Linear binary fragmentation of synthetic fractal-like agglomerates composed of spherical, equal-size, touching monomers is numerically investigated. Agglomerates of different morphologies are fragmented via random bond removal. The fragmentation algorithm relies on mapping each agglomerate onto an adjacency matrix. The numerically determined fragment size distributions are U-shaped, clusters break predominantly into two largely dissimilar fragments, becoming more uniform as the fractal dimension decreases. A symmetric beta distribution reproduces the fragment distribution rather accurately. Its exponent depends on the structure (fractal dimension) and number of monomers of the initial agglomerate. A universal fragment distribution, a function only of the initial fractal dimension, is derived by requiring that it satisfy the fragmentation conversation laws and the straight-chain limit. We argue that the fragmentation rate is proportional to the initial agglomerate size.

A methodology is introduced, the Collision Rate Method (CRM), to calculate the friction coefficient of power-law aggregates across the entire momentum-transfer regime. The friction coefficient is calculated via the ratio of two fictitious particle-aggregate collision rates evaluated in the continuum and slip-flow regimes. The effective collision rates are obtained from the numerical solution of the Laplace equation with Robin boundary condition. The methodology was justified by comparing the slip correction factor of straight-chains composed of up to 50 spherical monomers with literature results. We determined the validity of the CRM to lie in an extended slip-flow regime, the maximum monomer Knudsen number being 2. We calculated the adjusted-sphere radius, the radius of a sphere with the same slip correction factor as the chain, in slip flow. We found it to be weakly dependent on flow conditions, as specified by the carrier-gas mean free path, a dependence that leads to a weak effect on calculated slip correction factors. The CRM was combined with the Adjusted-Sphere Method to extend its validity to all Knudsen numbers. Excellent agreement of calculated, straight-chain, slip correction factors with literature values was obtained for monomer Knudsen numbers up to 100. Various characteristic length scales, geometric (equivalent volume radius, radius of gyration) and dynamic (equivalent hydrodynamic and mobility radii), were calculated.

The influence of geometric properties and particle size on mobility properties of fractal-like aggregates was studied in the mass and momentum-transfer transition regimes. Two methodologies were investigated. The Collision Rate Method (CRM) that determines the slip correction factor through the ratio of two fictitious Brownian particle-aggregate effective collision rates, and the Adjusted Sphere Method (ASM) that assumes the existence of a virtual, flow-independent adjusted sphere with the same slip correction factor as the aggregate over the entire transition regime. The simulated fractal-like aggregates were synthetic as they were generated via a cluster–cluster agglomeration algorithm. The CRM was used to calculate the adjusted-sphere radius of various aggregates: we found it to be weakly dependent on the monomer Knudsen number for Kn greater than 0.5. Numerical expressions for the aggregate orientationally-averaged projected area and the adjusted-sphere radius are proposed. Both expressions depend on geometric, non-ensemble averaged quantities: the radius of gyration and the number of monomers. The slip correction factor and the mobility radius of DLCA and RLCA aggregates were calculated using the ASM: for a given number of monomers, fractal dimension and prefactor, and Knudsen number their values were approximately constant (averaged over aggregate realizations). A fractal-like scaling law based on the mobility radius was found to hold. The mobility fractal dimension and prefactor were determined for different aggregates. The hydrodynamic radius, proportional to the friction coefficient, and the dynamic shape factor of DLCA and RLCA aggregates were also calculated.

The relationship between geometric and dynamic properties of fractal-like aggregates is studied in the continuum mass and momentum-transfer regimes. The synthetic aggregates were generated by a cluster-cluster aggregation algorithm. The analysis of their morphological features suggests that the fractal dimension is a descriptor of a cluster's large-scale structure, whereas the fractal prefactor is a local-structure indicator. For a constant fractal dimension, the prefactor becomes also an indicator of a cluster's shape anisotropy. The hydrodynamic radius of orientationally averaged aggregates was calculated via molecule-aggregate collision rates determined from the solution of a Laplace equation. An empirical expression that relates the aggregate hydrodynamic radius to its radius of gyration and the number of primary particles is proposed. The suggested expression depends only on geometrical quantities, being independent of statistical (ensemble-averaged) properties like the fractal dimension and prefactor. Hydrodynamic radius predictions for a variety of fractal-like aggregates are in very good agreement with predictions of other methods and literature values. Aggregate dynamic shape factors and DLCA individual monomer hydrodynamic shielding factors are also calculated.

