13,801 research outputs found
Evolution in range expansions with competition at rough boundaries.
When a biological population expands into new territory, genetic drift develops an enormous influence on evolution at the propagating front. In such range expansion processes, fluctuations in allele frequencies occur through stochastic spatial wandering of both genetic lineages and the boundaries between genetically segregated sectors. Laboratory experiments on microbial range expansions have shown that this stochastic wandering, transverse to the front, is superdiffusive due to the front's growing roughness, implying much faster loss of genetic diversity than predicted by simple flat front diffusive models. We study the evolutionary consequences of this superdiffusive wandering using two complementary numerical models of range expansions: the stepping stone model, and a new interpretation of the model of directed paths in random media, in the context of a roughening population front. Through these approaches we compute statistics for the times since common ancestry for pairs of individuals with a given spatial separation at the front, and we explore how environmental heterogeneities can locally suppress these superdiffusive fluctuations
Ergodic decompositions of stationary max-stable processes in terms of their spectral functions
We revisit conservative/dissipative and positive/null decompositions of
stationary max-stable processes. Originally, both decompositions were defined
in an abstract way based on the underlying non-singular flow representation. We
provide simple criteria which allow to tell whether a given spectral function
belongs to the conservative/dissipative or positive/null part of the de Haan
spectral representation. Specifically, we prove that a spectral function is
null-recurrent iff it converges to in the Ces\`{a}ro sense. For processes
with locally bounded sample paths we show that a spectral function is
dissipative iff it converges to . Surprisingly, for such processes a
spectral function is integrable a.s. iff it converges to a.s. Based on
these results, we provide new criteria for ergodicity, mixing, and existence of
a mixed moving maximum representation of a stationary max-stable process in
terms of its spectral functions. In particular, we study a decomposition of
max-stable processes which characterizes the mixing property.Comment: 21 pages, no figure
Vortex wandering in a forest of splayed columnar defects
We investigate the scaling properties of single flux lines in a random
pinning landscape consisting of splayed columnar defects. Such correlated
defects can be injected into Type II superconductors by inducing nuclear
fission or via direct heavy ion irradiation. The result is often very efficient
pinning of the vortices which gives, e.g., a strongly enhanced critical
current. The wandering exponent \zeta and the free energy exponent \omega of a
single flux line in such a disordered environment are obtained analytically
from scaling arguments combined with extreme-value statistics. In contrast to
the case of point disorder, where these exponents are universal, we find a
dependence of the exponents on details in the probability distribution of the
low lying energies of the columnar defects. The analytical results show
excellent agreement with numerical transfer matrix calculations in two and
three dimensions.Comment: 11 pages, 9 figure
Effects of Disorder on Electron Transport in Arrays of Quantum Dots
We investigate the zero-temperature transport of electrons in a model of
quantum dot arrays with a disordered background potential. One effect of the
disorder is that conduction through the array is possible only for voltages
across the array that exceed a critical voltage . We investigate the
behavior of arrays in three voltage regimes: below, at and above the critical
voltage. For voltages less than , we find that the features of the
invasion of charge onto the array depend on whether the dots have uniform or
varying capacitances. We compute the first conduction path at voltages just
above using a transfer-matrix style algorithm. It can be used to
elucidate the important energy and length scales. We find that the geometrical
structure of the first conducting path is essentially unaffected by the
addition of capacitive or tunneling resistance disorder. We also investigate
the effects of this added disorder to transport further above the threshold. We
use finite size scaling analysis to explore the nonlinear current-voltage
relationship near . The scaling of the current near ,
, gives similar values for the effective exponent
for all varieties of tunneling and capacitive disorder, when the current is
computed for voltages within a few percent of threshold. We do note that the
value of near the transition is not converged at this distance from
threshold and difficulties in obtaining its value in the limit
Vortex Line Fluctuations in Model High Temperature Superconductors
We carry out Monte Carlo simulations of the uniformly frustrated 3d XY model
as a model for vortex line fluctuations in a high Tc superconductor. A density
of vortex lines of f=1/25 is considered. We find two sharp phase transitions.
