63,795 research outputs found
Crossover from the pair contact process with diffusion to directed percolation
Crossover behaviors from the pair contact process with diffusion (PCPD) and
the driven PCPD (DPCPD) to the directed percolation (DP) are studied in one
dimension by introducing a single particle annihilation/branching dynamics. The
crossover exponents are estimated numerically as for the PCPD and for the DPCPD.
Nontriviality of the PCPD crossover exponent strongly supports non-DP nature of
the PCPD critical scaling, which is further evidenced by the anomalous critical
amplitude scaling near the PCPD point. In addition, we find that the DPCPD
crossover is consistent with the mean field prediction of the tricritical DP
class as expected
Crossover from the parity-conserving pair contact process with diffusion to other universality classes
The pair contact process with diffusion (PCPD) with modulo 2 conservation
(\pcpdt) [, ] is studied in one dimension, focused on the
crossover to other well established universality classes: the directed Ising
(DI) and the directed percolation (DP). First, we show that the \pcpdt shares
the critical behaviors with the PCPD, both with and without directional bias.
Second, the crossover from the \pcpdt to the DI is studied by including a
parity-conserving single-particle process (). We find the crossover
exponent , which is argued to be identical to that of the
PCPD-to-DP crossover by adding . This suggests that the PCPD
universality class has a well defined fixed point distinct from the DP. Third,
we study the crossover from a hybrid-type reaction-diffusion process belonging
to the DP [, ] to the DI by adding . We find
for the DP-to-DI crossover. The inequality of and
further supports the non-DP nature of the PCPD scaling. Finally, we
introduce a symmetry-breaking field in the dual spin language to study the
crossover from the \pcpdt to the DP. We find , which is
associated with a new independent route from the PCPD to the DP.Comment: 8 pages, 8 figure
Nontrivial critical crossover between directed percolation models: Effect of infinitely many absorbing states
At non-equilibrium phase transitions into absorbing (trapped) states, it is
well known that the directed percolation (DP) critical scaling is shared by two
classes of models with a single (S) absorbing state and with infinitely many
(IM) absorbing states. We study the crossover behavior in one dimension,
arising from a considerable reduction of the number of absorbing states
(typically from the IM-type to the S-type DP models), by following two
different (excitatory or inhibitory) routes which make the auxiliary field
density abruptly jump at the crossover. Along the excitatory route, the system
becomes overly activated even for an infinitesimal perturbation and its
crossover becomes discontinuous. Along the inhibitory route, we find continuous
crossover with the universal crossover exponent , which is
argued to be equal to , the relaxation time exponent of the DP
universality class on a general footing. This conjecture is also confirmed in
the case of the directed Ising (parity-conserving) class. Finally, we discuss
the effect of diffusion to the IM-type models and suggest an argument why
diffusive models with some hybrid-type reactions should belong to the DP class.Comment: 8 pages, 9 figure
Crossover in the Slow Decay of Dynamic Correlations in the Lorentz Model
The long-time behavior of transport coefficients in a model for spatially
heterogeneous media in two and three dimensions is investigated by Molecular
Dynamics simulations. The behavior of the velocity auto-correlation function is
rationalized in terms of a competition of the critical relaxation due to the
underlying percolation transition and the hydrodynamic power-law anomalies. In
two dimensions and in the absence of a diffusive mode, another power law
anomaly due to trapping is found with an exponent -3 instead of -2. Further,
the logarithmic divergence of the Burnett coefficient is corroborated in the
dilute limit; at finite density, however, it is dominated by stronger
divergences.Comment: Full-length paragraph added that exemplifies the relevance for dense
fluids and makes a connection to recently observed, novel long-time tails in
a hard-sphere flui
Density Expansion for the Mobility in a Quantum Lorentz Model
We consider the mobility of electrons in an environment of static hard-sphere
scatterers, which provides a realistic description of electrons in Helium gas.
A systematic expansion in the scatterer density is carried to second order
relative to the Boltzmann result, and the analytic contribution at this order
is derived, together with the known logarithmic term in the density expansion.
It is shown that existing experimental data are consistent with the existence
of the logarithmic term in the density expansion, but more precise experiments
are needed in order to unambiguously detect it. We show that our calculations
provide the necessary theoretical information for such an experiment, and give
a detailed discussion of a suitable parameter range.Comment: 17pp., REVTeX, 7 figure attached as 8 postscript files, db/94/
Does Scientific Progress Consist in Increasing Knowledge or Understanding?
Bird argues that scientific progress consists in increasing knowledge. DellsĂ©n objects that increasing knowledge is neither necessary nor sufficient for scientific progress, and argues that scientific progress rather consists in increasing understanding. DellsĂ©n also contends that unlike Birdâs view, his view can account for the scientific practices of using idealizations and of choosing simple theories over complex ones. I argue that DellsĂ©nâs criticisms against Birdâs view fail, and that increasing understanding cannot account for scientific progress, if acceptance, as opposed to belief, is required for scientific understanding
Comments on "Entropy of 2D Black Holes from Counting Microstates"
In a recent letter, Cadoni and Mignemi proposed a formulation for the
statistical computation of the 2D black holes entropy. We present a criticism
about their formulation.Comment: 5 pages, Latex, no figure
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