Communication: Evidence for non-ergodicity in quiescent states of periodically sheared suspensions.

We present simulations of an equilibrium statistical-mechanics model that uniformly samples the space of quiescent states of a periodically sheared suspension. In our simulations, we compute the structural properties of this model as a function of density. We compare the results of our simulations with the structural data obtained in the corresponding non-equilibrium model of Corté et al. [Nat. Phys. 4, 420 (2008)]. We find that the structural properties of the non-equilibrium model are very different from those of the equilibrium model, even though the two models have exactly the same set of accessible states. This observation shows that the dynamical protocol does not sample all quiescent states with equal probability. In particular, we find that, whilst quiescent states prepared in a non-equilibrium protocol can be hyperuniform [see D. Hexner and D. Levine, Phys. Rev. Lett. 114, 110602 (2015); E. Tjhung and L. Berthier, Phys. Rev. Lett. 114, 148301 (2015); and J. H. Weijs et al., Phys. Rev. Lett. 115, 108301 (2015)], ergodic sampling never leads to hyperuniformity. In addition, we observe ordering phase transitions and a percolation transition in the equilibrium model that do not show up in the non-equilibrium model. Conversely, the quiescent-to-diffusive transition in the dynamical model does not correspond to a phase transition, nor a percolation transition, in the equilibrium model.This work was supported by ERC Advanced Grant 227758 (COLSTRUCTION), EPSRC Programme Grant EP/I001352/1 and by the Swiss National Science Foundation (Grant No. P2EZP2-152188 and No. P300P2- 161078). K.J.S. acknowledges useful discussions with Nuno Araújo, Tristan Cragnolini, Daphne Klotsa, Erik Luijten, Stefano Martiniani, Anđela Šarić, Iskra Staneva, Jacob Stevenson, and Peter Wirnsberger.This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by AIP

Watersheds in disordered media

This is the final published version. It first appeared at http://journal.frontiersin.org/article/10.3389/fphy.2015.00005/full#h11.What is the best way to divide a rugged landscape? Since ancient times, watersheds separating adjacent water systems that flow, for example, toward different seas, have been used to delimit boundaries. Interestingly, serious and even tense border disputes between countries have relied on the subtle geometrical properties of these tortuous lines. For instance, slight and even anthropogenic modifications of landscapes can produce large changes in a watershed, and the effects can be highly nonlocal. Although the watershed concept arises naturally in geomorphology, where it plays a fundamental role in water management, landslide, and flood prevention, it also has important applications in seemingly unrelated fields such as image processing and medicine. Despite the far-reaching consequences of the scaling properties on watershed-related hydrological and political issues, it was only recently that a more profound and revealing connection has been disclosed between the concept of watershed and statistical physics of disordered systems. This review initially surveys the origin and definition of a watershed line in a geomorphological framework to subsequently introduce its basic geometrical and physical properties. Results on statistical properties of watersheds obtained from artificial model landscapes generated with long-range correlations are presented and shown to be in good qualitative and quantitative agreement with real landscapes.We acknowledge financial support from the European Research Council (ERC) Advanced Grant 319968-FlowCCS, the Brazilian Agencies CNPq, CAPES, FUNCAP and FINEP, the FUNCAP/CNPq Pronex grant, the National Institute of Science and Technology for Complex Systems in Brazil, the Portuguese Foundation for Science and Technology (FCT) under contracts no. IF/00255/2013, PEst-OE/FIS/UI0618/2014, and EXCL/FIS-NAN/0083/2012, and the Swiss National Science Foundation under Grant No. P2EZP2-152188

Turning intractable counting into sampling: Computing the configurational entropy of three-dimensional jammed packings.

We present a numerical calculation of the total number of disordered jammed configurations Ω of N repulsive, three-dimensional spheres in a fixed volume V. To make these calculations tractable, we increase the computational efficiency of the approach of Xu et al. [Phys. Rev. Lett. 106, 245502 (2011)10.1103/PhysRevLett.106.245502] and Asenjo et al. [Phys. Rev. Lett. 112, 098002 (2014)10.1103/PhysRevLett.112.098002] and we extend the method to allow computation of the configurational entropy as a function of pressure. The approach that we use computes the configurational entropy by sampling the absolute volume of basins of attraction of the stable packings in the potential energy landscape. We find a surprisingly strong correlation between the pressure of a configuration and the volume of its basin of attraction in the potential energy landscape. This relation is well described by a power law. Our methodology to compute the number of minima in the potential energy landscape should be applicable to a wide range of other enumeration problems in statistical physics, string theory, cosmology, and machine learning that aim to find the distribution of the extrema of a scalar cost function that depends on many degrees of freedom.We acknowledge useful discussions with Daniel Asenjo, Carl Goodrich, Silke Henkes, and Fabien Paillusson. S.M. acknowledges financial support by the Gates Cambridge Scholarship. K.J.S. acknowledges support by the Swiss National Science Foundation under Grant No. P2EZP2-152188 and No. P300P2-161078. J.D.S. acknowledges support by Marie Curie Grant 275544. D.F. and D.J.W. acknowledge support by EPSRC Programme Grant EP/I001352/1, by EPSRC grant EP/I000844/1 (D.F.) and ERC Advanced Grant RG59508 (D.J.W.)This is the author accepted manuscript. The final version is available from the American Physical Society via http://dx.doi.org/10.1103/PhysRevE.93.01290

Structural analysis of high-dimensional basins of attraction.

