713 research outputs found
Spatial fluctuations of a surviving particle in the trapping reaction
We consider the trapping reaction, , where and particles
have a diffusive dynamics characterized by diffusion constants and .
The interaction with particles can be formally incorporated in an effective
dynamics for one particle as was recently shown by Bray {\it et al}. [Phys.
Rev. E {\bf 67}, 060102 (2003)]. We use this method to compute, in space
dimension , the asymptotic behaviour of the spatial fluctuation,
, for a surviving particle in the perturbative regime,
, for the case of an initially uniform distribution of
particles. We show that, for , with
. By contrast, the fluctuations of paths constrained to return to
their starting point at time grow with the larger exponent 1/3. Numerical
tests are consistent with these predictions.Comment: 10 pages, 5 figure
An introduction to phase transitions in stochastic dynamical systems
We give an introduction to phase transitions in the steady states of systems
that evolve stochastically with equilibrium and nonequilibrium dynamics, the
latter defined as those that do not possess a time-reversal symmetry. We try as
much as possible to discuss both cases within the same conceptual framework,
focussing on dynamically attractive `peaks' in state space. A quantitative
characterisation of these peaks leads to expressions for the partition function
and free energy that extend from equilibrium steady states to their
nonequilibrium counterparts. We show that for certain classes of nonequilibrium
systems that have been exactly solved, these expressions provide precise
predictions of their macroscopic phase behaviour.Comment: Pedagogical talk contributed to the "Ageing and the Glass Transition"
Summer School, Luxembourg, September 2005. 12 pages, 8 figures, uses the IOP
'jpconf' document clas
Random Networks with Tunable Degree Distribution and Clustering
We present an algorithm for generating random networks with arbitrary degree
distribution and Clustering (frequency of triadic closure). We use this
algorithm to generate networks with exponential, power law, and poisson degree
distributions with variable levels of clustering. Such networks may be used as
models of social networks and as a testable null hypothesis about network
structure. Finally, we explore the effects of clustering on the point of the
phase transition where a giant component forms in a random network, and on the
size of the giant component. Some analysis of these effects is presented.Comment: 9 pages, 13 figures corrected typos, added two references,
reorganized reference
Perturbation theory for the one-dimensional trapping reaction
We consider the survival probability of a particle in the presence of a
finite number of diffusing traps in one dimension. Since the general solution
for this quantity is not known when the number of traps is greater than two, we
devise a perturbation series expansion in the diffusion constant of the
particle. We calculate the persistence exponent associated with the particle's
survival probability to second order and find that it is characterised by the
asymmetry in the number of traps initially positioned on each side of the
particle.Comment: 18 pages, no figures. Uses IOP Latex clas
Analysis of United Kingdom Off-Highway Construction Machinery Market and Its Consumers Using New-Sales Data
The off-highway construction machinery market and its consumers have attracted minimal previous research. This study addresses that void by analyzing annual United Kingdom (UK) (volume/portfolio) new-sales data for the 10 most popular products within that market, 1990–2010 inclusive. Graphical, descriptive statistical, Pearson-correlational, autocorrelational, and elementary modeling are employed to identify contrasts in sales regarding (1) high- and low-volume items; (2) growth trends and significant recessionary effects on volumes; (3) a demand change point circa 1997, since when annual product portfolio has changed little; and (4) product associations in consumer demand. Significant association is demonstrated between demand and construction output, especially with the value of new housing. Subsequently, consumption of wheeled loaders is modeled using construction volume, and demand for mini and crawler excavators is modeled using new-housing data. Time series trends for these machinery types are presented and forecast through 2015. The primary contribution of this study is a deeper understanding of the UK new-machinery market and the predilections of its consumers over the last two decades (to present)
Magnetic and Optical properties of strained films of multiferroic GdMnO3
The effects of strain on a film of mulitferroic GdMnO3 are investigated using
both magnetometry and magneto-optic spectroscopy. Optical spectra, in the
energy range 1.5eV - 3.5eV, were taken in Faraday geometry in an applied
magnetic field and also at remanence. This yielded rich information on the
effects of strain on the spin ordering in these films. Epitaxial films of
GdMnO3 were grown on SrTiO3 and LaAlO3 substrates. The LaAlO3 was twinned and
so produced a highly strained film whereas the strain was less for the film
grown on SrTiO3. The Ne\'el temperatures and coercive fields were measured
using zero field data and hysteresis loops obtained using a SQUID magnetometer.
Optical absorption data agreed with earlier work on bulk materials. The two
well known features in the optical spectrum, the charge transfer transition
between Mn d states at ~2eV and the band edge transition from the oxygen p band
to the d states at ~3eV are observed in the magnetic circular dichroism;
however they behaved very differently both as a function of magnetic field and
temperature. This is interpreted in terms of the magnetic ordering of the Mn
spins.Comment: 9 pages of text including figure
Free energy landscapes, dynamics and the edge of chaos in mean-field models of spin glasses
Metastable states in Ising spin-glass models are studied by finding iterative
solutions of mean-field equations for the local magnetizations. Two different
equations are studied: the TAP equations which are exact for the SK model, and
the simpler `naive-mean-field' (NMF) equations. The free-energy landscapes that
emerge are very different. For the TAP equations, the numerical studies confirm
the analytical results of Aspelmeier et al., which predict that TAP states
consist of close pairs of minima and index-one (one unstable direction) saddle
points, while for the NMF equations saddle points with large indices are found.
For TAP the barrier height between a minimum and its nearby saddle point scales
as (f-f_0)^{-1/3} where f is the free energy per spin of the solution and f_0
is the equilibrium free energy per spin. This means that for `pure states', for
which f-f_0 is of order 1/N, the barriers scale as N^{1/3}, but between states
for which f-f_0 is of order one the barriers are finite and also small so such
metastable states will be of limited physical significance. For the NMF
equations there are saddles of index K and we can demonstrate that their
complexity Sigma_K scales as a function of K/N. We have also employed an
iterative scheme with a free parameter that can be adjusted to bring the system
of equations close to the `edge of chaos'. Both for the TAP and NME equations
it is possible with this approach to find metastable states whose free energy
per spin is close to f_0. As N increases, it becomes harder and harder to find
solutions near the edge of chaos, but nevertheless the results which can be
obtained are competitive with those achieved by more time-consuming computing
methods and suggest that this method may be of general utility.Comment: 13 page
Voter Model with Time dependent Flip-rates
We introduce time variation in the flip-rates of the Voter Model. This type
of generalisation is relevant to models of ageing in language change, allowing
the representation of changes in speakers' learning rates over their lifetime
and may be applied to any other similar model in which interaction rates at the
microscopic level change with time. The mean time taken to reach consensus
varies in a nontrivial way with the rate of change of the flip-rates, varying
between bounds given by the mean consensus times for static homogeneous (the
original Voter Model) and static heterogeneous flip-rates. By considering the
mean time between interactions for each agent, we derive excellent estimates of
the mean consensus times and exit probabilities for any time scale of flip-rate
variation. The scaling of consensus times with population size on complex
networks is correctly predicted, and is as would be expected for the ordinary
voter model. Heterogeneity in the initial distribution of opinions has a strong
effect, considerably reducing the mean time to consensus, while increasing the
probability of survival of the opinion which initially occupies the most slowly
changing agents. The mean times to reach consensus for different states are
very different. An opinion originally held by the fastest changing agents has a
smaller chance to succeed, and takes much longer to do so than an evenly
distributed opinion.Comment: 16 pages, 6 figure
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