7,775 research outputs found
Spatial evolution of human dialects
The geographical pattern of human dialects is a result of history. Here, we
formulate a simple spatial model of language change which shows that the final
result of this historical evolution may, to some extent, be predictable. The
model shows that the boundaries of language dialect regions are controlled by a
length minimizing effect analogous to surface tension, mediated by variations
in population density which can induce curvature, and by the shape of coastline
or similar borders. The predictability of dialect regions arises because these
effects will drive many complex, randomized early states toward one of a
smaller number of stable final configurations. The model is able to reproduce
observations and predictions of dialectologists. These include dialect
continua, isogloss bundling, fanning, the wave-like spread of dialect features
from cities, and the impact of human movement on the number of dialects that an
area can support. The model also provides an analytical form for S\'{e}guy's
Curve giving the relationship between geographical and linguistic distance, and
a generalisation of the curve to account for the presence of a population
centre. A simple modification allows us to analytically characterize the
variation of language use by age in an area undergoing linguistic change
Shocks Generate Crossover Behaviour In Lattice Avalanches
A spatial avalanche model is introduced, in which avalanches increase
stability in the regions where they occur. Instability is driven globally by a
driving process that contains shocks. The system is typically subcritical, but
the shocks occasionally lift it into a near or super critical state from which
it rapidly retreats due to large avalanches. These shocks leave behind a
signature -- a distinct power--law crossover in the avalanche size
distribution. The model is inspired by landslide field data, but the principles
may be applied to any system that experiences stabilizing failures, possesses a
critical point, and is subject to an ongoing process of destabilization which
includes occasional dramatic destabilizing events
Crossover Behaviour In Driven Cascades
We propose a model which explains how power-law crossover behaviour can arise
in a system which is capable of experiencing cascading failure. In our model
the susceptibility of the system to cascades is described by a single number,
the propagation power, which measures the ease with which cascades propagate.
Physically, such a number could represent the density of unstable material in a
system, its internal connectivity, or the mean susceptibility of its component
parts to failure. We assume that the propagation power follows an upward
drifting Brownian motion between cascades, and drops discontinuously each time
a cascade occurs. Cascades are described by a continuous state branching
process with distributional properties determined by the value of the
propagation power when they occur. In common with many cascading models, pure
power law behaviour is exhibited at a critical level of propagation power, and
the mean cascade size diverges. This divergence constrains large systems to the
subcritical region. We show that as a result, crossover behaviour appears in
the cascade distribution when an average is performed over the distribution of
propagation power. We are able to analytically determine the exponents before
and after the crossover
The formation and arrangement of pits by a corrosive gas
When corroding or otherwise aggressive particles are incident on a surface,
pits can form. For example, under certain circumstances rock surfaces that are
exposed to salts can form regular tessellating patterns of pits known as
"tafoni". We introduce a simple lattice model in which a gas of corrosive
particles, described by a discrete convection diffusion equation, drifts onto a
surface. Each gas particle has a fixed probability of being absorbed and
causing damage at each contact. The surface is represented by a lattice of
strength numbers which reduce after each absorbtion event, with sites being
removed when their strength becomes negative. The model generates regular
formations of pits, with each pit having a characteristic trapezoidal geometry
determined by the particle bias, absorbtion probability and surface strength.
The formation of this geometry may be understood in terms of a first order
partial differential equation. By viewing pits as particle funnels, we are able
to relate the gradient of pit walls to absorbtion probability and particle
bias
Birdsong dialect patterns explained using magnetic domains
The songs and calls of many bird species, like human speech, form distinct
regional dialects. We suggest that the process of dialect formation is
analogous to the physical process of magnetic domain formation. We take the
coastal breeding grounds of the Puget Sound white crowned sparrow as an
example. Previous field studies suggest that birds of this species learn
multiple songs early in life, and when establishing a territory for the first
time, retain one of these dialects in order to match the majority of their
neighbours. We introduce a simple lattice model of the process, showing that
this matching behaviour can produce single dialect domains provided the death
rate of adult birds is sufficiently low. We relate death rate to thermodynamic
temperature in magnetic materials, and calculate the critical death rate by
analogy with the Ising model. Using parameters consistent with the known
behavior of these birds we show that coastal dialect domain shapes may be
explained by viewing them as low temperature "stripe states"
Infrequent social interaction can accelerate the spread of a persuasive idea
We study the spread of a persuasive new idea through a population of
continuous-time random walkers in one dimension. The idea spreads via social
gatherings involving groups of nearby walkers who act according to a biased
"majority rule": After each gathering, the group takes on the new idea if more
than a critical fraction of them
already hold it; otherwise they all reject it. The boundary of a domain where
the new idea has taken hold expands as a traveling wave in the density of new
idea holders. Our walkers move by L\'{e}vy motion, and we compute the wave
velocity analytically as a function of the frequency of social gatherings and
the exponent of the jump distribution. When this distribution is sufficiently
heavy tailed, then, counter to intuition, the idea can propagate faster if
social gatherings are held less frequently. When jumps are truncated, a
critical gathering frequency can emerge which maximizes propagation velocity.
We explore our model by simulation, confirming our analytical results
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