The ever increasing adoption of mobile technologies and ubiquitous services allows to sense human behavior at unprecedented level of details and scale. Wearable sensors, in particular, open up a new window on human mobility and proximity in a variety of indoor environments. Here we review stylized facts on the structural and dynamical properties of empirical networks of human face-to-face proximity, measured in three different real-world contexts: an academic conference, a hospital ward, and a museum exhibition. First, we discuss the structure of the aggregated contact networks, that project out the detailed ordering of contact events while preserving temporal heterogeneities in their weights. We show that the structural properties of aggregated networks highlight important differences and unexpected similarities across contexts, and discuss the additional complexity that arises from attributes that are typically associated with nodes in real-world interaction networks, such as role classes in hospitals. We then consider the empirical data at the finest level of detail, i.e., we consider time-dependent networks of face-to-face proximity between individuals. To gain insights on the effects that causal constraints have on spreading processes, we simulate the dynamics of a simple susceptible-infected model over the empirical time-resolved contact data. We show that the spreading pathways for the epidemic process are strongly affected by the temporal structure of the network data, and that the mere knowledge of static aggregated networks leads to erroneous conclusions about the transmission paths on the corresponding dynamical networks.

The SocioPatterns sensing platform uses wearable electronic badges to sense close-range proximity among individuals. It was used in an experiential exhibit that simulated a virtual epidemic among the visitors of the INFECTIOUS: STAY AWAY exhibition in the Science Gallery in Dublin, Ireland. The collected data was used to generate a high-resolution visualization that illustrates the variation in contact activity over the course of the exhibition.

A methodology to calculate the friction coefficient of an aggregate in the continuum regime is proposed. The friction coefficient and the monomer shielding factors, aggregate-average or individual, are related to the molecule-aggregate collision rate that is obtained from the molecular diffusion equation with an absorbing boundary condition on the aggregate surface. Calculated friction coefficients of straight chains are in very good agreement with previous results, suggesting that the friction coefficients may be accurately calculated from the product of the collision rate and an average momentum transfer, the latter being independent of aggregate morphology. Langevin-dynamics simulations show that the diffusive motion of straight-chain aggregates may be described either by a monomer-dependent or an aggregate-average random force, if the shielding factors are appropriately chosen.

Background: Nosocomial infections place a substantial burden on health care systems and represent one of the major issues in current public health, requiring notable efforts for its prevention. Understanding the dynamics of infection transmission in a hospital setting is essential for tailoring interventions and predicting the spread among individuals. Mathematical models need to be informed with accurate data on contacts among individuals.Methods and Findings: We used wearable active Radio-Frequency Identification Devices (RFID) to detect face-to-face contacts among individuals with a spatial resolution of about 1.5 meters, and a time resolution of 20 seconds. The study was conducted in a general pediatrics hospital ward, during a one-week period, and included 119 participants, with 51 health care workers, 37 patients, and 31 caregivers. Nearly 16,000 contacts were recorded during the study period, with a median of approximately 20 contacts per participants per day. Overall, 25% of the contacts involved a ward assistant, 23% a nurse, 22% a patient, 22% a caregiver, and 8% a physician. The majority of contacts were of brief duration, but long and frequent contacts especially between patients and caregivers were also found. In the setting under study, caregivers do not represent a significant potential for infection spread to a large number of individuals, as their interactions mainly involve the corresponding patient. Nurses would deserve priority in prevention strategies due to their central role in the potential propagation paths of infections.Conclusions: Our study shows the feasibility of accurate and reproducible measures of the pattern of contacts in a hospital setting. The obtained results are particularly useful for the study of the spread of respiratory infections, for monitoring critical patterns, and for setting up tailored prevention strategies. Proximity-sensing technology should be considered as a valuable tool for measuring such patterns and evaluating nosocomial prevention strategies in specific settings.

BACKGROUND:The spread of infectious diseases crucially depends on the pattern of contacts between individuals. Knowledge of these patterns is thus essential to inform models and computational efforts. However, there are few empirical studies available that provide estimates of the number and duration of contacts between social groups. Moreover, their space and time resolutions are limited, so that data are not explicit at the person-to-person level, and the dynamic nature of the contacts is disregarded. In this study, we aimed to assess the role of data-driven dynamic contact patterns between individuals, and in particular of their temporal aspects, in shaping the spread of a simulated epidemic in the population.METHODS:We considered high-resolution data about face-to-face interactions between the attendees at a conference, obtained from the deployment of an infrastructure based on radiofrequency identification (RFID) devices that assessed mutual face-to-face proximity. The spread of epidemics along these interactions was simulated using an SEIR (Susceptible, Exposed, Infectious, Recovered) model, using both the dynamic network of contacts defined by the collected data, and two aggregated versions of such networks, to assess the role of the data temporal aspects.RESULTS:We show that, on the timescales considered, an aggregated network taking into account the daily duration of contacts is a good approximation to the full resolution network, whereas a homogeneous representation that retains only the topology of the contact network fails to reproduce the size of the epidemic.CONCLUSIONS:These results have important implications for understanding the level of detail needed to correctly inform computational models for the study and management of real epidemics. Please see related article BMC Medicine, 2011, 9:88.

