Combinatorics of lattice paths with and without spikes

We derive a series of results on random walks on a d-dimensional hypercubic lattice (lattice paths). We introduce the notions of terse and simple paths corresponding to the path having no backtracking parts (spikes). These paths label equivalence classes which allow a rearrangement of the sum over paths. The basic combinatorial quantities of this construction are given. These formulas are useful when performing strong coupling (hopping parameter) expansions of lattice models. Some applications are described.Comment: Latex. 25 page

Large N reduction with overlap fermions

We revisit quenched reduction with fermions and explain how some old problems can be avoided using the overlap Dirac operator.Comment: Lattice2002(chiral) 3 pages, no figure

La boîte à outils géotechniques de demain: EN 1997-1: 202x Règles générales

This paper describes the development of the final Project Team (PT) draft of the next generation of Eurocode 7 Part 1 (EN 1997-1:202x). The use of Nationally Determined Parameters and the drive for ease-of-use is highlighted. Key changes from the previous version of EN 1997-1 are explained, including the introduction of the Geotechnical Design Model; revision of the Geotechnical Categories and their application; the implementation of Consequence Classes and Geotechnical Complexity Classes in achieving the reliability required by the Eurocodes; elaboration on the use of numerical methods within Eurocode 7; the treatment of rock on an equal basis with soil; and greater emphasis on the Observational Method.Postprint (published version

What causes the large extensions of red-supergiant atmospheres? Comparisons of interferometric observations with 1-D hydrostatic, 3-D convection, and 1-D pulsating model atmospheres

We present the atmospheric structure and the fundamental parameters of three red supergiants, increasing the sample of RSGs observed by near-infrared spectro-interferometry. Additionally, we test possible mechanisms that may explain the large observed atmospheric extensions of RSGs. We carried out spectro-interferometric observations of 3 RSGs in the near-infrared K-band with the VLTI/AMBER instrument at medium spectral resolution. To comprehend the extended atmospheres, we compared our observational results to predictions by available hydrostatic PHOENIX, available 3-D convection, and new 1-D self-excited pulsation models of RSGs. Our near-infrared flux spectra are well reproduced by the PHOENIX model atmospheres. The continuum visibility values are consistent with a limb-darkened disk as predicted by the PHOENIX models, allowing us to determine the angular diameter and the fundamental parameters of our sources. Nonetheless, in the case of V602 Car and HD 95686, the PHOENIX model visibilities do not predict the large observed extensions of molecular layers, most remarkably in the CO bands. Likewise, the 3-D convection models and the 1-D pulsation models with typical parameters of RSGs lead to compact atmospheric structures as well, which are similar to the structure of the hydrostatic PHOENIX models. They can also not explain the observed decreases in the visibilities and thus the large atmospheric molecular extensions. The full sample of our RSGs indicates increasing observed atmospheric extensions with increasing luminosity and decreasing surface gravity, and no correlation with effective temperature or variability amplitude, which supports a scenario of radiative acceleration on Doppler-shifted molecular lines.Comment: Accepted for publication in A&

Exact renormalization-group analysis of first order phase transitions in clock models

We analyze the exact behavior of the renormalization group flow in one-dimensional clock-models which undergo first order phase transitions by the presence of complex interactions. The flow, defined by decimation, is shown to be single-valued and continuous throughout its domain of definition, which contains the transition points. This fact is in disagreement with a recently proposed scenario for first order phase transitions claiming the existence of discontinuities of the renormalization group. The results are in partial agreement with the standard scenario. However in the vicinity of some fixed points of the critical surface the renormalized measure does not correspond to a renormalized Hamiltonian for some choices of renormalization blocks. These pathologies although similar to Griffiths-Pearce pathologies have a different physical origin: the complex character of the interactions. We elucidate the dynamical reason for such a pathological behavior: entire regions of coupling constants blow up under the renormalization group transformation. The flows provide non-perturbative patterns for the renormalization group behavior of electric conductivities in the quantum Hall effect.Comment: 13 pages + 3 ps figures not included, TeX, DFTUZ 91.3

Expansion for the solutions of the Bogomolny equations on the torus

We show that the solutions of the Bogomolny equations for the Abelian Higgs model on a two-dimensional torus, can be expanded in powers of a quantity epsilon measuring the departure of the area from the critical area. This allows a precise determination of the shape of the solutions for all magnetic fluxes and arbitrary position of the Higgs field zeroes. The expansion is carried out to 51 orders for a couple of representative cases, including the unit flux case. We analyse the behaviour of the expansion in the limit of large areas, in which case the solutions approach those on the plane. Our results suggest convergence all the way up to infinite area.Comment: 26 pages, 8 figures, slightly revised version as published in JHE

High temperature performance of a piezoelectric micro cantilever for vibration energy harvesting

Energy harvesters withstanding high temperatures could provide potentially unlimited energy to sensor nodes placed in harsh environments, where manual maintenance is difficult and costly. Experimental results on a classical microcantilever show a 67% drop of the maximum power when the temperature is increased up to 160 °C. This decrease is investigated using a lumped-parameters model which takes into account variations in material parameters with temperature, damping increase and thermal stresses induced by mismatched thermal coefficients in a composite cantilever. The model allows a description of the maximum power evolution as a function of temperature and input acceleration. Simulation results further show that an increase in damping and the apparition of thermal stresses are contributing to the power drop at 59% and 13% respectively

A Rigourous Treatment of the Lattice Renormalization Problem of F_B

The $B$-meson decay constant can be measured on the lattice using a $1/m_b$ expansion. To relate the physical quantity to Monte Carlo data one has to know the renormalization coefficient, $Z$, between the lattice operators and their continuum counterparts. We come back to this computation to resolve discrepancies found in previous calculations. We define and discuss in detail the renormalization procedure that allows the (perturbative) computation of $Z$. Comparing the one-loop calculations in the effective Lagrangian approach with the direct two-loop calculation of the two-point $B$-meson correlator in the limit of large $b$-quark mass, we prove that the two schemes give consistent results to order $\alpha_s$. We show that there is, however, a renormalization prescription ambiguity that can have sizeable numerical consequences. This ambiguity can be resolved in the framework of an $O(a)$ improved calculation, and we describe the correct prescription in that case. Finally we give the numerical values of $Z$ that correspond to the different types of lattice approximations discussed in the paper.Comment: 27 pages, 2 figures (Plain TeX, figures in an appended postscript file