84 research outputs found
Machine learning approaches for the optimization of packing densities in granular matter.
The fundamental question of how densely granular matter can pack and how this density depends on the shape of the constituent particles has been a longstanding scientific problem. Previous work has mainly focused on empirical approaches based on simulations or mean-field theory to investigate the effect of shape variation on the resulting packing densities, focusing on a small set of pre-defined shapes like dimers, ellipsoids, and spherocylinders. Here we discuss how machine learning methods can support the search for optimally dense packing shapes in a high-dimensional shape space. We apply dimensional reduction and regression techniques based on random forests and neural networks to find novel dense packing shapes by numerical optimization. Moreover, an investigation of the regression function in the dimensionally reduced shape representation allows us to identify directions in the packing density landscape that lead to a strongly non-monotonic variation of the packing density. The predictions obtained by machine learning are compared with packing simulations. Our approach can be more widely applied to optimize the properties of granular matter by varying the shape of its constituent particles
Edwards statistical mechanics for jammed granular matter
International audienc
Scale invariance and universality of force networks in static granular matter
Force networks form the skeleton of static granular matter. They are the key
ingredient to mechanical properties, such as stability, elasticity and sound
transmission, which are of utmost importance for civil engineering and
industrial processing. Previous studies have focused on the global structure of
external forces (the boundary condition), and on the probability distribution
of individual contact forces. The disordered spatial structure of the force
network, however, has remained elusive so far. Here we report evidence for
scale invariance of clusters of particles that interact via relatively strong
forces. We analyzed granular packings generated by molecular dynamics
simulations mimicking real granular matter; despite the visual variation, force
networks for various values of the confining pressure and other parameters have
identical scaling exponents and scaling function, and thus determine a
universality class. Remarkably, the flat ensemble of force configurations--a
simple generalization of equilibrium statistical mechanics--belongs to the same
universality class, while some widely studied simplified models do not.Comment: 15 pages, 4 figures; to appear in Natur
Enumeration of distinct mechanically stable disk packings in small systems
We create mechanically stable (MS) packings of bidisperse disks using an
algorithm in which we successively grow or shrink soft repulsive disks followed
by energy minimization until the overlaps are vanishingly small. We focus on
small systems because this enables us to enumerate nearly all distinct MS
packings. We measure the probability to obtain a MS packing at packing fraction
and find several notable results. First, the probability is highly
nonuniform. When averaged over narrow packing fraction intervals, the most
probable MS packing occurs at the highest and the probability decays
exponentially with decreasing . Even more striking, within each
packing-fraction interval, the probability can vary by many orders of
magnitude. By using two different packing-generation protocols, we show that
these results are robust and the packing frequencies do not change
qualitatively with different protocols.Comment: 4 pages, 3 figures, Conference Proceedings for X International
Workshop on Disordered System
Elementary processes governing the evolution of road networks
Urbanisation is a fundamental phenomenon whose quantitative characterisation
is still inadequate. We report here the empirical analysis of a unique data set
regarding almost 200 years of evolution of the road network in a large area
located north of Milan (Italy). We find that urbanisation is characterised by
the homogenisation of cell shapes, and by the stability throughout time of
high-centrality roads which constitute the backbone of the urban structure,
confirming the importance of historical paths. We show quantitatively that the
growth of the network is governed by two elementary processes: (i)
`densification', corresponding to an increase in the local density of roads
around existing urban centres and (ii) `exploration', whereby new roads trigger
the spatial evolution of the urbanisation front. The empirical identification
of such simple elementary mechanisms suggests the existence of general, simple
properties of urbanisation and opens new directions for its modelling and
quantitative description.Comment: 10 pages, 6 figure
Modeling the scaling properties of human mobility
While the fat tailed jump size and the waiting time distributions
characterizing individual human trajectories strongly suggest the relevance of
the continuous time random walk (CTRW) models of human mobility, no one
seriously believes that human traces are truly random. Given the importance of
human mobility, from epidemic modeling to traffic prediction and urban
planning, we need quantitative models that can account for the statistical
characteristics of individual human trajectories. Here we use empirical data on
human mobility, captured by mobile phone traces, to show that the predictions
of the CTRW models are in systematic conflict with the empirical results. We
introduce two principles that govern human trajectories, allowing us to build a
statistically self-consistent microscopic model for individual human mobility.
The model not only accounts for the empirically observed scaling laws but also
allows us to analytically predict most of the pertinent scaling exponents
A universal model for mobility and migration patterns
Introduced in its contemporary form by George Kingsley Zipf in 1946, but with
roots that go back to the work of Gaspard Monge in the 18th century, the
gravity law is the prevailing framework to predict population movement, cargo
shipping volume, inter-city phone calls, as well as bilateral trade flows
between nations. Despite its widespread use, it relies on adjustable parameters
that vary from region to region and suffers from known analytic
inconsistencies. Here we introduce a stochastic process capturing local
mobility decisions that helps us analytically derive commuting and mobility
fluxes that require as input only information on the population distribution.
The resulting radiation model predicts mobility patterns in good agreement with
mobility and transport patterns observed in a wide range of phenomena, from
long-term migration patterns to communication volume between different regions.
Given its parameter-free nature, the model can be applied in areas where we
lack previous mobility measurements, significantly improving the predictive
accuracy of most of phenomena affected by mobility and transport processes.Comment: Main text and supplementary informatio
Co-evolution of density and topology in a simple model of city formation
We study the influence that population density and the road network have on
each others' growth and evolution. We use a simple model of formation and
evolution of city roads which reproduces the most important empirical features
of street networks in cities. Within this framework, we explicitely introduce
the topology of the road network and analyze how it evolves and interact with
the evolution of population density. We show that accessibility issues -pushing
individuals to get closer to high centrality nodes- lead to high density
regions and the appearance of densely populated centers. In particular, this
model reproduces the empirical fact that the density profile decreases
exponentially from a core district. In this simplified model, the size of the
core district depends on the relative importance of transportation and rent
costs.Comment: 13 pages, 13 figure
Languages cool as they expand: Allometric scaling and the decreasing need for new words
We analyze the occurrence frequencies of over 15 million words recorded in millions of books published during the past two centuries in seven different languages. For all languages and chronological subsets of the data we confirm that two scaling regimes characterize the word frequency distributions, with only the more common words obeying the classic Zipf law. Using corpora of unprecedented size, we test the allometric scaling relation between the corpus size and the vocabulary size of growing languages to demonstrate a decreasing marginal need for new words, a feature that is likely related to the underlying correlations between words. We calculate the annual growth fluctuations of word use which has a decreasing trend as the corpus size increases, indicating a slowdown in linguistic evolution following language expansion. This ‘‘cooling pattern’’ forms the basis of a third statistical regularity, which unlike the Zipf and the Heaps law, is dynamical in nature
Fracturing ranked surfaces
Discretized landscapes can be mapped onto ranked surfaces, where every
element (site or bond) has a unique rank associated with its corresponding
relative height. By sequentially allocating these elements according to their
ranks and systematically preventing the occupation of bridges, namely elements
that, if occupied, would provide global connectivity, we disclose that bridges
hide a new tricritical point at an occupation fraction , where
is the percolation threshold of random percolation. For any value of in the
interval , our results show that the set of bridges has a
fractal dimension in two dimensions. In the limit , a self-similar fracture is revealed as a singly connected line
that divides the system in two domains. We then unveil how several seemingly
unrelated physical models tumble into the same universality class and also
present results for higher dimensions
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