BACKGROUND:Little quantitative information is available on the mixing patterns of children in school environments. Describing and understanding contacts between children at school would help quantify the transmission opportunities of respiratory infections and identify situations within schools where the risk of transmission is higher. We report on measurements carried out in a French school (6-12 years children), where we collected data on the time-resolved face-to-face proximity of children and teachers using a proximity-sensing infrastructure based on radio frequency identification devices.METHODS AND FINDINGS:Data on face-to-face interactions were collected on Thursday, October 1(st) and Friday, October 2(nd) 2009. We recorded 77,602 contact events between 242 individuals (232 children and 10 teachers). In this setting, each child has on average 323 contacts per day with 47 other children, leading to an average daily interaction time of 176 minutes. Most contacts are brief, but long contacts are also observed. Contacts occur mostly within each class, and each child spends on average three times more time in contact with classmates than with children of other classes. We describe the temporal evolution of the contact network and the trajectories followed by the children in the school, which constrain the contact patterns. We determine an exposure matrix aimed at informing mathematical models. This matrix exhibits a class and age structure which is very different from the homogeneous mixing hypothesis.CONCLUSIONS:We report on important properties of the contact patterns between school children that are relevant for modeling the propagation of diseases and for evaluating control measures. We discuss public health implications related to the management of schools in case of epidemics and pandemics. Our results can help define a prioritization of control measures based on preventive measures, case isolation, classes and school closures, that could reduce the disruption to education during epidemics.

We describe the experimental deployment of a network of wearable sensors that allows the tracking of the location and mutual proximity of individuals in a hospital ward, in real time and at a large scale. In the course of the deployment, all individuals accessing the premises were monitored for a period of one week, including health care personnel, patients, visitors and tutors. The data collected yields a rich dynamical picture of the contact patterns between individuals and between categories of individuals. As an example, here we show that by constructing a cumulative weighted contact network aggregating the dynamical data on the entire duration of the deployment, it is possible to reliably uncover persistent relations among individuals.

Transmission of hospital acquired infections (HAI) is mainly based on contacts between patients, patients and health care workers (HCWs) and between HCWs. Description and quantification of contacts at hospital are key information for HAIs epidemiology and implementing control measures.

The availability of new data sources on human mobility is opening new avenues for investigating the interplay of social networks, human mobility and dynamical processes such as epidemic spreading. Here we analyze data on the time-resolved face-to-face proximity of individuals in large-scale real-world scenarios. We compare two settings with very different properties, a scientific conference and a long-running museum exhibition. We track the behavioral networks of face-to-face proximity, and characterize them from both a static and a dynamic point of view, exposing important differences as well as striking similarities. We use our data to investigate the dynamics of a susceptible-infected model for epidemic spreading that unfolds on the dynamical networks of human proximity. The spreading patterns are markedly different for the conference and the museum case, and they are strongly impacted by the causal structure of the network data. A deeper study of the spreading paths shows that the mere knowledge of static aggregated networks would lead to erroneous conclusions about the transmission paths on the dynamical networks.

Nanoparticle agglomeration in a quiescent fluid is simulated by solving the Langevin equations of motion of a set of interacting monomers in the continuum regime. Monomers interact via a radial rapidly decaying intermonomer potential. The morphology of generated clusters is analyzed through their fractal dimension df and the cluster coordination number. The time evolution of the cluster fractal dimension is linked to the dynamics of two populations: small (k≤ 15) and large (k>15) clusters. At early times monomer-cluster agglomeration is the dominant agglomeration mechanism (d(f)=2.25) , whereas at late times cluster-cluster agglomeration dominates (d(f)=1.56). Clusters are found to be compact (mean coordination number of ∼5), tubular, and elongated. The local compact structure of the aggregates is attributed to the isotropy of the interaction potential, which allows rearrangement of bonded monomers, whereas the large-scale tubular structure is attributed to its relatively short attractive range. The cluster translational diffusion coefficient is determined to be inversely proportional to the cluster mass and the (per-unit-mass) friction coefficient of an isolated monomer, a consequence of the neglect of monomer shielding in a cluster. Clusters generated by unshielded Langevin equations are referred to as ideal clusters because the surface area accessible to the underlying fluid is found to be the sum of the accessible surface areas of the isolated monomers. Similarly, ideal clusters do not have, on average, a preferential orientation. The decrease in the numbers of clusters with time and a few collision kernel elements are evaluated and compared to analytical expressions.

A methodology to calculate the friction coefficient of an aggregate in the continuum regime is proposed. The friction coefficient and the monomer shielding factors, average or individual, are related to the molecule-aggregate collision rate, obtained from the molecular diffusion equation with an absorbing boundary condition on the aggregate surface. Calculated friction coefficients of linear chains are in very good agreement with previous results, suggesting that they may be accurately calculated from the product of the collision rate and an average momentum transfer, the latter being independent of aggregate morphology. Langevin-dynamics simulations show that aggregate diffusive motion may be described either by an aggregate-average or by a monomer-dependent random force, if the shielding factors are appropriately chosen. PACS numbers: 47.57.eb, 82.70.-y, 47.57.J∗ Present address: ISI Foundation, Turin 10133, Italy; lorenzo.isella@isi.it † Corresponding author: ioannis.drossinos@jrc.ec.europa.eu 1 ar X iv :1 00 7. 28 01 v1 [ co nd -m at .s of t] 1 6 Ju l 2 01 0