Dimensional study of the dynamical arrest in a random Lorentz gas

The random Lorentz gas is a minimal model for transport in heterogeneous media. Upon increasing the obstacle density, it exhibits a growing subdiffusive transport regime and then a dynamical arrest. Here, we study the dimensional dependence of the dynamical arrest, which can be mapped onto the void percolation transition for Poisson-distributed point obstacles. We numerically determine the arrest in dimensions d=2-6. Comparing the results with standard mode-coupling theory reveals that the dynamical theory prediction grows increasingly worse with $d$. In an effort to clarify the origin of this discrepancy, we relate the dynamical arrest in the RLG to the dynamic glass transition of the infinite-range Mari-Kurchan model glass former. Through a mixed static and dynamical analysis, we then extract an improved dimensional scaling form as well as a geometrical upper bound for the arrest. The results suggest that understanding the asymptotic behavior of the random Lorentz gas may be key to surmounting fundamental difficulties with the mode-coupling theory of glasses.Comment: 9 pages, 6 figure

Model of random packings of different size balls

We develop a model to describe the properties of random assemblies of polydisperse hard spheres. We show that the key features to describe the system are (i) the dependence between the free volume of a sphere and the various coordination numbers between the species, and (ii) the dependence of the coordination numbers with the concentration of species; quantities that are calculated analytically. The model predicts the density of random close packing and random loose packing of polydisperse systems for a given distribution of ball size and describes packings for any interparticle friction coefficient. The formalism allows to determine the optimal packing over different distributions and may help to treat packing problems of non-spherical particles which are notoriously difficult to solve.Comment: 6 pages, 6 figure

Hopping and the Stokes-Einstein relation breakdown in simple glass formers

One of the most actively debated issues in the study of the glass transition is whether a mean-field description is a reasonable starting point for understanding experimental glass formers. Although the mean-field theory of the glass transition -- like that of other statistical systems -- is exact when the spatial dimension $d\rightarrow\infty$, the evolution of systems properties with $d$ may not be smooth. Finite-dimensional effects could dramatically change what happens in physical dimensions, $d=2,3$. For standard phase transitions finite-dimensional effects are typically captured by renormalization group methods, but for glasses the corrections are much more subtle and only partially understood. Here, we investigate hopping between localized cages formed by neighboring particles in a model that allows to cleanly isolate that effect. By bringing together results from replica theory, cavity reconstruction, void percolation, and molecular dynamics, we obtain insights into how hopping induces a breakdown of the Stokes--Einstein relation and modifies the mean-field scenario in experimental systems. Although hopping is found to supersede the dynamical glass transition, it nonetheless leaves a sizable part of the critical regime untouched. By providing a constructive framework for identifying and quantifying the role of hopping, we thus take an important step towards describing dynamic facilitation in the framework of the mean-field theory of glasses.Comment: 27 pages, 13 figures (including supplementary information) - final version accepted for publication on PNA

Statistical theory of correlations in random packings of hard particles

A random packing of hard particles represents a fundamental model for granular matter. Despite its importance, analytical modeling of random packings remains difficult due to the existence of strong correlations which preclude the development of a simple theory. Here, we take inspiration from liquid theories for the $n$-particle angular correlation function to develop a formalism of random packings of hard particles from the bottom-up. A progressive expansion into a shell of particles converges in the large layer limit under a Kirkwood-like approximation of higher-order correlations. We apply the formalism to hard disks and predict the density of two-dimensional random close packing (RCP), $\phi_{\rm rcp} = 0.85\pm0.01$, and random loose packing (RLP), $\phi_{\rm rlp} = 0.67\pm0.01$. Our theory also predicts a phase diagram and angular correlation functions that are in good agreement with experimental and numerical data.Comment: 9 pages, 6 figures, to appear in PR

Thermodynamic crossovers in supercritical fluids

Can liquid-like and gas-like states be distinguished beyond the critical point, where the liquid-gas phase transition no longer exists and conventionally only a single supercritical fluid phase is defined? Recent experiments and simulations report strong evidence of dynamical crossovers above the critical temperature and pressure. Despite using different criteria, existing theoretical explanations generally consider a single crossover line separating liquid-like and gas-like states in the supercritical fluid phase. We argue that such a single-line scenario is inconsistent with the supercritical behavior of the Ising model, which has two crossover lines due to its symmetry, violating the universality principle of critical phenomena. To reconcile the inconsistency, we define two thermodynamic crossover lines in supercritical fluids as boundaries of liquid-like, indistinguishable and gas-like states. Near the critical point, the two crossover lines follow critical scalings with exponents of the Ising universality class, supported by calculations of theoretical models and analyses of experimental data from the standard database. The upper line agrees with crossovers independently estimated from the inelastic X-ray scattering data of supercritical argon, and from the small-angle neutron scattering data of supercritical carbon dioxide. The lower line is verified by the equation of states for the compressibility factor. This work provides a fundamental framework for understanding supercritical physics in general phase transitions.Comment: 23 pages, 21 figure

EnsNet: Ensconce Text in the Wild

A new method is proposed for removing text from natural images. The challenge is to first accurately localize text on the stroke-level and then replace it with a visually plausible background. Unlike previous methods that require image patches to erase scene text, our method, namely ensconce network (EnsNet), can operate end-to-end on a single image without any prior knowledge. The overall structure is an end-to-end trainable FCN-ResNet-18 network with a conditional generative adversarial network (cGAN). The feature of the former is first enhanced by a novel lateral connection structure and then refined by four carefully designed losses: multiscale regression loss and content loss, which capture the global discrepancy of different level features; texture loss and total variation loss, which primarily target filling the text region and preserving the reality of the background. The latter is a novel local-sensitive GAN, which attentively assesses the local consistency of the text erased regions. Both qualitative and quantitative sensitivity experiments on synthetic images and the ICDAR 2013 dataset demonstrate that each component of the EnsNet is essential to achieve a good performance. Moreover, our EnsNet can significantly outperform previous state-of-the-art methods in terms of all metrics. In addition, a qualitative experiment conducted on the SMBNet dataset further demonstrates that the proposed method can also preform well on general object (such as pedestrians) removal tasks. EnsNet is extremely fast, which can preform at 333 fps on an i5-8600 CPU device.Comment: 8 pages, 8 figures, 2 tables, accepted to appear in AAAI 201