233 research outputs found
Large-Deviation Functions for Nonlinear Functionals of a Gaussian Stationary Markov Process
We introduce a general method, based on a mapping onto quantum mechanics, for
investigating the large-T limit of the distribution P(r,T) of the nonlinear
functional r[V] = (1/T)\int_0^T dT' V[X(T')], where V(X) is an arbitrary
function of the stationary Gaussian Markov process X(T). For T tending to
infinity at fixed r we find that P(r,T) behaves as exp[-theta(r) T], where
theta(r) is a large deviation function. We present explicit results for a
number of special cases, including the case V(X) = X \theta(X) which is related
to the cooling and the heating degree days relevant to weather derivatives.Comment: 8 page
Persistence in a Stationary Time-series
We study the persistence in a class of continuous stochastic processes that
are stationary only under integer shifts of time. We show that under certain
conditions, the persistence of such a continuous process reduces to the
persistence of a corresponding discrete sequence obtained from the measurement
of the process only at integer times. We then construct a specific sequence for
which the persistence can be computed even though the sequence is
non-Markovian. We show that this may be considered as a limiting case of
persistence in the diffusion process on a hierarchical lattice.Comment: 8 pages revte
Persistence of a Continuous Stochastic Process with Discrete-Time Sampling: Non-Markov Processes
We consider the problem of `discrete-time persistence', which deals with the
zero-crossings of a continuous stochastic process, X(T), measured at discrete
times, T = n(\Delta T). For a Gaussian Stationary Process the persistence (no
crossing) probability decays as exp(-\theta_D T) = [\rho(a)]^n for large n,
where a = \exp[-(\Delta T)/2], and the discrete persistence exponent, \theta_D,
is given by \theta_D = \ln(\rho)/2\ln(a). Using the `Independent Interval
Approximation', we show how \theta_D varies with (\Delta T) for small (\Delta
T) and conclude that experimental measurements of persistence for smooth
processes, such as diffusion, are less sensitive to the effects of discrete
sampling than measurements of a randomly accelerated particle or random walker.
We extend the matrix method developed by us previously [Phys. Rev. E 64,
015151(R) (2001)] to determine \rho(a) for a two-dimensional random walk and
the one-dimensional random acceleration problem. We also consider `alternating
persistence', which corresponds to a < 0, and calculate \rho(a) for this case.Comment: 14 pages plus 8 figure
Survival in equilibrium step fluctuations
We report the results of analytic and numerical investigations of the time
scale of survival or non-zero-crossing probability in equilibrium step
fluctuations described by Langevin equations appropriate for
attachment/detachment and edge-diffusion limited kinetics. An exact relation
between long-time behaviors of the survival probability and the autocorrelation
function is established and numerically verified. is shown to exhibit
simple scaling behavior as a function of system size and sampling time. Our
theoretical results are in agreement with those obtained from an analysis of
experimental dynamical STM data on step fluctuations on Al/Si(111) and Ag(111)
surfaces.Comment: RevTeX, 4 pages, 3 figure
Mass-Transport Models with Multiple-Chipping Processes
We study mass-transport models with multiple-chipping processes. The rates of
these processes are dependent on the chip size and mass of the fragmenting
site. In this context, we consider k-chip moves (where k = 1, 2, 3, ....); and
combinations of 1-chip, 2-chip and 3-chip moves. The corresponding mean-field
(MF) equations are solved to obtain the steady-state probability distributions,
P (m) vs. m. We also undertake Monte Carlo (MC) simulations of these models.
The MC results are in excellent agreement with the corresponding MF results,
demonstrating that MF theory is exact for these models.Comment: 18 pages, 4 figures, To appear in European Physical Journal
Fraction of uninfected walkers in the one-dimensional Potts model
The dynamics of the one-dimensional q-state Potts model, in the zero
temperature limit, can be formulated through the motion of random walkers which
either annihilate (A + A -> 0) or coalesce (A + A -> A) with a q-dependent
probability. We consider all of the walkers in this model to be mutually
infectious. Whenever two walkers meet, they experience mutual contamination.
Walkers which avoid an encounter with another random walker up to time t remain
uninfected. The fraction of uninfected walkers is investigated numerically and
found to decay algebraically, U(t) \sim t^{-\phi(q)}, with a nontrivial
exponent \phi(q). Our study is extended to include the coupled
diffusion-limited reaction A+A -> B, B+B -> A in one dimension with equal
initial densities of A and B particles. We find that the density of walkers
decays in this model as \rho(t) \sim t^{-1/2}. The fraction of sites unvisited
by either an A or a B particle is found to obey a power law, P(t) \sim
t^{-\theta} with \theta \simeq 1.33. We discuss these exponents within the
context of the q-state Potts model and present numerical evidence that the
fraction of walkers which remain uninfected decays as U(t) \sim t^{-\phi},
where \phi \simeq 1.13 when infection occurs between like particles only, and
\phi \simeq 1.93 when we also include cross-species contamination.Comment: Expanded introduction with more discussion of related wor
Cosmological Unparticle Correlators
We introduce and study an extension of the correlator of unparticle matter
operators in a cosmological environment. Starting from FRW spaces we specialize
to a de Sitter spacetime and derive its inflationary power spectrum which we
find to be almost flat. We finally investigate some consequences of requiring
the existence of a unitary boundary conformal field theory in the framework of
the dS/CFT correspondence.Comment: 8 pages, 1 figure, to appear on Phys. Lett.
