260 research outputs found
Use, production and conservation of palm fiber in South America: A review
South American ethnic groups traditionally use palm fiber, which provides materials for domestic, commercial, and ceremonial purposes. A literature review of 185 references was carried out in order to identify and understand the extent of palm fiber production and the sustainability of harvesting and use in South America. The reports recorded 111 palm species and 37 genera used for fiber in the region; the genera Attalea, Astrocaryum and Syagrus had the highest diversity of fiber-producing species. Mauritia flexuosa and Astrocaryum chambira were the species mostly reported and with the largest number of object types manufactured with their fibers. The geographical distribution of the species use nearly overlaps the natural distribution of palms in South America, reaching its highest diversity in northern Amazonia, where palms are used mostly by indigenous people and peasants. The techniques used for extraction, harvesting and processing are usually basic and minimal. Most species are represented by wild populations found on common lands, the little detailed information available suggests that when use is intensive it is mosly unsustainable, and those with a greater market demand usually become locally extinct. Market demand, ecosystem conservation, and management practices used to boost fiber production are the major variables determining the sustainability of fiber extraction
Exact Fourier expansion in cylindrical coordinates for the three-dimensional Helmholtz Green function
A new method is presented for Fourier decomposition of the Helmholtz Green
Function in cylindrical coordinates, which is equivalent to obtaining the
solution of the Helmholtz equation for a general ring source. The Fourier
coefficients of the Helmholtz Green function are split into their half
advanced+half retarded and half advanced-half retarded components. Closed form
solutions are given for these components in terms of a Horn function and a
Kampe de Feriet function, respectively. The systems of partial differential
equations associated with these two-dimensional hypergeometric functions are
used to construct a fourth-order ordinary differential equation which both
components satisfy. A second fourth-order ordinary differential equation for
the general Fourier coefficent is derived from an integral representation of
the coefficient, and both differential equations are shown to be equivalent.
Series solutions for the various Fourier coefficients are also given, mostly in
terms of Legendre functions and Bessel/Hankel functions. These are derived from
the closed form hypergeometric solutions or an integral representation, or
both. Numerical calculations comparing different methods of calculating the
Fourier coefficients are presented
Exponents appearing in heterogeneous reaction-diffusion models in one dimension
We study the following 1D two-species reaction diffusion model : there is a
small concentration of B-particles with diffusion constant in an
homogenous background of W-particles with diffusion constant ; two
W-particles of the majority species either coagulate ()
or annihilate () with the respective
probabilities and ; a B-particle and a
W-particle annihilate () with probability 1. The
exponent describing the asymptotic time decay of
the minority B-species concentration can be viewed as a generalization of the
exponent of persistent spins in the zero-temperature Glauber dynamics of the 1D
-state Potts model starting from a random initial condition : the
W-particles represent domain walls, and the exponent
characterizes the time decay of the probability that a diffusive "spectator"
does not meet a domain wall up to time . We extend the methods introduced by
Derrida, Hakim and Pasquier ({\em Phys. Rev. Lett.} {\bf 75} 751 (1995); Saclay
preprint T96/013, to appear in {\em J. Stat. Phys.} (1996)) for the problem of
persistent spins, to compute the exponent in perturbation
at first order in for arbitrary and at first order in
for arbitrary .Comment: 29 pages. The three figures are not included, but are available upon
reques
Kang-Redner Anomaly in Cluster-Cluster Aggregation
The large time, small mass, asymptotic behavior of the average mass
distribution \pb is studied in a -dimensional system of diffusing
aggregating particles for . By means of both a renormalization
group computation as well as a direct re-summation of leading terms in the
small reaction-rate expansion of the average mass distribution, it is shown
that \pb \sim \frac{1}{t^d} (\frac{m^{1/d}}{\sqrt{t}})^{e_{KR}} for , where and . In two
dimensions, it is shown that \pb \sim \frac{\ln(m) \ln(t)}{t^2} for . Numerical simulations in two dimensions supporting the analytical
results are also presented.Comment: 11 pages, 6 figures, Revtex
Diffusion-controlled annihilation with initially separated reactants: The death of an particle island in the particle sea
We consider the diffusion-controlled annihilation dynamics with
equal species diffusivities in the system where an island of particles is
surrounded by the uniform sea of particles . We show that once the initial
