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We present numerical simulations that allow us to compute the number of ways in which N particles can pack into a given volume V. Our technique modifies the method of Xu, Frenkel, and Liu [Phys. Rev. Lett. 106, 245502 (2011)] and outperforms existing direct enumeration methods by more than 200 orders of magnitude. We use our approach to study the system size dependence of the number of distinct packings of a system of up to 128 polydisperse soft disks. We show that, even though granular particles are distinguishable, we have to include a factor 1/N1 to ensure that the entropy does not change when exchanging particles between systems in the same macroscopic state. Our simulations provide strong evidence that the packing entropy, when properly defined, is extensive. As different packings are created with unequal probabilities, it is natural to express the packing entropy as S = - Σipi In Pi - ln N!, where Pi denotes the probability to generate the ith packing. We can compute this quantity reliably and it is also extensive. The granular entropy thus (re)defined, while distinct from the one proposed by Edwards [J. Phys. Condens. Matter 2, SA63 (1990)], does have all the properties Edwards assumed. [ABSTRACT FROM AUTHOR]

Granular materials are not in thermodynamic equilibrium. Nevertheless, concepts borrowed from equilibrium statistical mechanics are extensively used to characterise granular systems. One often-invoked concept is the so-called granular entropy. In this paper, we consider what it would take to compute granular entropy numerically. Our focus is the analogy (or, more accurately, lack thereof) between statistical mechanical ensembles, as used in Monte Carlo simulations of thermal systems, and preparation protocols used in the generation of granular packings. Attempts to phrase the description of granular media in ‘thermal’ Monte Carlo language reveal some awkward problems. Whilst some of these problems had been reported in the existing literature, the present perspective yields new insights. [ABSTRACT FROM AUTHOR]

A molecular dynamics study of a two-dimensional system of particles interacting through a Lennard-Jones pairwise potential is performed at a fixed temperature and vanishing external pressure. As the temperature is increased, a solid-to-liquid transition occurs. When the melting temperature Tc is approached from below, there is a proliferation of dislocation pairs and the elastic constant approaches the value predicted by the KTHNY theory. In addition, as Tc is approached from above, the relaxation time increases, consistent with an approach to criticality. However, simulations fail to produce a stable hexatic phase using systems with up to 90,000 particles. A significant jump in enthalpy at Tc is observed, consistent with either a first order or a continuous transition. The role of external pressure is discussed. [ABSTRACT FROM AUTHOR]

Background Accurate 1-year bleeding risk estimation after hospital discharge for acute coronary syndrome (ACS) may help clinicians guide the type and duration of antithrombotic therapy. Currently there are no predictive models for this purpose. The aim of this study was to derive and validate a simple clinical tool for bedside risk estimation of 1-year post-discharge serious bleeding in ACS patients. Methods The risk score was derived and internally validated in the BleeMACS (Bleeding complications in a Multicenter registry of patients discharged with diagnosis of Acute Coronary Syndrome) registry, an observational international registry involving 15,401 patients surviving admission for ACS and undergoing percutaneous coronary intervention (PCI) from 2003 to 2014, engaging 15 hospitals from 10 countries located in America, Europe and Asia. External validation was conducted in the SWEDEHEART population, with 96,239 ACS patients underwent PCI and 93,150 without PCI. Results Seven independent predictors of bleeding were identified and included in the BleeMACS score: age, hypertension, vascular disease, history of bleeding, malignancy, creatinine and hemoglobin. The BleeMACS risk score exhibited a C-statistic value of 0.71 (95% CI 0.68–0.74) in the derivation cohort and 0.72 (95% CI 0.67–0.76) in the internal validation sample. In the SWEDEHEART external validation cohort, the C-statistic was 0.65 (95% CI 0.64–0.66) for PCI patients and 0.63 (95% CI 0.62–0.64) for non-PCI patients. The calibration was excellent in the derivation and validation cohorts. Conclusions The BleeMACS bleeding risk score is a simple tool useful for identifying those ACS patients at higher risk of serious 1-year post-discharge bleeding. ClinicalTrials . gov Identifier : NCT02466854 [ABSTRACT FROM AUTHOR]