The low T phase is an ordered vortex line lattice. The high T normal phase is a
vortex line liquid with much entangling, cutting, and loop excitations. An
intermediate phase is found which is characterized as a vortex line liquid of
disentangled lines. In this phase, the system displays superconducting
properties in the direction parallel to the magnetic field, but normal behavior
in planes perpendicular to the magnetic field.Comment: 38 pages, LaTeX 15 figures (upon request to
[email protected]
Phase Transitions in a Model Anisotropic High Tc Superconductor
We carry out simulations of the anisotropic uniformly frustrated 3D XY model,
as a model for vortex line fluctuations in high Tc superconductors. We compute
the phase diagram as a function of temperature and anisotropy, for a fixed
applied magnetic field. We find that superconducting coherence parallel to the
field persists into the vortex line liquid state, and that this transition lies
well below the "mean-field" cross-over from the vortex line liquid to the
normal state.Comment: 23 pages + 19 ps figure
Contact process on generalized Fibonacci chains: infinite-modulation criticality and double-log periodic oscillations
We study the nonequilibrium phase transition of the contact process with
aperiodic transition rates using a real-space renormalization group as well as
Monte-Carlo simulations. The transition rates are modulated according to the
generalized Fibonacci sequences defined by the inflation rules A AB
and B A. For and 2, the aperiodic fluctuations are irrelevant, and
the nonequilibrium transition is in the clean directed percolation universality
class. For , the aperiodic fluctuations are relevant. We develop a
complete theory of the resulting unconventional "infinite-modulation" critical
point which is characterized by activated dynamical scaling. Moreover,
observables such as the survival probability and the size of the active cloud
display pronounced double-log periodic oscillations in time which reflect the
discrete scale invariance of the aperiodic chains. We illustrate our theory by
extensive numerical results, and we discuss relations to phase transitions in
other quasiperiodic systems.Comment: 12 pages, 9 eps figures included, final version as publishe
The Mysteries of Trend
Trends are ubiquitous in economic discourse, play a role in much economic theory, and have been intensively studied in econometrics over the last three decades. Yet the empirical economist, forecaster, and policy maker have little guidance from theory about the source and nature of trend behavior, even less guidance about practical formulations, and are heavily reliant on a limited class of stochastic trend, deterministic drift, and structural break models to use in applications. A vast econometric literature has emerged but the nature of trend remains elusive. In spite of being the dominant characteristic in much economic data, having a role in policy assessment that is often vital, and attracting intense academic and popular interest that extends well beyond the subject of economics, trends are little understood. This essay discusses some implications of these limitations, mentions some research opportunities, and briefly illustrates the extent of the difficulties in learning about trend phenomena even when the time series are far longer than those that are available in economics.Climate change, Etymology of trend, Paleoclimatology, Policy, Stochastic trend
Conserved Quantities in Models of Classical Chaos
Quantum chaos is a major subject of interest in condensed matter theory, and
has recently motivated new questions in the study of classical chaos. In
particular, recent studies have uncovered interesting physics in the
relationship between chaos and conserved quantities in models of quantum chaos.
In this paper, we investigate this relationship in two simple models of
classical chaos: the infinite-temperature Heisenberg spin chain, and the
directed polymer in a random medium. We relate these models by drawing
analogies between the energy landscape over which the directed polymer moves
and the magnetization of the spin chain. We find that the coupling of the chaos
to these conserved quantities results in, among other things, a marked
transition from the rough perturbation profiles predicted by analogy to the KPZ
equation to smooth, triangular profiles with reduced wandering exponents. These
results suggest that diffusive conserved quantities can, in some cases, be the
dominant forces shaping the development of chaos in classical systems.Comment: This was an undergraduate research paper by Henry Ando, which we are
posting now because it is relevant to some continuing wor
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