Fluctuating commutative geometry

We use the framework of noncommutative geometry to define a discrete model for fluctuating geometry. Instead of considering ordinary geometry and its metric fluctuations, we consider generalized geometries where topology and dimension can also fluctuate. The model describes the geometry of spaces with a countable number n of points. The spectral principle of Connes and Chamseddine is used to define dynamics. We show that this simple model has two phases. The expectation value , the average number of points in the universe, is finite in one phase and diverges in the other. Moreover, the dimension delta is a dynamical observable in our model, and plays the role of an order parameter. The computation of is discussed and an upper bound is found, < 2. We also address another discrete model defined on a fixed d = 1 dimension, where topology fluctuates. We comment on a possible spontaneous localization of topology.

Fluctuating dimension in a discrete model for quantum gravity based on the spectral principle

The spectral principle of Connes and Chamseddine is used as a starting point to define a discrete model for Euclidean quantum gravity. Instead of summing over ordinary geometries, we consider the sum over generalized geometries where topology, metric, and dimension can fluctuate. The model describes the geometry of spaces with a countable number n of points, and is related to the Gaussian unitary ensemble of Hermitian matrices. We show that this simple model has two phases. The expectation value , the average number of points in the Universe, is finite in one phase and diverges in the other. We compute the critical point as well as the critical exponent of . Moreover, the space-time dimension delta is a dynamical observable in our model, and plays the role of an order parameter. The computation of is discussed and an upper bound is found, < 2.

Spectral analysis and low-frequency multipath mitigation for kinematic applications

Low-frequency multipath is still one of the major challenges for high precision GPS relative positioning. In kinematic applications, mainly, due to geometry changes, the low-frequency multipath is difficult to be removed or modeled. Spectral analysis has a powerful technique to analyze this kind of non-stationary signals: the wavelet transform. However, some processes and specific ways of processing are necessary to work together in order to detect and efficiently mitigate low-frequency multipath. In this paper, these processes are discussed. Some experiments were carried out in a kinematic mode with a controlled and known vehicle movement. The data were collected in the presence of a reflector surface placed close to the vehicle to cause, mainly, low-frequency multipath. From theanalyses realized, the results in terms of double difference residuals and statistical tests showed that the proposed methodology is very efficient to detect and mitigate low-frequency multipath effects. © 2008 IEEE.

Experimental observation of infrared spectral enlargement in As 2S3 suspended core microstructured fiber

The development of chalcogenide glasses fibers for application in the infrared wavelength region between 1 and 10 μm is a big opportunity. More particularly, the possibility to generate efficient non linear effects above 2 μm is a real challenge. We present in this work the elaboration and optical characterizations of suspended core microstructured optical fibers elaborated from the As2S3 chalcogenide glass. As an alternative to the stack and draw process a mechanical machining has been used to the elaboration of the preforms. The drawing of these preforms into fibers allows reaching a suspended core geometry, in which a 2.5 μm diameter core is linked to the fiber clad region by three supporting struts. The zero dispersion wavelength is thus shifted towards 2 μm. At 1.55 μm our fibers exhibit a dispersion around -250 ps/nm/km. Their background level of losses is below 0,5 dB/m. By pumping them at 1.55 μm with a ps source, we observe self phase modulation as well as Raman generation. Finally a strong spectral enlargement is obtained with an average output power of - 5 dbm. © 2010 SPIE.