Vortex configurations in the large N limit

We study the properties of vortex-like configurations which are solutions of the SU(N) Yang-Mills classical equations of motion. We show that these solutions are concentrated along a two-dimensional wall with size growing with the number of colors.Comment: 13 pages, 4 postscript figure

Recursive formulas for Welschinger invariants of the projective plane

Welschinger invariants of the real projective plane can be computed via the enumeration of enriched graphs, called marked floor diagrams. By a purely combinatorial study of these objects, we prove a Caporaso-Harris type formula which allows one to compute Welschinger invariants for configurations of points with any number of complex conjugated points.Comment: 18 pages, 2 figure

On maximally inflected hyperbolic curves

In this note we study the distribution of real inflection points among the ovals of a real non-singular hyperbolic curve of even degree. Using Hilbert's method we show that for any integers $d$ and $r$ such that $4\leq r \leq 2d^2-2d$, there is a non-singular hyperbolic curve of degree $2d$ in $\mathbb R^2$ with exactly $r$ line segments in the boundary of its convex hull. We also give a complete classification of possible distributions of inflection points among the ovals of a maximally inflected non-singular hyperbolic curve of degree $6$.Comment: 13 pages, 8 figure

Numerical evaluation of three non-coaxial kinematic models using the distinct element method for elliptical granular materials

This is the accepted version of the following article: [Jiang, M. J., Liu, J. D., and Arroyo, M. (2016) Numerical evaluation of three non-coaxial kinematic models using the distinct element method for elliptical granular materials. Int. J. Numer. Anal. Meth. Geomech., 40: 2468–2488. doi: 10.1002/nag.2540.], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nag.2540/fullThis paper presents a numerical evaluation of three non-coaxial kinematic models by performing Distinct Element Method (DEM) simple shear tests on specimens composed of elliptical particles with different aspect ratios of 1.4 and 1.7. The models evaluated are the double-shearing model, the double-sliding free-rotating model and the double slip and rotation rate model (DSR2 model). Two modes of monotonic and cyclic simple shear tests were simulated to evaluate the role played by the inherent anisotropy of the specimens. The main findings are supported by all the DEM simple shear tests, irrespective of particle shape, specimen density or shear mode. The evaluation demonstrates that the assumption in the double-shearing model is inconsistent with the DEM results and that the energy dissipation requirements in the double-sliding free-rotating model appear to be too restrictive to describe the kinematic flow of elliptical particle systems. In contrast, the predictions made by the DSR2 model agree reasonably well with the DEM data, which demonstrates that the DSR2 model can effectively predict the non-coaxial kinematic behavior of elliptical particle systems.Peer ReviewedPostprint (author's final draft

Use of tire derived aggregate in tunnel cut-and-cover

A case-history is reported in which tire derived aggregate (TDA) was successfully applied to reduce the weight of fill upon a cut-and-cover railway tunnel. Subsequent 3D numerical analyses are used to explore the effect of different assumptions about the constitutive model of the TDA material. Alternative dispositions of TDA around the tunnel section are also examined. Reductions of up to 60% in lining bending moment may be achieved. For the case analyzed the elastic description of the TDA has little influence on tunnel lining loads, although is important for fill settlement estimates.Peer ReviewedPostprint (author's final draft

Topological susceptibility and Instanton size distribution from over-improved cooling

We measure the topological susceptibility by cooling with an over-improved action. In contrast with usual cooling, large instantons survive over-improved cooling {\em indefinitely}. By varying the parameter of the over-improved cooling action, we measure the instanton size distribution.Comment: 4 uuencoded PostScript pages, contribution to LAT95 (fig.2 simplified to conserve space; available upon request

Real-time Quantum evolution in the Classical approximation and beyond

With the goal in mind of deriving a method to compute quantum corrections for the real-time evolution in quantum field theory, we analyze the problem from the perspective of the Wigner function. We argue that this provides the most natural way to justify and extend the classical approximation. A simple proposal is presented that can allow to give systematic quantum corrections to the evolution of expectation values and/or an estimate of the errors committed when using the classical approximation. The method is applied to the case of a few degrees of freedom and compared with other methods and with the exact quantum results. An analysis of the dependence of the numerical effort involved as a function of the number of variables is given, which allow us to be optimistic about its applicability in a quantum field theoretical context.Comment: 32 pages, 6 figure

Cooling, Physical Scales and Topology

We develop a cooling method controlled by a physical cooling radius that defines a scale below which fluctuations are smoothed out while leaving physics unchanged at all larger scales. We apply this method to study topological properties of lattice gauge theories, in particular the behaviour of instantons, dislocations and instanton--anti-instanton pairs. Monte Carlo results for the SU(2) topology are presented. We find that the method provides a means to prevent instanton--anti-instanton annihilation under cooling. While the instanton sizes are largely independent from the smoothing scale, the density and pair separations are determined by the particular choice made for this quantity. We discuss the questions this raises for the "physicality" of these concepts.Comment: 25 pages, 8 figures, minor corrections, references adde

La boîte à outils géotechnique de demain: conception des structures géotechniques selon EN 1997: 202x

This paper shows how three new concepts – ‘Design Cases’ (introduced in prEN 1990), the ‘Geotechnical Design Model’ (prEN 1997-1), and the ‘Ground Model’ (prEN 1997-2) – are combined (in prEN 1997-3) to provide a comprehensive and flexible set of tools for the design of specific geotechnical structures. The paper presents flow charts divided between: a) reliability management, b) ground modelling, c) verification of the design, and d) structure execution, which provide guidelines for navigating prEN 1990 and prEN 1997.Postprint (published version

DEM simulation of soil-tool interaction under extraterrestrial environmental effects

In contrast to terrestrial environment, the harsh lunar environment conditions include lower gravity acceleration, ultra-high vacuum and high (low) temperature in the daytime (night-time). This paper focuses on the effects of those mentioned features on soil cutting tests, a simplified excavation test, to reduce the risk of lunar excavation missions. Soil behavior and blade performance were analyzed under different environmental conditions. The results show that: (1) the cutting resistance and the energy consumption increase linearly with the gravity. The bending moment has a bigger increasing rate in low gravity fields due to a decreasing moment arm; (2) the cutting resistance, energy consumption and bending moment increase significantly because of the raised soil strength on the lunar environment, especially in low gravity fields. Under the lunar environment, the proportions of cutting resistance, bending moment and energy consumption due to the effect of the van der Waals forces are significant. Thus, they should be taken into consideration when planning excavations on the Moon. Therefore, considering that the maximum frictional force between the excavator and the lunar surface is proportional to the gravity acceleration, the same excavator that works efficiently on the Earth may not be able to work properly on the Moon.Peer ReviewedPostprint (author's final draft