A Zoll counterexample to a geodesic length conjecture

We construct a counterexample to a conjectured inequality L<2D, relating the diameter D and the least length L of a nontrivial closed geodesic, for a Riemannian metric on the 2-sphere. The construction relies on Guillemin's theorem concerning the existence of Zoll surfaces integrating an arbitrary infinitesimal odd deformation of the round metric. Thus the round metric is not optimal for the ratio L/D.Comment: 10 pages; to appear in Geometric and Functional Analysi

Temperature and Disorder Chaos in Three-Dimensional Ising Spin Glasses

We study the effects of small temperature as well as disorder perturbations on the equilibrium state of three-dimensional Ising spin glasses via an alternate scaling ansatz. By using Monte Carlo simulations, we show that temperature and disorder perturbations yield chaotic changes in the equilibrium state and that temperature chaos is considerably harder to observe than disorder chaos.Comment: 4 pages, 3 figures, 1 tabl

Transverse Instability of Avalanches in Granular Flows down Incline

Avalanche experiments on an erodible substrate are treated in the framework of ``partial fluidization'' model of dense granular flows. The model identifies a family of propagating soliton-like avalanches with shape and velocity controlled by the inclination angle and the depth of substrate. At high inclination angles the solitons display a transverse instability, followed by coarsening and fingering similar to recent experimental observation. A primary cause for the transverse instability is directly related to the dependence of soliton velocity on the granular mass trapped in the avalanche.Comment: 3 figures, 4 pages, submitted to Phys Rev Let

Is Second Harmonic Generation a reliable tool for studying solid-solid phase transition and structural purity?

International audienceThe second harmonic generation (SHG) is a nonlinear optical effect occurring only in noncentrosymmetric space groups. Two photons (at the fundamental angular frequency ω) can interact in a noncentric crystal structure to give a new photon at twice the fundamental frequency (2ω). In previous studies, we demonstrated that the measurement of the intensity of the signal at 2ω (SHG signal) is a very sensitive probe to detect the noncentrosymmetry of crystal arrangements such as conglomerates [1]. This technique was also used, in rare occasions, to follow centrosymmetric to noncentrosymmetric solid-solid phase transitions [2], [3]. Because of the origin of the SHG signal, only centric to noncentric or noncentric to noncentric phase transitions can be investigated via SHG. However, SHG has proved to be highly sensitive even to a slight deviation from centrosymmetric conditions and could be used to detect noncentric nuclei and as a consequence to follow the nucleation of new phases. This could give great information about the order of the transition (as defined by Ehrenfest classification). Indeed, if the transition is of the first-order kind the signal should be discontinuous at the temperature transition but continuous in the case of a second order transition.In this study, we present the results obtained using a device developed to perform SHG measurements versus temperature for the solid-solid phase transition (from centrosymmetric to noncentrosymmetric structures) of several compounds. The case of 3-Hydroxybenzoic Acid is particularly considered. MHBA is an intermediate in the production of germicides, plasticizer and pharmaceuticals and exhibits two polymorphic forms [4] one of which is noncentrosymmetric. Finally, we evaluate the potential of the SHG signal measurements to follow phase transitions by comparison with other usual techniques such as Differential Scanning Calorimetry (DSC), X-Ray Diffraction or Raman Spectroscopy.REFERENCES[1] A. Galland, V.Dupray, B.Berton, S. Morin-Grognet, M. Sanselme, H. Atmani and G.Coquerel, “Spotting Conglomerates by Second Harmonic Generation,” Crystal Growth & Design, vol. 9, no. 6, pp. 2713–2718, Jun. 2009.[2] J. P. Dougherty and S. K. Kurtz, “A second harmonic analyzer for the detection of non- centrosymmetry,” Journal of Applied Crystallography, vol. 9, no. 2, pp. 145–158, Apr. 1976.[3] L. Smilowitz, B. F. Henson, and J. J. Romero, “Intercomparison of Calorimetry, Raman Spectroscopy, and Second Harmonic Generation Applied to Solid−Solid Phase Transitions,” The Journal of Physical Chemistry A, vol. 113, no. 35, pp. 9650–9657, Sep. 2009. [4] F. L. Nordström and Å. C. Rasmuson, “Polymorphism and thermodynamics of m- hydroxybenzoic acid,” European Journal of Pharmaceutical Sciences, vol. 28, no. 5, pp. 377– 384, Aug. 2006

