In Defense of Logical Universalism: Taking Issue with Jean van Heijenoort

Van Heijenoort??s main contribution to history and philosophy of modern logic was his distinction between two basic views of logic, first, the absolutist, or universalist, view of the founding fathers, Frege, Peano, and Russell, which dominated the first, classical period of history of modern logic, and, second, the relativist, or model-theoretic, view, inherited from Boole, Schr?der, and L?wenheim, which has dominated the second, contemporary period of that history. In my paper, I present the man Jean van Heijenoort (Sect. 1); then I describe his way of arguing for the second view (Sect. 2); and finally I come down in favor of the first view (Sect. 3). There, I specify the version of universalism for which I am prepared to argue (Sect. 3, introduction). Choosing ZFC to play the part of universal, logical (in a nowadays forgotten sense) system, I show, through an example, how the usual model theory can be naturally given its proper place, from the universalist point of view, in the logical framework of ZFC; I outline another, not rival but complementary, semantics for admissible extensions of ZFC in the very same logical framework; I propose a way to get universalism out of the predicaments in which universalists themselves believed it to be (Sect. 3.1). Thus, if universalists of the classical period did not, in fact, construct these semantics, it was not that their universalism forbade them, in principle, to do so. The historical defeat of universalism was not technical in character. Neither was it philosophical. Indeed, it was hardly more than the victory of technicism over the very possibility of a philosophical dispute (Sect. 3.2).     

Sensitivity kernel for surface scattering in a waveguide

Using the Born approximation, a linearized sensitivity kernel is derived to describe the relationship between a local change at the free surface and its effect on the acoustic propagation in the water column. The structure of the surface scattering kernel is investigated numerically and experimentally for the case of a waveguide at the ultrasonic scale. To better demonstrate the sensitivity of the multipath propagation to the introduction of a localized perturbation at the air-water interface, the kernel is formulated both in terms of point-to-point and beam-to-beam representations. Agreement between theory and experiment suggests applications to sensitivity analysis of the wavefield for sea surface perturbations.     

Enhancing the emergence rate of coherent wavefronts from ocean ambient noise correlations using spatio-temporal filters

Extracting coherent wavefronts between passive receivers using cross-correlations of ambient noise (CAN) provides a means for monitoring the seismoacoustic environment without using active sources. However, using cross-correlations between single receivers can require a long recording time in order to extract stable coherent arrivals from CAN. This becomes an issue if the propagation medium fluctuates significantly during the recording period. To address this issue, this article presents a general spatio-temporal filtering procedure to enhance the emergence rate for coherent wavefronts extracted from time-averaged ambient noise correlations between two spatially separated arrays. The robustness of this array-based CAN technique is investigated using ambient shipping noise recorded over 24?h in the frequency band [250-850 Hz] on two vertical line arrays deployed 143?m apart in shallow water (depth 20?m). Experimental results confirm that the array-based CAN technique can significantly reduce the recording duration (e.g., from 22?h to 30?min) required for extracting coherent wavefronts of sufficient amplitude (e.g., 20?dB over residual temporal fluctations) when compared to conventional CAN implementations between single pairs of hydrophones. These improvements of the CAN technique could benefit the development of noise-based ocean monitoring applications such as passive acoustic tomography.     

Tri-polarized MIMO systems in real-world channels: Channel investigation and performance analysis

Polarized multi-antenna systems are an effective solution for reducing inter-antenna spacing while still maintaining low inter-antenna correlation. Traditionally, only dual-polarized antenna systems are used for polarized transceivers. In this paper, tri-polarized antenna systems are investigated. Starting from the polarization mechanisms in the wireless propagation channel, it is shown that dual-polarized MIMO systems show high sensitivity to the transmitter and receiver orientation, which may be very critical in practical applications. Tri-polarized MIMO systems are introduced as a solution to obtain a robust MIMO performances, which are independent of the transmitter and receiver orientation. The performances of dual- and tri-polarized MIMO systems are evaluated on real-world measured channels, and the limits of each of these systems is highlighted.     

Tri-polarized spectrum sensing based on an experimental outdoor-to-indoor cognitive-radio scenario

Compared to classical spatially separated multiple antenna system, cross-polarized co-located antenna systems are an interesting way to reduce equipment size while reducing the inter-antenna correlation. In this paper the spectrum sensing of a Cognitive Radio (CR) system taking advantage of polarization diversity under Rayleigh fading is investigated and compared to an equivalent system using spatial diversity. This analysis is based on a theoretical formulation applied to a real-world scenario. For this purpose, an outdoor-to-indoor measurement campaign at a frequency of 3.5 GHz is realized, where an indoor secondary user senses the signals received from an outdoor primary base station. The signals received at each antenna are first combined and then applied to an energy detector. The theoretical expressions are simulated in the measurement context. The detection probability behavior as a function of distance between the Primary Transmitter (PTx) and the Secondary Terminal (STE) and the inter-antenna correlation effect on the sensing performance are studied.     

Measurement accuracy of a mono-fiber optical probe in a bubbly flow

The measurement accuracy of a mono-fiber optical probe is studied experimentally using isolated bubbles rising freely in a still liquid. The dwell time of the probe tip within the gas phase, which is obtained from both the optical probe signal and high-speed visualization, is compared with the value expected for a non-perturbed bubble. The difference originates mainly from the intrusive nature of the optical probe, which modifies the bubble behavior when it comes into contact with the probe tip. This interaction increases the dwell time if the bubble is pierced by the probe near its pole, and shortens it for piercing near the equator. The mean dwell time, obtained by averaging for various piercing locations, is shortened and the local void fraction indicated by the probe is thus underestimated. It is shown that the void fraction error can be correlated with a modified Weber number, and this correlation is helpful for sensor selection and for uncertainty estimate. In addition, the distribution of gas dwell time usually differs from the response expected for an ideal probe. This deviation results from the dependence of the dwell time error on the piercing location. The dwell time distribution can be used to infer the dependence of the dwell time on the piercing location. Finally, the deformation of long fibers during the bubble-probe interaction significantly increases the measurement error. Observed results are consistent with data of Andreotti (2009), which were measured in an airlift flow, suggesting that present results are applicable also to the case of moving liquid. Conclusions of this study could be applied also to conductivity probes or more generally to the interaction of a bubble with any kind of thin, intrusive sensor or fiber.     

A moment method for splashing and evaporation processes of polydisperse sprays

A new moment method for the modelling of polydisperse sprays is proposed that simultaneously takes into account the dispersion in droplet size and droplet velocity. For the derivation of this Eulerian method the kinetic spray equation is used which constitutes a partial differential equation for the probability density function of droplets. To reduce the complex kinetic spray equation to a form that can be managed with the available numerical procedures, moment transforms with respect to the droplet velocity and the droplet size are conducted. The resulting moment equations are closed by choosing an approximate probability density function which applies to polydisperse sprays. The method is successfully tested for configurations in which a polydisperse spray is either splashed, evaporated or effected by a Stokes drag force. The tests are organised in such a way that crossing of two spray distributions is always included. The new method is able to capture the polydisperse nature of sprays as well as the bi-(or multi-) modal character of the droplet velocity distribution function, for example, when droplets cross each other.