Metrics on semistable and numerically effective Higgs bundles

We provide notions of numerical effectiveness and numerical flatness for Higgs vector bundles on compact K\"ahler manifolds in terms of fibre metrics. We prove several properties of bundles satisfying such conditions and in particular we show that numerically flat Higgs bundles have vanishing Chern classes, and that they admit filtrations whose quotients are stable flat Higgs bundles. We compare these definitions with those previously given in the case of projective varieties. Finally we study the relations between numerically effectiveness and semistability, establishing semistability criteria for Higgs bundles on projective manifolds of any dimension.Comment: 25 pages. Changes in the expositio

Numerically flat Higgs vector bundles

After providing a suitable definition of numerical effectiveness for Higgs bundles, and a related notion of numerical flatness, in this paper we prove, together with some side results, that all Chern classes of a Higgs-numerically flat Higgs bundle vanish, and that a Higgs bundle is Higgs-numerically flat if and only if it is has a filtration whose quotients are flat stable Higgs bundles. We also study the relation between these numerical properties of Higgs bundles and (semi)stability.Comment: 11 page

Experimental results on evaporation waves

We address an experimental investigation of evaporation waves. They are obtained when a liquid contained in a vertical glass tube is suddenly depressurized from a high initial pressure down to the atmospheric one. After the release of pressure, the state of the liquid, which is at ambient pressure and the initial temperature, is well known to be metastable when the corresponding stable state is vapour. For moderately large evaporation rates (moderately large initial to ambient pressure ratios), the vapour-liquid interface ultimately evolves into an evaporation wave in which a highly corrugated front propagates downwards into the liquid with a well defined mean velocity. This mean velocity turns out to be a function of the ratio between the initial and the ambient pressures. In addition, attention to some new phenomena not previously reported is brought

Positivity for Higgs vector bundles: criteria and applications

Working in the category of smooth projective varieties over an algebraically closed field of characteristic 0, we review notions of ampleness and numerical nefness for Higgs bundles which "feel" the Higgs field and formulate criteria of the Barton-Kleiman type for these notions. We give an application to minimal surfaces of general type that saturate the Miyaoka-Yau inequality, showing that their cotangent bundle is ample. This will use results by Langer that imply that also for varieties over algebraically closed field of characteristic zero the so-called Simpson system is stable.Comment: 12 pages. v2: minor change in one exampl

Contact line depinning from sharp edges

With aim of finding mathematical criteria for contact line depinning from sharp corners, we have studied the equilibrium and stability of a semi-infinite planar liquid layer pinned at the vertex of a wedge. Equilibrium is compatible with a fan of apparent contact angles $\theta_0$ bracketed by the equilibrium contact angles of both flanks of the wedge, so the contact line could remain pinned if $\theta_0$ is within this fan. However, the analysis of the stability of these solutions, studied exploiting the variational structure of the problem through turning-point arguments, shows that the equilibrium becomes unstable at critical depinning advancing $\theta_0^a$ and receding $\theta_0^r$ contact angles, which are found as subcritical saddle-node bifurcations. Equilibrium is thus possible (stable) within the interval $\theta_0^a < \theta_0 <\theta_0^a$ but the contact line depins from the vertex beyond these critical angles if they occur within the equilibrium fan.Comment: 9 pages, 5 figure

Escisión de fibrados en G(1,4) y sus variedades

La memoria se divide en dos partes diferenciadas. En la primera, correspondiente al capítulo uno, se clasifican los fibrados sin cohomología intermedia de la Grassamanniana G(1,4) de las rectas de P4. A diferencia de lo que ocurre en la Grassamanniana de rectas P3, se obtienen familias infinitas de fibrados. Como paso particular de la clasificación se caracterizan cohomológicamente las sumas directas de fibrados trivales y fibrados universales de la Grassamanniana, Q, S y S (y sus twists). La segunda parte, dividida en dos capítulos (2 y 3), consiste en la clasificación de las subvariedades lisas y de dimensión tres de G(1,4), llamadas congruencias, que además verifican que el fibrado universal cociente, Q, restringido a ellas escinde en suma directa de fibrados no lineales. La clasificación se hace interpretando geométricamente tanto el significado que tiene esta escisión, como el del número de secciones globales independientes que tienen los correspondientes fibrados lineale

On a conjecture about Higgs bundles for rank 2 and some inequalities

We briefly review an open conjecture about Higgs bundles that are semistable with after pulling back to any curve, and prove it in the rank 2 case. We also prove a set of inequalities holding for H-nef Higgs bundles that generalize some of the Fulton-Lazarsfeld inequalities for numerically effective vector bundles.Comment: 13 pages. v2: 14 pages. Some results have been strengthened and the exposition has been reorganized. v3: minor changes, final version to appear in Mediterranean J. Mat

Self-Turbulent Flame Speeds

International audienceThis paper reports an experimental investigation of premixed propane andmethane-air flames propagating freely in tubes 1.5 m long and with diameters rangingfrom 26 to 141 mm. The thermo-acoustic instability was eliminated by means of anovel acoustic absorber placed at the closed end of the tube. We first remark that theflame can adopt different shapes either quasi-axisymmetric and normal to the meandirection of propagation, or inclined with a larger propagation speed because of theincrease in flame surface area. The minima of the propagation speeds, correspondingto non-tilted flame propagation, are then analyzed using analytical models for theself-turbulent flame propagation. The concept of a cut-off wavelength appears to berelevant to explain the different behaviors observed on the rich side of methane-ai