1,321,510 research outputs found
Anomalous diffusion mediated by atom deposition into a porous substrate
Constant flux atom deposition into a porous medium is shown to generate a
dense overlayer and a diffusion profile. Scaling analysis shows that the
overlayer acts as a dynamic control for atomic diffusion in the porous
substrate. This is modeled by generalizing the porous diffusion equation with a
time-dependent diffusion coefficient equivalent to a nonlinear rescaling of
timeComment: 4 page
Early Warning Analysis for Social Diffusion Events
There is considerable interest in developing predictive capabilities for
social diffusion processes, for instance to permit early identification of
emerging contentious situations, rapid detection of disease outbreaks, or
accurate forecasting of the ultimate reach of potentially viral ideas or
behaviors. This paper proposes a new approach to this predictive analytics
problem, in which analysis of meso-scale network dynamics is leveraged to
generate useful predictions for complex social phenomena. We begin by deriving
a stochastic hybrid dynamical systems (S-HDS) model for diffusion processes
taking place over social networks with realistic topologies; this modeling
approach is inspired by recent work in biology demonstrating that S-HDS offer a
useful mathematical formalism with which to represent complex, multi-scale
biological network dynamics. We then perform formal stochastic reachability
analysis with this S-HDS model and conclude that the outcomes of social
diffusion processes may depend crucially upon the way the early dynamics of the
process interacts with the underlying network's community structure and
core-periphery structure. This theoretical finding provides the foundations for
developing a machine learning algorithm that enables accurate early warning
analysis for social diffusion events. The utility of the warning algorithm, and
the power of network-based predictive metrics, are demonstrated through an
empirical investigation of the propagation of political memes over social media
networks. Additionally, we illustrate the potential of the approach for
security informatics applications through case studies involving early warning
analysis of large-scale protests events and politically-motivated cyber
attacks
Cosmology with matter diffusion
We construct a viable cosmological model based on velocity diffusion of
matter particles. In order to ensure the conservation of the total
energy-momentum tensor in the presence of diffusion, we include a cosmological
scalar field which we identify with the dark energy component of the
Universe. The model is characterized by only one new degree of freedom, the
diffusion parameter . The standard CDM model can be recovered
by setting . If diffusion takes place () the dynamics of
the matter and of the dark energy fields are coupled. We argue that the
existence of a diffusion mechanism in the Universe can serve as a theoretical
motivation for interacting models. We constrain the background dynamics of the
diffusion model with Supernovae, H(z) and BAO data. We also perform a
perturbative analysis of this model in order to understand structure formation
in the Universe. We calculate the impact of diffusion both on the CMB spectrum,
with particular attention to the integrated Sachs-Wolfe signal, and on the
matter power spectrum . The latter analysis places strong constraints on
the magnitude of the diffusion mechanism but does not rule out the model.Comment: 20 pages, 8 figures, accepted for publication in JCA
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