenges audiences to reconsider what they understand about good and evil in their contemporary times
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