Search results for "05.45.-a"
showing 5 items of 5 documents
Advances in photonic reservoir computing
2017
We review a novel paradigm that has emerged in analogue neuromorphic optical computing. The goal is to implement a reservoir computer in optics, where information is encoded in the intensity and phase of the optical field. Reservoir computing is a bio-inspired approach especially suited for processing time-dependent information. The reservoir’s complex and high-dimensional transient response to the input signal is capable of universal computation. The reservoir does not need to be trained, which makes it very well suited for optics. As such, much of the promise of photonic reservoirs lies in their minimal hardware requirements, a tremendous advantage over other hardware-intensive neural net…
Cross-Kerr nonlinearity: a stability analysis
2015
We analyse the combined effect of the radiation-pressure and cross-Kerr nonlinearity on the stationary solution of the dynamics of a nanomechanical resonator interacting with an electromagnetic cavity. Within this setup, we show how the optical bistability picture induced by the radiation-pressure force is modified by the presence of the cross-Kerr interaction term. More specifically, we show how the optically bistable region, characterising the pure radiation-pressure case, is reduced by the presence of a cross-Kerr coupling term. At the same time, the upper unstable branch is extended by the presence of a moderate cross-Kerr term, while it is reduced for larger values of the cross-Kerr co…
Statistics of nonlinear stochastic dynamical systems under Lévy noises by a convolution quadrature approach
2010
This paper describes a novel numerical approach to find the statistics of the non-stationary response of scalar non-linear systems excited by L\'evy white noises. The proposed numerical procedure relies on the introduction of an integral transform of Wiener-Hopf type into the equation governing the characteristic function. Once this equation is rewritten as partial integro-differential equation, it is then solved by applying the method of convolution quadrature originally proposed by Lubich, here extended to deal with this particular integral transform. The proposed approach is relevant for two reasons: 1) Statistics of systems with several different drift terms can be handled in an efficie…
Intermittency in the homopolar disk-dynamo
2006
We study a modified Bullard dynamo and show that this system is equivalent to a nonlinear oscillator subject to a multiplicative noise. The stability analysis of this oscillator is performed. Two bifurcations are identified, first towards an \lq\lq intermittent\rq\rq state where the absorbing (non-dynamo) state is no more stable but the most probable value of the amplitude of the oscillator is still zero and secondly towards a \lq\lq turbulent\rq\rq (dynamo) state where it is possible to define unambiguously a (non-zero) most probable value around which the amplitude of the oscillator fluctuates. The bifurcation diagram of this system exhibits three regions which are analytically characteri…
ETAT TOPOLOGIQUE DE L'ESPACE TEMPS A L'ECHELLE 0
2002
We propose in this research a new solution regarding the existence and the content of the initial spacetime singularity. In the context of topological field theory we consider that the initial singularity of space-time corresponds to a zero size singular gravitational instanton characterized by a Riemannian metric configuration (++++) in dimension D = 4. Connected with some unexpected topological data corresponding to the zero scale of space-time, the initial singularity is thus not considered in terms of divergences of physical fields but can be resolved in the frame of topological field theory. We get this result from the physical observation that the pre-spacetime is in a thermal equilib…