155 research outputs found
Emergent user behavior on Twitter modelled by a stochastic differential equation
Data from the social-media site, Twitter, is used to study the fluctuations
in tweet rates of brand names. The tweet rates are the result of a strongly
correlated user behavior, which leads to bursty collective dynamics with a
characteristic 1/f noise. Here we use the aggregated "user interest" in a brand
name to model collective human dynamics by a stochastic differential equation
with multiplicative noise. The model is supported by a detailed analysis of the
tweet rate fluctuations and it reproduces both the exact bursty dynamics found
in the data and the 1/f noise
Rotation-limited growth of three dimensional body-centered cubic crystals
According to classical grain growth laws, grain growth is driven by the
minimization of surface energy and will continue until a single grain prevails.
These laws do not take into account the lattice anisotropy and the details of
the microscopic rearrangement of mass between grains. Here we consider
coarsening of body-centered cubic polycrystalline materials in three dimensions
using the phase field crystal model. We observe as function of the quenching
depth, a cross over between a state where grain rotation halts and the growth
stagnates and a state where grains coarsen rapidly by coalescence through
rotation and alignment of the lattices of neighboring grains. We show that the
grain rotation per volume change of a grain follows a power law with an
exponent of . The scaling exponent is consistent with theoretical
considerations based on the conservation of dislocations
Elasticity with Arbitrarily Shaped Inhomogeneity
A classical problem in elasticity theory involves an inhomogeneity embedded
in a material of given stress and shear moduli. The inhomogeneity is a region
of arbitrary shape whose stress and shear moduli differ from those of the
surrounding medium. In this paper we present a new, semi-analytic method for
finding the stress tensor for an infinite plate with such an inhomogeneity. The
solution involves two conformal maps, one from the inside and the second from
the outside of the unit circle to the inside, and respectively outside, of the
inhomogeneity. The method provides a solution by matching the conformal maps on
the boundary between the inhomogeneity and the surrounding material. This
matching converges well only for relatively mild distortions of the unit circle
due to reasons which will be discussed in the article. We provide a comparison
of the present result to known previous results.Comment: (10 pages, 10 figures
Correlations Between Human Mobility and Social Interaction Reveal General Activity Patterns
A day in the life of a person involves a broad range of activities which are
common across many people. Going beyond diurnal cycles, a central question is:
to what extent do individuals act according to patterns shared across an entire
population? Here we investigate the interplay between different activity types,
namely communication, motion, and physical proximity by analyzing data
collected from smartphones distributed among 638 individuals. We explore two
central questions: Which underlying principles govern the formation of the
activity patterns? Are the patterns specific to each individual or shared
across the entire population? We find that statistics of the entire population
allows us to successfully predict 71\% of the activity and 85\% of the
inactivity involved in communication, mobility, and physical proximity.
Surprisingly, individual level statistics only result in marginally better
predictions, indicating that a majority of activity patterns are shared across
{our sample population}. Finally, we predict short-term activity patterns using
a generalized linear model, which suggests that a simple linear description
might be sufficient to explain a wide range of actions, whether they be of
social or of physical character
Communication dynamics in finite capacity social networks
In communication networks structure and dynamics are tightly coupled. The
structure controls the flow of information and is itself shaped by the
dynamical process of information exchanged between nodes. In order to reconcile
structure and dynamics, a generic model, based on the local interaction between
nodes, is considered for the communication in large social networks. In
agreement with data from a large human organization, we show that the flow is
non-Markovian and controlled by the temporal limitations of individuals. We
confirm the versatility of our model by predicting simultaneously the
degree-dependent node activity, the balance between information input and
output of nodes and the degree distribution. Finally, we quantify the
limitations to network analysis when it is based on data sampled over a finite
period of time.Comment: Physical Review Letter, accepted (5 pages, 4 figures
Controlling wetting with electrolytic solutions: phase-field simulations of a droplet-conductor system
The wetting properties of immiscible two-phase systems are crucial in a wide
range of applications, from lab-on-a-chip devices to field-scale oil recovery.
It has long been known that effective wetting properties can be altered by the
application of an electric field; a phenomenon coined as electrowetting. Here,
we consider theoretically and numerically a single droplet sitting on an
(insulated) conductor, i.e., within a capacitor. The droplet consists of a pure
phase without solutes, while the surrounding fluid contains a symmetric
monovalent electrolyte, and the interface between them is impermeable. Using
nonlinear Poisson--Boltzmann theory, we present a theoretical prediction of the
dependency of the apparent contact angle on the applied electric potential. We
then present well-resolved dynamic simulations of electrowetting using a
phase-field model, where the entire two-phase electrokinetic problem, including
the electric double layers (EDLs), is resolved. The simulations show that,
while the contact angle on scales smaller than the EDL is unaffected by the
application of an electric field, an apparent contact angle forms on scales
beyond the EDL. This contact angle relaxes in time towards a saturated apparent
contact angle. The dependency of the contact angle upon applied electric
potential is in good compliance with the theoretical prediction. The only
phenomenological parameter in the prediction is shown to only depend on the
permeability ratio between the two phases. Based on the resulting unified
description, we obtain an effective expression of the contact angle which can
be used in more macroscopic numerical simulations, i.e. where the
electrokinetic problem is not fully resolved
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