Theory of random packings

We review a recently proposed theory of random packings. We describe the volume fluctuations in jammed matter through a volume function, amenable to analytical and numerical calculations. We combine an extended statistical mechanics approach 'a la Edwards' (where the role traditionally played by the energy and temperature in thermal systems is substituted by the volume and compactivity) with a constraint on mechanical stability imposed by the isostatic condition. We show how such approaches can bring results that can be compared to experiments and allow for an exploitation of the statistical mechanics framework. The key result is the use of a relation between the local Voronoi volume of the constituent grains and the number of neighbors in contact that permits a simple combination of the two approaches to develop a theory of random packings. We predict the density of random loose packing (RLP) and random close packing (RCP) in close agreement with experiments and develop a phase diagram of jammed matter that provides a unifying view of the disordered hard sphere packing problem and further shedding light on a diverse spectrum of data, including the RLP state. Theoretical results are well reproduced by numerical simulations that confirm the essential role played by friction in determining both the RLP and RCP limits. Finally we present an extended discussion on the existence of geometrical and mechanical coordination numbers and how to measure both quantities in experiments and computer simulations.Comment: 9 pages, 5 figures. arXiv admin note: text overlap with arXiv:0808.219

Quantifying Long-Term Scientific Impact

The lack of predictability of citation-based measures frequently used to gauge impact, from impact factors to short-term citations, raises a fundamental question: Is there long-term predictability in citation patterns? Here, we derive a mechanistic model for the citation dynamics of individual papers, allowing us to collapse the citation histories of papers from different journals and disciplines into a single curve, indicating that all papers tend to follow the same universal temporal pattern. The observed patterns not only help us uncover basic mechanisms that govern scientific impact but also offer reliable measures of influence that may have potential policy implications

Distribution of volumes and coordination number in jammed matter: mesoscopic ensemble

We investigate the distribution of the volume and coordination number associated to each particle in a jammed packing of monodisperse hard sphere using the mesoscopic ensemble developed in Nature 453, 606 (2008). Theory predicts an exponential distribution of the orientational volumes for random close packings and random loose packings. A comparison with computer generated packings reveals deviations from the theoretical prediction in the volume distribution, which can be better modeled by a compressed exponential function. On the other hand, the average of the volumes is well reproduced by the theory leading to good predictions of the limiting densities of RCP and RLP. We discuss a more exact theory to capture the volume distribution in its entire range. The available data suggests a plausible order/disorder transition defining random close packings. Finally, we consider an extended ensemble to calculate the coordination number distribution which is shown to be of an exponential and inverse exponential form for coordinations larger and smaller than the average, respectively, in reasonable agreement with the simulated data.Comment: 20 pages, 6 figures, accepted by JSTA

Modeling and Predicting Popularity Dynamics via Reinforced Poisson Processes

An ability to predict the popularity dynamics of individual items within a complex evolving system has important implications in an array of areas. Here we propose a generative probabilistic framework using a reinforced Poisson process to model explicitly the process through which individual items gain their popularity. This model distinguishes itself from existing models via its capability of modeling the arrival process of popularity and its remarkable power at predicting the popularity of individual items. It possesses the flexibility of applying Bayesian treatment to further improve the predictive power using a conjugate prior. Extensive experiments on a longitudinal citation dataset demonstrate that this model consistently outperforms existing popularity prediction methods.Comment: 8 pages, 5 figure; 3 table

From Micro to Macro: Uncovering and Predicting Information Cascading Process with Behavioral Dynamics

Cascades are ubiquitous in various network environments. How to predict these cascades is highly nontrivial in several vital applications, such as viral marketing, epidemic prevention and traffic management. Most previous works mainly focus on predicting the final cascade sizes. As cascades are typical dynamic processes, it is always interesting and important to predict the cascade size at any time, or predict the time when a cascade will reach a certain size (e.g. an threshold for outbreak). In this paper, we unify all these tasks into a fundamental problem: cascading process prediction. That is, given the early stage of a cascade, how to predict its cumulative cascade size of any later time? For such a challenging problem, how to understand the micro mechanism that drives and generates the macro phenomenons (i.e. cascading proceese) is essential. Here we introduce behavioral dynamics as the micro mechanism to describe the dynamic process of a node's neighbors get infected by a cascade after this node get infected (i.e. one-hop subcascades). Through data-driven analysis, we find out the common principles and patterns lying in behavioral dynamics and propose a novel Networked Weibull Regression model for behavioral dynamics modeling. After that we propose a novel method for predicting cascading processes by effectively aggregating behavioral dynamics, and propose a scalable solution to approximate the cascading process with a theoretical guarantee. We extensively evaluate the proposed method on a large scale social network dataset. The results demonstrate that the proposed method can significantly outperform other state-of-the-art baselines in multiple tasks including cascade size prediction, outbreak time prediction and cascading process prediction.Comment: 10 pages, 11 figure

Multiplexed biomarker detection using x-ray fluorescence of composition-encoded nanoparticles

Multiple DNA and protein biomarkers have been detected based on characteristic x-ray fluorescence of a panel of metal and alloy nanoparticles, which are modified with ligands of biomarkers to create a one-to-one correspondence and immobilized on ligand-modified substrates after forming complexes with target biomarkers in three-strand or sandwich configuration. By determining the presence and concentration of nanoparticles using x-ray fluorescence, the nature and amount of biomarkers can be detected with limits of 1 nM for DNA and 1 ng/ml for protein. By combining high penetrating ability of x-rays, this method allows quantitative imaging of multiple biomarkers

Thermally Annealled Plasmonic Nanostructures

Localized surface plasmon resonance (LSPR) is induced in metal nanoparticles by resonance between incident photons and conduction electrons in nanoparticles. For noble metal nanoparticles, LSPR can lead to strong absorbance of ultraviolet-violet light. Although it is well known that LSPR depends on the size and shape of nanoparticles, the inter-particle spacing, the dielectric properties of metal and the surrounding medium, the temperature dependence of LSPR is not well understood. By thermally annealing gold nanoparticle arrays formed by nanosphere lithography, a shift of LSPR peak upon heating has been shown. The thermal characteristics of the plasmonic nanoparticles have been further used to detect chemicals such as explosive and mercury vapors, which allow direct visual observation of the presence of mercury vapor, as well as thermal desorption measurement

Granular dynamics in compaction and stress relaxation

Elastic and dissipative properties of granular assemblies under uniaxial compression are studied both experimentally and by numerical simulations. Following a novel compaction procedure at varying oscillatory pressures, the stress response to a step-strain reveals an exponential relaxation followed by a slow logarithmic decay. Simulations indicate that the latter arises from the coupling between damping and collective grain motion predominantly through sliding. We characterize an analogous "glass transition" for packed grains, below which the system shows aging in time-dependent sliding correlation functions.Comment: 5 pages, 5 figure