359 research outputs found
Phase Space Transport in Noisy Hamiltonian Systems
This paper analyses the effect of low amplitude friction and noise in
accelerating phase space transport in time-independent Hamiltonian systems that
exhibit global stochasticity. Numerical experiments reveal that even very weak
non-Hamiltonian perturbations can dramatically increase the rate at which an
ensemble of orbits penetrates obstructions like cantori or Arnold webs, thus
accelerating the approach towards an invariant measure, i.e., a
near-microcanonical population of the accessible phase space region. An
investigation of first passage times through cantori leads to three
conclusions, namely: (i) that, at least for white noise, the detailed form of
the perturbation is unimportant, (ii) that the presence or absence of friction
is largely irrelevant, and (iii) that, overall, the amplitude of the response
to weak noise scales logarithmically in the amplitude of the noise.Comment: 13 pages, 3 Postscript figures, latex, no macors. Annals of the New
York Academy of Sciences, in pres
On the influence of noise on chaos in nearly Hamiltonian systems
The simultaneous influence of small damping and white noise on Hamiltonian
systems with chaotic motion is studied on the model of periodically kicked
rotor. In the region of parameters where damping alone turns the motion into
regular, the level of noise that can restore the chaos is studied. This
restoration is created by two mechanisms: by fluctuation induced transfer of
the phase trajectory to domains of local instability, that can be described by
the averaging of the local instability index, and by destabilization of motion
within the islands of stability by fluctuation induced parametric modulation of
the stability matrix, that can be described by the methods developed in the
theory of Anderson localization in one-dimensional systems.Comment: 10 pages REVTEX, 9 figures EP
On the Evolution Equation for Magnetic Geodesics
In this paper we prove the existence of long time solutions for the parabolic
equation for closed magnetic geodesics.Comment: In this paper we prove the existence of long time solutions for the
parabolic equation for closed magnetic geodesic
Harnack inequality and regularity for degenerate quasilinear elliptic equations
We prove Harnack inequality and local regularity results for weak solutions
of a quasilinear degenerate equation in divergence form under natural growth
conditions. The degeneracy is given by a suitable power of a strong
weight. Regularity results are achieved under minimal assumptions on the
coefficients and, as an application, we prove local estimates
for solutions of a degenerate equation in non divergence form
Markov Properties of Electrical Discharge Current Fluctuations in Plasma
Using the Markovian method, we study the stochastic nature of electrical
discharge current fluctuations in the Helium plasma. Sinusoidal trends are
extracted from the data set by the Fourier-Detrended Fluctuation analysis and
consequently cleaned data is retrieved. We determine the Markov time scale of
the detrended data set by using likelihood analysis. We also estimate the
Kramers-Moyal's coefficients of the discharge current fluctuations and derive
the corresponding Fokker-Planck equation. In addition, the obtained Langevin
equation enables us to reconstruct discharge time series with similar
statistical properties compared with the observed in the experiment. We also
provide an exact decomposition of temporal correlation function by using
Kramers-Moyal's coefficients. We show that for the stationary time series, the
two point temporal correlation function has an exponential decaying behavior
with a characteristic correlation time scale. Our results confirm that, there
is no definite relation between correlation and Markov time scales. However
both of them behave as monotonic increasing function of discharge current
intensity. Finally to complete our analysis, the multifractal behavior of
reconstructed time series using its Keramers-Moyal's coefficients and original
data set are investigated. Extended self similarity analysis demonstrates that
fluctuations in our experimental setup deviates from Kolmogorov (K41) theory
for fully developed turbulence regime.Comment: 25 pages, 9 figures and 4 tables. V3: Added comments, references,
figures and major correction
Analytical Results for Individual and Group Selection of Any Intensity
The idea of evolutionary game theory is to relate the payoff of a game to reproductive success (= fitness). An underlying assumption in most models is that fitness is a linear function of the payoff. For stochastic evolutionary dynamics in finite populations, this leads to analytical results in the limit of weak selection, where the game has a small effect on overall fitness. But this linear function makes the analysis of strong selection difficult. Here, we show that analytical results can be obtained for any intensity of selection, if fitness is defined as an exponential function of payoff. This approach also works for group selection (= multi-level selection). We discuss the difference between our approach and that of inclusive fitness theory
Soil nutrients and beta diversity in the Bornean Dipterocarpaceae: evidence for niche partitioning by tropical rain forest trees
