Cooperative effects and disorder: A scaling analysis of the spectrum of the effective atomic Hamiltonian

We study numerically the spectrum of the non-Hermitian effective Hamiltonian that describes the dipolar interaction of a gas of $N\gg 1$ atoms with the radiation field. We analyze the interplay between cooperative effects and disorder for both scalar and vectorial radiation fields. We show that for dense gases, the resonance width distribution follows, both in the scalar and vectorial cases, a power law $P(\Gamma) \sim \Gamma^{-4/3}$ that originates from cooperative effects between more than two atoms. This power law is different from the $P(\Gamma) \sim \Gamma^{-1}$ behavior, which has been considered as a signature of Anderson localization of light in random systems. We show that in dilute clouds, the center of the energy distribution is described by Wigner's semicircle law in the scalar and vectorial cases. For dense gases, this law is replaced in the vectorial case by the Laplace distribution. Finally, we show that in the scalar case the degree of resonance overlap increases as a power law of the system size for dilute gases, but decays exponentially with the system size for dense clouds.Comment: 11 pages, 12 figure

An assessment of warm fog: Nucleation, control, and recommended research

A state-of-the-art survey is given of warm fog research which has been performed up to, and including, 1974. Topics covered are nucleation, growth, coalescence, fog structures and visibility, effects of surface films, drop size spectrum, optical properties, instrumentation, liquid water content, condensation nuclei. Included is a summary of all reported fog modification experiments. Additional data is provided on air flow, turbulence, a summary of recommendations on instruments to be developed for determining turbulence, air flow, etc., as well as recommendations of various fog research tasks which should be performed for a better understanding of fog microphysics

On the Ehrenfest theorem of quantum mechanics

We give a mathematically rigorous derivation of Ehrenfest's equations for the evolution of position and momentum expectation values, under general and natural assumptions which include atomic and molecular Hamiltonians with Coulomb interactions.Comment: To appear in J. Math. Phy

Effect of superradiance on transport of diffusing photons in cold atomic gases

We show that in atomic gases cooperative effects like superradiance and subradiance lead to a potential between two atoms that decays like $1/r$. In the case of superradiance, this potential is attractive for close enough atoms and can be interpreted as a coherent mesoscopic effect. The contribution of superradiant pairs to multiple scattering properties of a dilute gas, such as photon elastic mean free path and group velocity, is significantly different from that of independent atoms. We discuss the conditions under which these effects may be observed and compare our results to recent experiments on photon transport in cold atomic gases.Comment: 4 pages and 1 figur

Roles of cooperative effects and disorder in photon localization: The case of a vector radiation field

We numerically study photon escape rates from three-dimensional atomic gases and investigate the respective roles of cooperative effects and disorder in photon localization, while taking into account the vectorial nature of light. A scaling behavior is observed for the escape rates, and photons undergo a crossover from delocalization toward localization as the optical thickness of the cloud is increased. This result indicates that light localization is dominated by cooperative effects rather than disorder. We compare our results with those obtained in the case of a scalar radiation field and find no significant differences. We conclude that the scalar model constitutes an excellent approximation when considering photon escape rates from atomic gases.Comment: 9 pages, 9 figure

Functional modelling in evolvable assembly systems

The design and reconfiguration of adaptive production systems is a key driver in modern advanced manufacturing. We summarise the use of an ap-proach from the field of functional modelling to capture the function, behaviour, and structure of a system. This model is an integral part of the Evolvable Assembly Systems architecture, allowing the system to adapt its behaviour in response to changing product requirements. The integrated approach is illustrated with an example taken from a real EAS instantiation

Photon localization and Dicke superradiance in atomic gases

Photon propagation in a gas of N atoms is studied using an effective Hamiltonian describing photon mediated atomic dipolar interactions. The density P(\Gamma) of photon escape rates is determined from the spectrum of the N x N random matrix \Gamma_{ij} = \sin (x_{ij}) / x_{ij}, where x_{ij} is the dimensionless random distance between any two atoms. Varying disorder and system size, a scaling behavior is observed for the escape rates. It is explained using microscopic calculations and a stochastic model which emphasizes the role of cooperative effects in photon localization and provides an interesting relation with statistical properties of "small world networks".Comment: 4 pages, 5 figure

DFM synthesis approach based on product-process interface modelling. Application to the peen forming process.

Engineering design approach are curently CAD-centred design process. Manufacturing information is selected and assessed very late in the design process and above all as a reactive task instead of being proactive to lead the design choices. DFM appraoches are therefore assesment methods that compare several design alternatives and not real design approaches at all. Main added value of this research work concerns the use of a product-process interface model to jointly manage both the product and the manufacturing data in a proactive DFM way. The DFM synthesis approach and the interface model are presented via the description of the DFM software platform