4,405 research outputs found
Glass transition and random walks on complex energy landscapes
We present a simple mathematical model of glassy dynamics seen as a random
walk in a directed, weighted network of minima taken as a representation of the
energy landscape. Our approach gives a broader perspective to previous studies
focusing on particular examples of energy landscapes obtained by sampling
energy minima and saddles of small systems. We point out how the relation
between the energies of the minima and their number of neighbors should be
studied in connection with the network's global topology, and show how the
tools developed in complex network theory can be put to use in this context
Random inelasticity and velocity fluctuations in a driven granular gas
We analyze the deviations from Maxwell-Boltzmann statistics found in recent
experiments studying velocity distributions in two-dimensional granular gases
driven into a non-equilibrium stationary state by a strong vertical vibration.
We show that in its simplest version, the ``stochastic thermostat'' model of
heated inelastic hard spheres, contrary to what has been hitherto stated, is
incompatible with the experimental data, although predicting a reminiscent high
velocity stretched exponential behavior with an exponent 3/2. The experimental
observations lead to refine a recently proposed random restitution coefficient
model. Very good agreement is then found with experimental velocity
distributions within this framework, which appears self-consistent and further
provides relevant probes to investigate the universality of the velocity
statistics.Comment: 5 pages, 5 eps figure
Free cooling and inelastic collapse of granular gases in high dimensions
The connection between granular gases and sticky gases has recently been
considered, leading to the conjecture that inelastic collapse is avoided for
space dimensions higher than 4. We report Molecular Dynamics simulations of
hard inelastic spheres in dimensions 4, 5 and 6. The evolution of the granular
medium is monitored throughout the cooling process. The behaviour is found to
be very similar to that of a two-dimensional system, with a shearing-like
instability of the velocity field and inelastic collapse when collisions are
inelastic enough, showing that the connection with sticky gases needs to be
revised.Comment: 6 pages, 6 figures (7 postscript files), submitted to EPJ
Can co-location be used as a proxy for face-to-face contacts?
Technological advances have led to a strong increase in the number of data
collection efforts aimed at measuring co-presence of individuals at different
spatial resolutions. It is however unclear how much co-presence data can inform
us on actual face-to-face contacts, of particular interest to study the
structure of a population in social groups or for use in data-driven models of
information or epidemic spreading processes. Here, we address this issue by
leveraging data sets containing high resolution face-to-face contacts as well
as a coarser spatial localisation of individuals, both temporally resolved, in
various contexts. The co-presence and the face-to-face contact temporal
networks share a number of structural and statistical features, but the former
is (by definition) much denser than the latter. We thus consider several
down-sampling methods that generate surrogate contact networks from the
co-presence signal and compare them with the real face-to-face data. We show
that these surrogate networks reproduce some features of the real data but are
only partially able to identify the most central nodes of the face-to-face
network. We then address the issue of using such down-sampled co-presence data
in data-driven simulations of epidemic processes, and in identifying efficient
containment strategies. We show that the performance of the various sampling
methods strongly varies depending on context. We discuss the consequences of
our results with respect to data collection strategies and methodologies
Epidemic risk from friendship network data: an equivalence with a non-uniform sampling of contact networks
Contacts between individuals play an important role in determining how
infectious diseases spread. Various methods to gather data on such contacts
co-exist, from surveys to wearable sensors. Comparisons of data obtained by
different methods in the same context are however scarce, in particular with
respect to their use in data-driven models of spreading processes. Here, we use
a combined data set describing contacts registered by sensors and friendship
relations in the same population to address this issue in a case study. We
investigate if the use of the friendship network is equivalent to a sampling
procedure performed on the sensor contact network with respect to the outcome
of simulations of spreading processes: such an equivalence might indeed give
hints on ways to compensate for the incompleteness of contact data deduced from
surveys. We show that this is indeed the case for these data, for a
specifically designed sampling procedure, in which respondents report their
neighbors with a probability depending on their contact time. We study the
impact of this specific sampling procedure on several data sets, discuss
limitations of our approach and its possible applications in the use of data
sets of various origins in data-driven simulations of epidemic processes
On the properties of small-world network models
We study the small-world networks recently introduced by Watts and Strogatz
[Nature {\bf 393}, 440 (1998)], using analytical as well as numerical tools. We
characterize the geometrical properties resulting from the coexistence of a
local structure and random long-range connections, and we examine their
evolution with size and disorder strength. We show that any finite value of the
disorder is able to trigger a ``small-world'' behaviour as soon as the initial
lattice is big enough, and study the crossover between a regular lattice and a
``small-world'' one. These results are corroborated by the investigation of an
Ising model defined on the network, showing for every finite disorder fraction
a crossover from a high-temperature region dominated by the underlying
one-dimensional structure to a mean-field like low-temperature region. In
particular there exists a finite-temperature ferromagnetic phase transition as
soon as the disorder strength is finite.Comment: 19 pages including 15 figures, version accepted for publication in
EPJ
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