1 The relative importance of niche- and dispersal-mediated processes in structuring diverse tropical plant communities remains poorly understood. Here, we link mesoscale beta diversity to soil variation throughout a lowland Bornean watershed underlain by alluvium, sedimentary and granite parent materials ( c . 340 ha, 8–200 m a.s.l.). We test the hypothesis that species turnover across the habitat gradient reflects interspecific partitioning of soil resources. 2 Floristic inventories (≥ 1 cm d.b.h.) of the Dipterocarpaceae, the dominant Bornean canopy tree family, were combined with extensive soil analyses in 30 (0.16 ha) plots. Six samples per plot were analysed for total C, N, P, K, Ca and Mg, exchangeable K, Ca and Mg, extractable P, texture, and pH. 3 Extractable P, exchangeable K, and total C, N and P varied significantly among substrates and were highest on alluvium. Thirty-one dipterocarp species ( n = 2634 individuals, five genera) were recorded. Dipterocarp density was similar across substrates, but richness and diversity were highest on nutrient-poor granite and lowest on nutrient-rich alluvium. 4 Eighteen of 22 species were positively or negatively associated with parent material. In 8 of 16 abundant species, tree distribution (≥ 10 cm d.b.h.) was more strongly non-random than juveniles (1–10 cm d.b.h.), suggesting higher juvenile mortality in unsuitable habitats. The dominant species Dipterocarpus sublamellatus (> 50% of stems) was indifferent to substrate, but nine of 11 ‘subdominant’ species (> 8 individuals ha −1 ) were substrate specialists. 5 Eighteen of 22 species were significantly associated with soil nutrients, especially P, Mg and Ca. Floristic variation was significantly correlated with edaphic and geographical distance for all stems ≥ 1 cm d.b.h. in Mantel analyses. However, juvenile variation (1–10 cm d.b.h.) was more strongly related to geographical distance than edaphic factors, while the converse held for established trees (≥ 10 cm d.b.h.), suggesting increased importance of niche processes with size class. 6 Pervasive dipterocarp associations with soil factors suggest that niche partitioning structures dipterocarp tree communities. Yet, much floristic variation unrelated to soil was correlated with geographical distance between plots, suggesting that dispersal and niche processes jointly determine mesoscale beta diversity in the Bornean Dipterocarpaceae. Journal of Ecology (2005) doi: 10.1111/j.1365-2745.2005.01077.xPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72822/1/j.1365-2745.2005.01077.x.pd
Approximating Fixation Probabilities in the Generalized Moran Process
We consider the Moran process, as generalized by Lieberman, Hauert and Nowak
(Nature, 433:312--316, 2005). A population resides on the vertices of a finite,
connected, undirected graph and, at each time step, an individual is chosen at
random with probability proportional to its assigned 'fitness' value. It
reproduces, placing a copy of itself on a neighbouring vertex chosen uniformly
at random, replacing the individual that was there. The initial population
consists of a single mutant of fitness placed uniformly at random, with
every other vertex occupied by an individual of fitness 1. The main quantities
of interest are the probabilities that the descendants of the initial mutant
come to occupy the whole graph (fixation) and that they die out (extinction);
almost surely, these are the only possibilities. In general, exact computation
of these quantities by standard Markov chain techniques requires solving a
system of linear equations of size exponential in the order of the graph so is
not feasible. We show that, with high probability, the number of steps needed
to reach fixation or extinction is bounded by a polynomial in the number of
vertices in the graph. This bound allows us to construct fully polynomial
randomized approximation schemes (FPRAS) for the probability of fixation (when
) and of extinction (for all ).Comment: updated to the final version, which appeared in Algorithmic
Measurement of the Bottom-Strange Meson Mixing Phase in the Full CDF Data Set
We report a measurement of the bottom-strange meson mixing phase \beta_s
using the time evolution of B0_s -> J/\psi (->\mu+\mu-) \phi (-> K+ K-) decays
in which the quark-flavor content of the bottom-strange meson is identified at
production. This measurement uses the full data set of proton-antiproton
collisions at sqrt(s)= 1.96 TeV collected by the Collider Detector experiment
at the Fermilab Tevatron, corresponding to 9.6 fb-1 of integrated luminosity.
We report confidence regions in the two-dimensional space of \beta_s and the
B0_s decay-width difference \Delta\Gamma_s, and measure \beta_s in [-\pi/2,
-1.51] U [-0.06, 0.30] U [1.26, \pi/2] at the 68% confidence level, in
agreement with the standard model expectation. Assuming the standard model
value of \beta_s, we also determine \Delta\Gamma_s = 0.068 +- 0.026 (stat) +-
0.009 (syst) ps-1 and the mean B0_s lifetime, \tau_s = 1.528 +- 0.019 (stat) +-
0.009 (syst) ps, which are consistent and competitive with determinations by
other experiments.Comment: 8 pages, 2 figures, Phys. Rev. Lett 109, 171802 (2012
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