Snow spectral albedo at Summit, Greenland: measurements and numerical simulations based on physical and chemical properties of the snowpack

The broadband albedo of surface snow is determined both by the near-surface profile of the physical and chemical properties of the snowpack and by the spectral and angular characteristics of the incident solar radiation. Simultaneous measurements of the physical and chemical properties of snow were carried out at Summit Camp, Greenland (72°36´ N, 38°25´ W, 3210 m a.s.l.) in May and June 2011, along with spectral albedo measurements. One of the main objectives of the field campaign was to test our ability to predict snow spectral albedo by comparing the measured albedo to the albedo calculated with a radiative transfer model, using measured snow physical and chemical properties. To achieve this goal, we made daily measurements of the snow spectral albedo in the range 350–2200 nm and recorded snow stratigraphic information down to roughly 80 cm. The snow specific surface area (SSA) was measured using the DUFISSS instrument (DUal Frequency Integrating Sphere for Snow SSA measurement, Gallet et al., 2009). Samples were also collected for chemical analyses including black carbon (BC) and dust, to evaluate the impact of light absorbing particulate matter in snow. This is one of the most comprehensive albedo-related data sets combining chemical analysis, snow physical properties and spectral albedo measurements obtained in a polar environment. The surface albedo was calculated from density, SSA, BC and dust profiles using the DISORT model (DIScrete Ordinate Radiative Transfer, Stamnes et al., 1988) and compared to the measured values. Results indicate that the energy absorbed by the snowpack through the whole spectrum considered can be inferred within 1.10%. This accuracy is only slightly better than that which can be obtained considering pure snow, meaning that the impact of impurities on the snow albedo is small at Summit. In the near infrared, minor deviations in albedo up to 0.014 can be due to the accuracy of radiation and SSA measurements and to the surface roughness, whereas deviations up to 0.05 can be explained by the spatial heterogeneity of the snowpack at small scales, the assumption of spherical snow grains made for DISORT simulations and the vertical resolution of measurements of surface layer physical properties. At 1430 and around 1800 nm the discrepancies are larger and independent of the snow properties; we propose that they are due to errors in the ice refractive index at these wavelengths. This work contributes to the development of physically based albedo schemes in detailed snowpack models, and to the improvement of retrieval algorithms for estimating snow properties from remote sensing data

A Landscape Analysis of Constraint Satisfaction Problems

We discuss an analysis of Constraint Satisfaction problems, such as Sphere Packing, K-SAT and Graph Coloring, in terms of an effective energy landscape. Several intriguing geometrical properties of the solution space become in this light familiar in terms of the well-studied ones of rugged (glassy) energy landscapes. A `benchmark' algorithm naturally suggested by this construction finds solutions in polynomial time up to a point beyond the `clustering' and in some cases even the `thermodynamic' transitions. This point has a simple geometric meaning and can be in principle determined with standard Statistical Mechanical methods, thus pushing the analytic bound up to which problems are guaranteed to be easy. We illustrate this for the graph three and four-coloring problem. For Packing problems the present discussion allows to better characterize the `J-point', proposed as a systematic definition of Random Close Packing, and to place it in the context of other theories of glasses.Comment: 17 pages, 69 citations, 12 figure

An improved lower bound for (1,<=2)-identifying codes in the king grid

We call a subset $C$ of vertices of a graph $G$ a $(1,\leq \ell)$-identifying code if for all subsets $X$ of vertices with size at most $\ell$, the sets $\{c\in C |\exists u \in X, d(u,c)\leq 1\}$ are distinct. The concept of identifying codes was introduced in 1998 by Karpovsky, Chakrabarty and Levitin. Identifying codes have been studied in various grids. In particular, it has been shown that there exists a $(1,\leq 2)$-identifying code in the king grid with density 3/7 and that there are no such identifying codes with density smaller than 5/12. Using a suitable frame and a discharging procedure, we improve the lower bound by showing that any $(1,\leq 2)$-identifying code of the king grid has density at least 47/111

Simulating seeded vacuum decay in a cold atom system

We propose to test the concept of seeded vacuum decay in cosmology using an analogue gravity Bose-Einstein condensate system. The role of the nucleation seed is played by a vortex within the condensate. We present two complementary theoretical analyses that demonstrate seeded decay is the dominant decay mechanism of the false vacuum. First, we adapt the standard instanton methods to the Gross-Pitaevskii equation. Second, we use the truncated Wigner method to study vacuum decay.Comment: 5 Pages, 4 figures, new intro in v