Solomonoff Induction Violates Nicod's Criterion

Nicod's criterion states that observing a black raven is evidence for the hypothesis H that all ravens are black. We show that Solomonoff induction does not satisfy Nicod's criterion: there are time steps in which observing black ravens decreases the belief in H. Moreover, while observing any computable infinite string compatible with H, the belief in H decreases infinitely often when using the unnormalized Solomonoff prior, but only finitely often when using the normalized Solomonoff prior. We argue that the fault is not with Solomonoff induction; instead we should reject Nicod's criterion.Comment: ALT 201

Generation of second mode solitary waves by the interaction of a first mode soliton with a sill

International audienceResults of an experimental and theoretical study of the interaction of a first mode internal solitary wave with a localised bottom topography (sill) are presented. Laboratory experiments have been performed in a 10m long and 0.33m wide channel filled with a stratified fluid. The interface between the two layers (fresh and salt water) is diffuse and has a finite thickness. Soliton-type disturbances of the interface having characteristics of the first baroclinic mode are generated at one channel end. They move along the channel and encounter an underwater obstacle (sill) in the middle of the channel, where they break into reflected and transmitted waves. Two types of internal waves are produced by the interaction: a fast first mode internal soliton and a slower (by a factor of approximately 3) second mode soliton-like wave. A numerical model, based on the two-dimensional Navier-Stokes equations in the Boussinesq approximation, is used tore produce the laboratory experiment. The detailed analysis of the horizontal and vertical structures of transmitted and reflected waves showed that the fast reflected and transmitted waves observed in the experiment can be interpreted as a first mode internal solitary wave whose characteristics are very close to those of the K-dV solitons. It is also demonstrated that the slow speed waves, generated during the interaction behind the first fast wave have vertical and horizontal structures very close to the second mode internal K-dV solitons

Steps towards the development of an experimentally verified simulation of pool nucleate boiling on a silicon wafer with artificial sites

Nucleate boiling is a very effective heat transfer cooling process, used in numerous industrial applications. Despite intensive research over decades, a reliable model of nucleate pool boiling is still not available. This paper presents a numerical and experimental investigation of nucleate boiling from artificial nucleation sites. The numerical investigation described in the first section of the paper is carried out by a hybrid mechanistic numerical code first developed at the University of Ljubljana to simulate the temperature field in a heated stainless steel plate with a large number of nucleation sites during pool boiling of water at atmospheric pressure. It is now being redeveloped to interpret experiments on pool boiling at artificial sites on a silicon plate and as a design tool to investigate different arrangements of sites to achieve high heat fluxes. The code combines full simulation of the temperature field in the solid wall with simplified models or correlations for processes in the liquid-vapour region. The current capabilities and limitations of the code are reviewed and improvements are discussed. Examples are given of the removal of computational constraints on the activation of sites in close proximity and improvements to the bubble growth model. Preliminary simulations are presented to compare the wall conditions to be used in the experiments on silicon at Edinburgh University with the conditions in current experiments on thin metal foils at Ljubljana. An experimental rig for boiling experiments with artificial cavities on a 0.38 mm thick silicon wafer immersed in FC-72, developed at Edinburgh University, is described in the second part of the paper

A hierarchy of avalanche models on arbitrary topography

We use the non-Cartesian, topography-based equations of mass and momentum balance for gravity driven frictional flows of Luca etal. (Math. Mod. Meth. Appl. Sci. 19, 127-171 (2009)) to motivate a study on various approximations of avalanche models for single-phase granular materials. By introducing scaling approximations we develop a hierarchy of model equations which differ by degrees in shallowness, basal curvature, peculiarity of constitutive formulation (non-Newtonian viscous fluids, Savage-Hutter model) and velocity profile parametrization. An interesting result is that differences due to the constitutive behaviour are largely eliminated by scaling approximations. Emphasis is on avalanche flows; however, most equations presented here can be used in the dynamics of other thin films on arbitrary surface

Waveguide containing a backward-wave slab

We have considered theoretically the waveguide properties of a plane two-layered waveguide, whose one layer is a usual magnetodielectric (forward-wave medium), but another one is a slab of so-called backward-wave material (BW-material), whose both permittivity and permeability are negative. We have analyzed the properties of eigenwaves in this waveguide. In particular, it was found that there exist waves of both TE and TM polarizations, whose fields decay exponentially from the interface of the two slabs inside both layers, and their slow-wave factor tends to infinity at small frequencies. Thus, this waveguiding system supports super-slow waves with extremely short wavelengthes, as compared to the free-space wavelength and the cross section size. Other peculiarities of the spectrum are also discussed

Electron-phonon interaction in the solid form of the smallest fullerene C20_{20}

The electron-phonon coupling of a theoretically devised carbon phase made by assembling the smallest fullerenes C$_{20}$ is calculated from first principles. The structure consists of C$_{20}$ cages in an {\it fcc} lattice interlinked by two bridging carbon atoms in the interstitial tetrahedral sites ({\it fcc}-C$_{22}$). The crystal is insulating but can be made metallic by doping with interstitial alkali atoms. In the compound NaC$_{22}$ the calculated coupling constant $\lambda/N(0)$ is 0.28 eV, a value much larger than in C$_{60}$, as expected from the larger curvature of C$_{20}$. On the basis of the McMillan's formula, the calculated $\lambda$=1.12 and a $\mu^*$ assumed in the range 0.3-0.1 a superconducting T$_c$ in the range 15-55 K is predicted.Comment: 7 page