We propose an efficient Monte Carlo method for the computation of the volumes of high-dimensional bodies with arbitrary shape. We start with a region of known volume within the interior of the manifold and then use the multistate Bennett acceptance-ratio method to compute the dimensionless free-energy difference between a series of equilibrium simulations performed within this object. The method produces results that are in excellent agreement with thermodynamic integration, as well as a direct estimate of the associated statistical uncertainties. The histogram method also allows us to directly obtain an estimate of the interior radial probability density profile, thus yielding useful insight into the structural properties of such a high-dimensional body. We illustrate the method by analyzing the effect of structural disorder on the basins of attraction of mechanically stable packings of soft repulsive spheres.EPSRC No. EP/I001352/1 and. EP/I000844/1 EU Marie Curie Grant 275544 ERC Grant RG5950

Contraindications of sentinel lymph node biopsy: Áre there any really?

BACKGROUND: One of the most exciting and talked about new surgical techniques in breast cancer surgery is the sentinel lymph node biopsy. It is an alternative procedure to standard axillary lymph node dissection, which makes possible less invasive surgery and side effects for patients with early breast cancer that wouldn't benefit further from axillary lymph node clearance. Sentinel lymph node biopsy helps to accurately evaluate the status of the axilla and the extent of disease, but also determines appropriate adjuvant treatment and long-term follow-up. However, like all surgical procedures, the sentinel lymph node biopsy is not appropriate for each and every patient. METHODS: In this article we review the absolute and relative contraindications of the procedure in respect to clinically positive axilla, neoadjuvant therapy, tumor size, multicentric and multifocal disease, in situ carcinoma, pregnancy, age, body-mass index, allergies to dye and/or radio colloid and prior breast and/or axillary surgery. RESULTS: Certain conditions involving host factors and tumor biologic characteristics may have a negative impact on the success rate and accuracy of the procedure. The overall fraction of patients unsuitable or with multiple risk factors that may compromise the success of the sentinel lymph node biopsy, is very small. Nevertheless, these patients need to be successfully identified, appropriately advised and cautioned, and so do the surgeons that perform the procedure. CONCLUSION: When performed by an experienced multi-disciplinary team, the SLNB is a highly effective and accurate alternative to standard level I and II axillary clearance in the vast majority of patients with early breast cancer

Numerical test of the Edwards conjecture shows that all packings are equally probable at jamming

In the late 1980s, Sam Edwards proposed a possible statistical-mechanical framework to describe the properties of disordered granular materials1. A key assumption underlying the theory was that all jammed packings are equally likely. In the intervening years it has never been possible to test this bold hypothesis directly. Here we present simulations that provide direct evidence that at the unjamming point, all packings of soft repulsive particles are equally likely, even though generically, jammed packings are not. Typically, jammed granular systems are observed precisely at the unjamming point since grains are not very compressible. Our results therefore support Edwards’ original conjecture. We also present evidence that at unjamming the configurational entropy of the system is maximal.S.M. acknowledges financial support by the Gates Cambridge Scholarship. K.J.S. acknowledges support by the Swiss National Science Foundation under Grant No. P2EZP2-152188 and No. P300P2-161078. D.F. acknowledges support by EPSRC Programme Grant EP/I001352/1 and EPSRC grant EP/I000844/1. K.R. and B.C. acknowledge the support of NSF-DMR 1409093 and the W. M. Keck Foundation

Communication: Evidence for non-ergodicity in quiescent states of periodically sheared suspensions

We present simulations of an equilibrium statistical-mechanics model that uniformly samples the space of quiescent states of a periodically sheared suspension. In our simulations, we compute the structural properties of this model as a function of density. We compare the results of our simulations with the structural data obtained in the corresponding non-equilibrium model of Corté et al. [Nat. Phys. 4, 420 (2008)]. We find that the structural properties of the non-equilibrium model are very different from those of the equilibrium model, even though the two models have exactly the same set of accessible states. This observation shows that the dynamical protocol does not sample all quiescent states with equal probability. In particular, we find that, whilst quiescent states prepared in a non-equilibrium protocol can be hyperuniform [see D. Hexner and D. Levine, Phys. Rev. Lett. 114, 110602 (2015); E. Tjhung and L. Berthier, Phys. Rev. Lett. 114, 148301 (2015); and J. H. Weijs et al., Phys. Rev. Lett. 115, 108301 (2015)], ergodic sampling never leads to hyperuniformity. In addition, we observe ordering phase transitions and a percolation transition in the equilibrium model that do not show up in the non-equilibrium model. Conversely, the quiescent-to-diffusive transition in the dynamical model does not correspond to a phase transition, nor a percolation transition, in the equilibrium model.This work was supported by ERC Advanced Grant 227758 (COLSTRUCTION), EPSRC Programme Grant EP/I001352/1 and by the Swiss National Science Foundation (Grant No. P2EZP2-152188 and No. P300P2- 161078). K.J.S. acknowledges useful discussions with Nuno Araújo, Tristan Cragnolini, Daphne Klotsa, Erik Luijten, Stefano Martiniani, Anđela Šarić, Iskra Staneva, Jacob Stevenson, and Peter Wirnsberger.This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by AIP

Shortest path and Schramm-Loewner Evolution

We numerically show that the statistical properties of the shortest path on critical percolation clusters are consistent with the ones predicted for Schramm-Loewner evolution (SLE) curves for κ = 1.04 ± 0.02. The shortest path results from a global optimization process. To identify it, one needs to explore an entire area. Establishing a relation with SLE permits to generate curves statistically equivalent to the shortest path from a Brownian motion. We numerically analyze the winding angle, the left passage probability, and the driving function of the shortest path and compare them to the distributions predicted for SLE curves with the same fractal dimension. The consistency with SLE opens the possibility of using a solid theoretical framework to describe the shortest path and it raises relevant questions regarding conformal invariance and domain Markov properties, which we also discuss.ISSN:2045-232