708 research outputs found
Is local scale invariance a generic property of ageing phenomena ?
In contrast to recent claims by Enss, Henkel, Picone, and Schollwoeck [J.
Phys. A 37, 10479] it is shown that the critical autoresponse function of the
1+1-dimensional contact process is not in agreement with the predictions of
local scale invariance.Comment: 7 pages, 3 figures, final form, c++ source code on reques
Power requirements for electron cyclotron current drive and ion cyclotron resonance heating for sawtooth control in ITER
13MW of electron cyclotron current drive (ECCD) power deposited inside the q
= 1 surface is likely to reduce the sawtooth period in ITER baseline scenario
below the level empirically predicted to trigger neo-classical tearing modes
(NTMs). However, since the ECCD control scheme is solely predicated upon
changing the local magnetic shear, it is prudent to plan to use a complementary
scheme which directly decreases the potential energy of the kink mode in order
to reduce the sawtooth period. In the event that the natural sawtooth period is
longer than expected, due to enhanced alpha particle stabilisation for
instance, this ancillary sawtooth control can be provided from > 10MW of ion
cyclotron resonance heating (ICRH) power with a resonance just inside the q = 1
surface. Both ECCD and ICRH control schemes would benefit greatly from active
feedback of the deposition with respect to the rational surface. If the q = 1
surface can be maintained closer to the magnetic axis, the efficacy of ECCD and
ICRH schemes significantly increases, the negative effect on the fusion gain is
reduced, and off-axis negative-ion neutral beam injection (NNBI) can also be
considered for sawtooth control. Consequently, schemes to reduce the q = 1
radius are highly desirable, such as early heating to delay the current
penetration and, of course, active sawtooth destabilisation to mediate small
frequent sawteeth and retain a small q = 1 radius.Comment: 29 pages, 16 figure
Nonequilibrium wetting of finite samples
As a canonical model for wetting far from thermal equilibrium we study a
Kardar-Parisi-Zhang interface growing on top of a hard-core substrate.
Depending on the average growth velocity the model exhibits a non-equilibrium
wetting transition which is characterized by an additional surface critical
exponent theta. Simulating the single-step model in one spatial dimension we
provide accurate numerical estimates for theta and investigate the distribution
of contact points between the substrate and the interface as a function of
time. Moreover, we study the influence of finite-size effects, in particular
the time needed until a finite substrate is completely covered by the wetting
layer for the first time.Comment: 17 pages, 8 figures, revisio
Pair contact process with diffusion - A new type of nonequilibrium critical behavior?
Recently Carlon et. al. investigated the critical behavior of the pair
contact process with diffusion [cond-mat/9912347]. Using density matrix
renormalization group methods, they estimate the critical exponents, raising
the possibility that the transition might belong to the same universality class
as branching annihilating random walks with even numbers of offspring. This is
surprising since the model does not have an explicit parity-conserving
symmetry. In order to understand this contradiction, we estimate the critical
exponents by Monte Carlo simulations. The results suggest that the transition
might belong to a different universality class that has not been investigated
before.Comment: RevTeX, 3 pages, 2 eps figures, adapted to final version of
cond-mat/991234
Non-equilibrium Phase Transitions with Long-Range Interactions
This review article gives an overview of recent progress in the field of
non-equilibrium phase transitions into absorbing states with long-range
interactions. It focuses on two possible types of long-range interactions. The
first one is to replace nearest-neighbor couplings by unrestricted Levy flights
with a power-law distribution P(r) ~ r^(-d-sigma) controlled by an exponent
sigma. Similarly, the temporal evolution can be modified by introducing waiting
times Dt between subsequent moves which are distributed algebraically as P(Dt)~
(Dt)^(-1-kappa). It turns out that such systems with Levy-distributed
long-range interactions still exhibit a continuous phase transition with
critical exponents varying continuously with sigma and/or kappa in certain
ranges of the parameter space. In a field-theoretical framework such
algebraically distributed long-range interactions can be accounted for by
replacing the differential operators nabla^2 and d/dt with fractional
derivatives nabla^sigma and (d/dt)^kappa. As another possibility, one may
introduce algebraically decaying long-range interactions which cannot exceed
the actual distance to the nearest particle. Such interactions are motivated by
studies of non-equilibrium growth processes and may be interpreted as Levy
flights cut off at the actual distance to the nearest particle. In the
continuum limit such truncated Levy flights can be described to leading order
by terms involving fractional powers of the density field while the
differential operators remain short-ranged.Comment: LaTeX, 39 pages, 13 figures, minor revision
Correlated Initial Conditions in Directed Percolation
We investigate the influence of correlated initial conditions on the temporal
evolution of a (d+1)-dimensional critical directed percolation process.
Generating initial states with correlations ~r^(sigma-d) we
observe that the density of active sites in Monte-Carlo simulations evolves as
rho(t)~t^kappa. The exponent kappa depends continuously on sigma and varies in
the range -beta/nu_{||}<=kappa<=eta. Our numerical results are confirmed by an
exact field-theoretical renormalization group calculation.Comment: 10 pages, RevTeX, including 5 encapsulated postscript figure
Binary spreading process with parity conservation
Recently there has been a debate concerning the universal properties of the
phase transition in the pair contact process with diffusion (PCPD) . Although some of the critical exponents seem to coincide with
those of the so-called parity-conserving universality class, it was suggested
that the PCPD might represent an independent class of phase transitions. This
point of view is motivated by the argument that the PCPD does not conserve
parity of the particle number. In the present work we pose the question what
happens if the parity conservation law is restored. To this end we consider the
the reaction-diffusion process . Surprisingly this
process displays the same type of critical behavior, leading to the conclusion
that the most important characteristics of the PCPD is the use of binary
reactions for spreading, regardless of whether parity is conserved or not.Comment: RevTex, 4pages, 4 eps figure
Yang-Lee zeros for a nonequilibrium phase transition
Equilibrium systems which exhibit a phase transition can be studied by
investigating the complex zeros of the partition function. This method,
pioneered by Yang and Lee, has been widely used in equilibrium statistical
physics. We show that an analogous treatment is possible for a nonequilibrium
phase transition into an absorbing state. By investigating the complex zeros of
the survival probability of directed percolation processes we demonstrate that
the zeros provide information about universal properties. Moreover we identify
certain non-trivial points where the survival probability for bond percolation
can be computed exactly.Comment: LaTeX, IOP-style, 13 pages, 10 eps figure
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