3,087 research outputs found
On the Graceful Game
A graceful labeling of a graph with edges consists of labeling the
vertices of with distinct integers from to such that, when each
edge is assigned as induced label the absolute difference of the labels of its
endpoints, all induced edge labels are distinct. Rosa established two well
known conjectures: all trees are graceful (1966) and all triangular cacti are
graceful (1988). In order to contribute to both conjectures we study graceful
labelings in the context of graph games. The Graceful game was introduced by
Tuza in 2017 as a two-players game on a connected graph in which the players
Alice and Bob take turns labeling the vertices with distinct integers from 0 to
. Alice's goal is to gracefully label the graph as Bob's goal is to prevent
it from happening. In this work, we study winning strategies for Alice and Bob
in complete graphs, paths, cycles, complete bipartite graphs, caterpillars,
prisms, wheels, helms, webs, gear graphs, hypercubes and some powers of paths
A general creation-annihilation model with absorbing states
A one dimensional non-equilibrium stochastic model is proposed where each
site of the lattice is occupied by a particle, which may be of type A or B. The
time evolution of the model occurs through three processes: autocatalytic
generation of A and B particles and spontaneous conversion A to B. The
two-parameter phase diagram of the model is obtained in one- and two-site mean
field approximations, as well as through numerical simulations and exact
solution of finite systems extrapolated to the thermodynamic limit. A
continuous line of transitions between an active and an absorbing phase is
found. This critical line starts at a point where the model is equivalent to
the contact process and ends at a point which corresponds to the voter model,
where two absorbing states coexist. Thus, the critical line ends at a point
where the transition is discontinuous. Estimates of critical exponents are
obtained through the simulations and finite-size-scaling extrapolations, and
the crossover between universality classes as the voter model transition is
approached is studied.Comment: 9 pages and 17 figure
Crossovers from parity conserving to directed percolation universality
The crossover behavior of various models exhibiting phase transition to
absorbing phase with parity conserving class has been investigated by numerical
simulations and cluster mean-field method. In case of models exhibiting Z_2
symmetric absorbing phases (the NEKIMCA and Grassberger's A stochastic cellular
automaton) the introduction of an external symmetry breaking field causes a
crossover to kink parity conserving models characterized by dynamical scaling
of the directed percolation (DP) and the crossover exponent: 1/\phi ~ 0.53(2).
In case an even offspringed branching and annihilating random walk model (dual
to NEKIMCA) the introduction of spontaneous particle decay destroys the parity
conservation and results in a crossover to the DP class characterized by the
crossover exponent: 1/\phi\simeq 0.205(5). The two different kinds of crossover
operators can't be mapped onto each other and the resulting models show a
diversity within the DP universality class in one dimension. These
'sub-classes' differ in cluster scaling exponents.Comment: 6 pages, 6 figures, accepted version in PR
A comparative study for the pair-creation contact process using series expansions
A comparative study between two distinct perturbative series expansions for
the pair-creation contact process is presented. In contrast to the ordinary
contact process, whose supercritical series expansions provide accurate
estimates for its critical behavior, the supercritical approach does not work
properly when applied to the pair-creation process. To circumvent this problem
a procedure is introduced in which one-site creation is added to the
pair-creation. An alternative method is the generation of subcritical series
expansions which works even for the case of the pure pair-creation process.
Differently from the supercritical case, the subcritical series yields
estimates that are compatible with numerical simulations
A supercritical series analysis for the generalized contact process with diffusion
We study a model that generalizes the CP with diffusion. An additional
transition is included in the model so that at a particular point of its phase
diagram a crossover from the directed percolation to the compact directed
percolation class will happen. We are particularly interested in the effect of
diffusion on the properties of the crossover between the universality classes.
To address this point, we develop a supercritical series expansion for the
ultimate survival probability and analyse this series using d-log Pad\'e and
partial differential approximants. We also obtain approximate solutions in the
one- and two-site dynamical mean-field approximations. We find evidences that,
at variance to what happens in mean-field approximations, the crossover
exponent remains close to even for quite high diffusion rates, and
therefore the critical line in the neighborhood of the multicritical point
apparently does not reproduce the mean-field result (which leads to )
as the diffusion rate grows without bound
Asymptotic behavior of the entropy of chains placed on stripes
By using the transfer matrix approach, we investigate the asymptotic behavior
of the entropy of flexible chains with monomers each placed on stripes. In
the limit of high density of monomers, we study the behavior of the entropy as
a function of the density of monomers and the width of the stripe, inspired by
recent analytical studies of this problem for the particular case of dimers
(M=2). We obtain the entropy in the asymptotic regime of high densities for
chains with monomers, as well as for the special case of polymers,
where , and find that the results show a regular behavior similar
to the one found analytically for dimers. We also verify that in the
low-density limit the mean-field expression for the entropy is followed by the
results from our transfer matrix calculations
- …