Real Roots of Random Polynomials and Zero Crossing Properties of Diffusion Equation
We study various statistical properties of real roots of three different
classes of random polynomials which recently attracted a vivid interest in the
context of probability theory and quantum chaos. We first focus on gap
probabilities on the real axis, i.e. the probability that these polynomials
have no real root in a given interval. For generalized Kac polynomials, indexed
by an integer d, of large degree n, one finds that the probability of no real
root in the interval [0,1] decays as a power law n^{-\theta(d)} where \theta(d)
> 0 is the persistence exponent of the diffusion equation with random initial
conditions in spatial dimension d. For n \gg 1 even, the probability that they
have no real root on the full real axis decays like
n^{-2(\theta(2)+\theta(d))}. For Weyl polynomials and Binomial polynomials,
this probability decays respectively like \exp{(-2\theta_{\infty}} \sqrt{n})
and \exp{(-\pi \theta_{\infty} \sqrt{n})} where \theta_{\infty} is such that
\theta(d) = 2^{-3/2} \theta_{\infty} \sqrt{d} in large dimension d. We also
show that the probability that such polynomials have exactly k roots on a given
interval [a,b] has a scaling form given by \exp{(-N_{ab} \tilde
\phi(k/N_{ab}))} where N_{ab} is the mean number of real roots in [a,b] and
\tilde \phi(x) a universal scaling function. We develop a simple Mean Field
(MF) theory reproducing qualitatively these scaling behaviors, and improve
systematically this MF approach using the method of persistence with partial
survival, which in some cases yields exact results. Finally, we show that the
probability density function of the largest absolute value of the real roots
has a universal algebraic tail with exponent {-2}. These analytical results are
confirmed by detailed numerical computations.Comment: 32 pages, 16 figure
Ground-state phase diagram of the one-dimensional half-filled extended Hubbard model
We revisit the ground-state phase diagram of the one-dimensional half-filled
extended Hubbard model with on-site (U) and nearest-neighbor (V) repulsive
interactions. In the first half of the paper, using the weak-coupling
renormalization-group approach (g-ology) including second-order corrections to
the coupling constants, we show that bond-charge-density-wave (BCDW) phase
exists for U \approx 2V in between charge-density-wave (CDW) and
spin-density-wave (SDW) phases. We find that the umklapp scattering of
parallel-spin electrons disfavors the BCDW state and leads to a bicritical
point where the CDW-BCDW and SDW-BCDW continuous-transition lines merge into
the CDW-SDW first-order transition line. In the second half of the paper, we
investigate the phase diagram of the extended Hubbard model with either
additional staggered site potential \Delta or bond alternation \delta. Although
the alternating site potential \Delta strongly favors the CDW state (that is, a
band insulator), the BCDW state is not destroyed completely and occupies a
finite region in the phase diagram. Our result is a natural generalization of
the work by Fabrizio, Gogolin, and Nersesyan [Phys. Rev. Lett. 83, 2014
(1999)], who predicted the existence of a spontaneously dimerized insulating
state between a band insulator and a Mott insulator in the phase diagram of the
ionic Hubbard model. The bond alternation \delta destroys the SDW state and
changes it into the BCDW state (or Peierls insulating state). As a result the
phase diagram of the model with \delta contains only a single critical line
separating the Peierls insulator phase and the CDW phase. The addition of
\Delta or \delta changes the universality class of the CDW-BCDW transition from
the Gaussian transition into the Ising transition.Comment: 24 pages, 20 figures, published versio
Cell elongation in the grass pulvinus in response to geotropic stimulation and auxin application
Horizontally-placed segments of Avena sativa L. shoots show a negative geotropic response after a period of 30 min. This response is based on cell elongation on the lower side of the leaf-sheath base (pulvinus). Triticum aestivum L., Hordeum vulgare L. and Secale cereale L. also show geotropic responses that are similar to those in Avena shoots. The pulvinus is a highly specialized organ with radial symmetry and is made up of epidermal, vascular, parenchymatous and collenchymatous tissues. Statoliths, which are confined to parenchyma cells around the vascular bundles, sediment towards the gravitational field within 10–15 min of geotropic stimulation. Collenchymatous cells occur as prominent bundle caps, and in Avena , they occupy about 30% of the volume of the pulvinus. Geotropic stimulation causes a 3- to 5-fold increase in the length of the cells on the side nearest to the center of the gravitational field. Growth can also be initiated in vertically-held pulvini by the application of indole-3-acetic acid, 1-naphthaleneacetic acid or 2.4-dichlorophenoxyacetic acid. 2.3.5.-triiodobenzoic acid interferes with growth response produced by geotropic stimulation as well as with the response caused by auxin application. Gibberellic acid and kinetin have no visible effect on the growth of the pulvinus. Polarization microscopy shows a unique, non-uniform stretching of the elongating collenchymatous cells. Nonelongated collenchymatous cells appear uniformally anisotropic. After geotropic stimulation or auxin application, they appear alternately anisotropic and almost isotropic. Such a pattern of cell elongation is also observed in collenchyma cells of geotropically-stimulated shoots of Rumex acetosa L., a dicotyledon.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47463/1/425_2004_Article_BF00385422.pd
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