Kinematical test of large extra dimension in beta decay experiments

The forthcoming experiments on neutrino mass measurement using beta decay, open a new window to explore the large extra dimension model. The Kaluza–Klein tower of neutrinos in large extra dimension contributes to the Kurie function of beta decay that can be tested kinematically. In addition to providing an alternative approach using just the kinematical properties, we show that KATRIN can probe the compactification radius of extra dimensions down to 0.2 μm which is better, at least by a factor of two, than the upper limits from neutrino oscillation experiments.     

Fettuntersuchung

Ohne Zusammenfassung     

A 3D pseudospectral method for cylindrical coordinates. Application to the simulations of rotating cavity flows

The present work proposes a collocation spectral method for solving the three-dimensional Navier–Stokes equations using cylindrical coordinates. The whole diameter $-R?r?R$ is discretized with an even number of radial Gauss–Lobatto collocation points and an angular shift is introduced in the Fourier transform that avoid pole and parity conditions usually required. The method keeps the spectral convergence that reduces the number of grid points with respect to lower-order numerical methods. The grid-points distribution densifies the mesh only near the boundaries that makes the algorithm well-suited to simulate rotating cavity flows where thin layers develop along the walls. Comparisons with reliable experimental and numerical results of the literature show good quantitative agreements for flows driven by rotating discs in tall cylinders and thin inter-disc cavities. Associated to a spectral vanishing viscosity [E. Séverac, E. Serre, A spectral vanishing viscosity for the LES of turbulent flows within rotating cavities, J. Comp. Phys. 226 (2007) 1234–1255], the method provides very promising LES results of turbulent cavity flows.     

On recurrence and transience of self-interacting random walks

Let µ₁,...,µ _k be d-dimensional probabilitymeasures in ? ^d with mean 0. At each time we choose one of the measures based on the history of the process and take a step according to that measure. We give conditions for transience of such processes and also construct examples of recurrent processes of this type. In particular, in dimension 3 we give the complete picture: every walk generated by two measures is transient and there exists a recurrent walk generated by three measures.     

Black wattle tannin as a zinc phosphating coating sealer

This paper reports an investigation into the use of condensed black wattle tannin as an environmental friendly sealer after zinc phosphating of carbon steel. In order to verify the sealer efficiency against corrosion, electrochemical impedance spectroscopy, potentiodynamic polarisation and salt spray tests were performed. To verify the pore modifications and phase compositions, SEM, electron dispersive spectroscopy and X‐ray diffraction analysis were carried out. The influence of the sealer on the adherence of finishing coatings was analysed. The results show that the tannin/sealer did not affect the final coating adhesion and improved the corrosion resistance of sealed samples. Copyright © 2013 John Wiley & Sons, Ltd.     

I Am the Cat Who Walks by Himself

The city of lions. Beaulieu-sur-Dordogne. The war starts. Drôle de guerre. Going to work. Going to school. Fleeing from village to village. Playing cat and mouse. The second landing. Return to Beaulieu. Return to Paris. Joining the boyscouts. Learning languages. Israel becomes independent. Arrival in Haifa. Kalay high school. Military training. The Hebrew Technion in Haifa. Relativity. Asher Peres. Metallurgy. Return to France. Escape from jail. Aviva.I am the cat who walks by himself, and all places are alike to me.Rudyard KiplingI am grateful to all those who contributed to this Festschrift which celebrates my 70th birthday and therefore the beginning of my eighth decade. In the Jewish religion, there is a prayer, “she-hehhyanu” to thank the Lord for having kept us alive and let us reach this day. I am an atheist and I have no Lord to thank, but I wish to thank many other people who are no longer alive and who helped me reach this point.     

Nonamenable products are not treeable

LetX andY be infinite graphs such that the automorphism group ofX is nonamenable and the automorphism group ofY has an infinite orbit. We prove that there is no automorphism-invariant measure on the set of spanning trees in the direct productX×Y. This implies that the minimal spanning forest corresponding to i.i.d. edge-weights in such a product has infinitely many connected components almost surely. Research partially supported by NSF grant DMS-9803597.     

Intersection-equivalence of Brownian paths and certain branching processes

We show that sample paths of Brownian motion (and other stable processes) intersect the same sets as certain random Cantor sets constructed by a branching process. With this approach, the classical result that two independent Brownian paths in four dimensions do not intersect reduces to the dying out of a critical branching process, and estimates due to Lawler (1982) for the long-range intersection probability of several random walk paths, reduce to Kolmogrov's 1938 law for the lifetime of a critical branching process. Extensions to random walks with long jumps and applications to Hausdorff dimension are also derived.