number of particles in the island is large enough, then at any system's
dimensionality the death of the majority of particles occurs in the {\it
universal scaling regime} within which of the particles die at
the island expansion stage and the remaining at the stage of its
subsequent contraction. In the quasistatic approximation the scaling of the
reaction zone has been obtained for the cases of mean-field ()
and fluctuation () dynamics of the front.Comment: 4 RevTex pages, 1 PNG figure and 1 EPS figur
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
Random Walks in Logarithmic and Power-Law Potentials, Nonuniversal Persistence, and Vortex Dynamics in the Two-Dimensional XY Model
The Langevin equation for a particle (`random walker') moving in
d-dimensional space under an attractive central force, and driven by a Gaussian
white noise, is considered for the case of a power-law force, F(r) = -
Ar^{-sigma}. The `persistence probability', P_0(t), that the particle has not
visited the origin up to time t, is calculated. For sigma > 1, the force is
asymptotically irrelevant (with respect to the noise), and the asymptotics of
P_0(t) are those of a free random walker. For sigma < 1, the noise is
(dangerously) irrelevant and the asymptotics of P_0(t) can be extracted from a
weak noise limit within a path-integral formalism. For the case sigma=1,
corresponding to a logarithmic potential, the noise is exactly marginal. In
this case, P_0(t) decays as a power-law, P_0(t) \sim t^{-theta}, with an
exponent theta that depends continuously on the ratio of the strength of the
potential to the strength of the noise. This case, with d=2, is relevant to the
annihilation dynamics of a vortex-antivortex pair in the two-dimensional XY
model. Although the noise is multiplicative in the latter case, the relevant
Langevin equation can be transformed to the standard form discussed in the
first part of the paper. The mean annihilation time for a pair initially
separated by r is given by t(r) \sim r^2 ln(r/a) where a is a microscopic
cut-off (the vortex core size). Implications for the nonequilibrium critical
dynamics of the system are discussed and compared to numerical simulation
results.Comment: 10 pages, 1 figur
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
Persistence properties of a system of coagulating and annihilating random walkers
We study a d-dimensional system of diffusing particles that on contact either
annihilate with probability 1/(q-1) or coagulate with probability (q-2)/(q-1).
In 1-dimension, the system models the zero temperature Glauber dynamics of
domain walls in the q-state Potts model. We calculate P(m,t), the probability
that a randomly chosen lattice site contains a particle whose ancestors have
undergone exactly (m-1) coagulations. Using perturbative renormalization group
analysis for d < 2, we show that, if the number of coagulations m is much less
than the typical number M(t), then P(m,t) ~ m^(z/d) t^(-theta), with theta=d Q
+ Q(Q-1/2) epsilon + O(epsilon^2), z=(2Q-1) epsilon + (2 Q-1) (Q-1)(1/2+A Q)
epsilon^2 +O(epsilon^3), where Q=(q-1)/q, epsilon =2-d and A =-0.006. M(t) is
shown to scale as t^(d/2-delta), where delta = d (1 -Q)+(Q-1)(Q-1/2) epsilon+
O(epsilon^2). In two dimensions, we show that P(m,t) ~ ln(t)^(Q(3-2Q))
ln(m)^((2Q-1)^2) t^(-2Q) for m << t^(2 Q-1). The 1-dimensional results
corresponding to epsilon=1 are compared with results from Monte Carlo
simulations.Comment: 12 pages, revtex, 5 figure
Reaction Diffusion Models in One Dimension with Disorder
We study a large class of 1D reaction diffusion models with quenched disorder
using a real space renormalization group method (RSRG) which yields exact
results at large time. Particles (e.g. of several species) undergo diffusion
with random local bias (Sinai model) and react upon meeting. We obtain the
large time decay of the density of each specie, their associated universal
amplitudes, and the spatial distribution of particles. We also derive the
spectrum of exponents which characterize the convergence towards the asymptotic
states. For reactions with several asymptotic states, we analyze the dynamical
phase diagram and obtain the critical exponents at the transitions. We also
study persistence properties for single particles and for patterns. We compute
the decay exponents for the probability of no crossing of a given point by,
respectively, the single particle trajectories () or the thermally
averaged packets (). The generalized persistence exponents
associated to n crossings are also obtained. Specifying to the process or A with probabilities , we compute exactly the exponents
and characterizing the survival up to time t of a domain
without any merging or with mergings respectively, and and
characterizing the survival up to time t of a particle A without
any coalescence or with coalescences respectively.
obey hypergeometric equations and are numerically surprisingly close to pure
system exponents (though associated to a completely different diffusion
length). Additional disorder in the reaction rates, as well as some open
questions, are also discussed.Comment: 54 pages, Late
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