Random Walks in the Park
Habitat conservation areas must allow
enough room for animals to survive: one must ensure that their home range
is preserved. Relying on the analogy between the monitored positions of an
animal searching its habitat, and a path drawn at random, this paper
provides a formula to compute a mathematical estimate of the home range,
be it for individual animals or for herds. Most interestingly, this
general result reveals that, in the elementary model where individual
animals move around independently and food supplies have not reached their
limits, the size of the home range grows very slowly when the group
becomes larger and larger. Indeed, going from 10 to 100 individuals will
only double the home range of the herd - whatever the species. Such a
universal conclusion illustrates the power of the conceptual tools that
mathematicians and theoretical physicists have developed to treat random
processes. A seminal point in the development of this toolbox was
Einstein's 1905 description, through molecular collisions, of the anarchic
motion exhibited by pollen grains in water. This is now known as Brownian
motion, in memory of the British botanist who reported the observation.
From botany to habitat conservation - maybe not so much of a random walk
after all!
***
LZ11347
Tiny Black Holes may leave relic radiation behind them...
Some theories predict that tiny black holes -- weighing from less
than an ounce to millions of tons -- form immediately after the big
bang. In a recent paper, we showed that the tiniest of these black
holes would generate a distinctive background of gravitational
waves. All black holes leak energy via a process known as Hawking
radiation: the smallest black holes evaporate completely in less than
a second, black holes weighing as much as a star survive trillions of
times longer than the present age of the universe. Small "primordial"
black holes decay so fast that it was thought they left no relics
behind them. We showed that gravitational wave emitted as the black
holes evaporates would survive until the present day. These
gravitational waves have very high frequencies and could not be seen
with any detector currently on the drawing board. However, this is
the first time anyone has identified a "signal" generated by a
population of tiny black holes in the very early universe, and one day
it might be used to test models of the big bang which predict that
these black holes exist.
***
LF12857ER
The best place to survive
A prey, hunted by a population of "blind" predators moving randomly in a
complex labyrinth (network), has to choose a place to stay. Are there places
better than others to survive as long as possible? In this paper it is shown
that the answer depend on the large scale geometry of the labyrinth: if it
is such that a predator returns to its starting point with certainty
(recurrent network), then all sites, at large times, are equivalent, while,
in the opposite case (transient network) the survival probability can
strongly depend on the chosen site, and it is possible to study "geometric
strategies" in order to survive longer. This result applies to a large
variety of different problems and situations, ranging from chemical
reactions in disordered media to biological processes in human body and
information spreading in social systems.
***
LX11561
An entangled photon photonic machine gun
Photons are like teenagers - they are obsessed with the question of
whether they are the same or different as their peers. For this reason
individual photons of light are actually hard to create - the photons
from lights and lasers like to bunch together. However, because single
photons would be an important resource for quantum communication and
computation, there is a considerable worldwide effort to produce them.
In practise having these single photons would only be the first step -
there would then be a long and complicated process to manipulate their
quantum states so they become "entangled". Entangled quantum states are
the driving resource of quantum information theory. We outline a
technique which will enable certain single photons sources to produce
entangled states directly, at a high repetition rate, thereby
circumventing many of the obstacles on the road to building an optical
quantum computer.
***
LE12747
“PHOTONS REVEAL THEMSELVES”
What do photons look like? Researchers have provided insight into this question by studying the interaction between a pair of photons in a nonlinear crystal. By varying the degree of overlap of the photon pair members, while monitoring the strength of their interaction, it is possible to see behavior previously unobservable. The physical principle is identical to that used to characterize ultrafast laser pulses, but the novel aspect of this work is that it is conducted at the photon level. Pairs of photons are prepared in entangled quantum states using standard experimental techniques, and one photon of each pair is subjected to a controlled time delay. The pairs are then reunited in a nonlinear crystal, where the pairs are combined into single photons through upconversion. By varying the time delay while monitoring the upconversion rate, a 'temporal portrait' of the photon pairs is obtained. The results thus demonstrate an ultrafast correlation between
the members of each pair, with a temporal width of 28 femtoseconds, corresponding to a correlation length of only 8 microns.
***
EDJ1044
Percolating Cities
In this work we model the formation of a city. Based on empirical
findings, we show that the city emerges in a process that can be
successfully described as a two-dimensional bond percolation.
In the presented approach, the evolution of the urban system is driven
by the growth of the road/street network that brings the system to the
point (the percolation threshold) where it changes its structure and
transforms from the collection of separated settlements into a new
interconnected structure – the city. In this respect, the city formation
resembles physical phenomena, such as diffusion in disordered media,
polymerization, forest fires, or conduction, that are modeled within
the bond percolation theory.
The process leading to the city was deduced by analyzing the way people
divide their land into the smallest units – the land parcels.
***
LH12029
Might black holes reveal their inner secrets?
Black holes harbor a spacetime singularity of
infinite curvature, where classical spacetime
physics breaks down, and current theory cannot
predict what will happen. However, the singularity
is invisible from the outside because strong gravity
traps all signals, even light, behind an event horizon.
In this paper we show, using a simplifying approximation,
that it might be possible to destroy the horizon, if matter
is tossed into the black hole so as to make it spin faster
than a certain limit. One could thus expose a "naked" singularity
unless, as we suspect, effects beyond our approximation
intervene to protect the horizon.
