25 research outputs found
Condensation phase transition in nonlinear fitness networks
We analyze the condensation phase transitions in out-of-equilibrium complex
networks in a unifying framework which includes the nonlinear model and the
fitness model as its appropriate limits. We show a novel phase structure which
depends on both the fitness parameter and the nonlinear exponent. The
occurrence of the condensation phase transitions in the dynamical evolution of
the network is demonstrated by using Bianconi-Barabasi method. We find that the
nonlinear and the fitness preferential attachment mechanisms play important
roles in formation of an interesting phase structure.Comment: 6 pages, 5 figure
Dynamics of condensation in growing complex networks
A condensation transition was predicted for growing technological networks
evolving by preferential attachment and competing quality of their nodes, as
described by the fitness model.
When this condensation occurs a node acquires a finite fraction of all the
links of the network. Earlier studies based on steady state degree distribution
and on the mapping to Bose-Einstein condensation, were able to identify the
critical point. Here we characterize the dynamics of condensation and we
present evidence that below the condensation temperature there is a slow down
of the dynamics and that a single node (not necessarily the best node in the
network) emerges as the winner for very long times. The characteristic time t*
at which this phenomenon occurs diverges both at the critical point and at when new links are attached deterministically to the highest quality node
of the network.Comment: (4 pages,3 figures
Zero-range processes with saturated condensation: the steady state and dynamics
We study a class of zero-range processes in which the real-space condensation
phenomenon does not occur and is replaced by a saturated condensation: that is,
an extensive number of finite-size "condensates" in the steady state. We
determine the conditions under which this occurs, and investigate the dynamics
of relaxation to the steady state. We identify two stages: a rapid initial
growth of condensates followed by a slow process of activated evaporation and
condensation. We analyze these nonequilibrium dynamics with a combination of
meanfield approximations, first-passage time calculations and a
fluctuation-dissipation type approach.Comment: 21 pages, 12 figure
Nonequilibrium dynamics of fully frustrated Ising models at T=0
We consider two fully frustrated Ising models: the antiferromagnetic
triangular model in a field of strength, , as well as the Villain
model on the square lattice. After a quench from a disordered initial state to
T=0 we study the nonequilibrium dynamics of both models by Monte Carlo
simulations. In a finite system of linear size, , we define and measure
sample dependent "first passage time", , which is the number of Monte
Carlo steps until the energy is relaxed to the ground-state value. The
distribution of , in particular its mean value, , is shown to
obey the scaling relation, , for both models.
Scaling of the autocorrelation function of the antiferromagnetic triangular
model is shown to involve logarithmic corrections, both at H=0 and at the
field-induced Kosterlitz-Thouless transition, however the autocorrelation
exponent is found to be dependent.Comment: 7 pages, 8 figure
Quantum statistics in Network Geometry with Fractional Flavor
(23 pages, 6 figures)(23 pages, 6 figures
Condensation in randomly perturbed zero-range processes
The zero-range process is a stochastic interacting particle system that
exhibits a condensation transition under certain conditions on the dynamics. It
has recently been found that a small perturbation of a generic class of jump
rates leads to a drastic change of the phase diagram and prevents condensation
in an extended parameter range. We complement this study with rigorous results
on a finite critical density and quenched free energy in the thermodynamic
limit, as well as quantitative heuristic results for small and large noise
which are supported by detailed simulation data. While our new results support
the initial findings, they also shed new light on the actual (limited)
relevance in large finite systems, which we discuss via fundamental diagrams
obtained from exact numerics for finite systems.Comment: 18 pages, 6 figure
1D Aging
We derive exact expressions for a number of aging functions that are scaling
limits of non-equilibrium correlations, R(tw,tw+t) as tw --> infinity with t/tw
--> theta, in the 1D homogenous q-state Potts model for all q with T=0 dynamics
following a quench from infinite temperature. One such quantity is (the
two-point, two-time correlation function) when
n/sqrt(tw) --> z. Exact, closed-form expressions are also obtained when one or
more interludes of infinite temperature dynamics occur. Our derivations express
the scaling limit via coalescing Brownian paths and a ``Brownian space-time
spanning tree,'' which also yields other aging functions, such as the
persistence probability of no spin flip at 0 between tw and tw+t.Comment: 4 pages (RevTeX); 2 figures; submitted to Physical Review Letter
Characterization of the stretched exponential trap-time distributions in one-dimensional coupled map lattices
Stretched exponential distributions and relaxation responses are encountered
in a wide range of physical systems such as glasses, polymers and spin glasses.
As found recently, this type of behavior occurs also for the distribution
function of certain trap time in a number of coupled dynamical systems. We
analyze a one-dimensional mathematical model of coupled chaotic oscillators
which reproduces an experimental set-up of coupled diode-resonators and
identify the necessary ingredients for stretched exponential distributions.Comment: 8 pages, 8 figure
Slow stress relaxation in randomly disordered nematic elastomers and gels
Randomly disordered (polydomain) liquid crystalline elastomers align under
stress. We study the dynamics of stress relaxation before, during and after the
Polydomain-Monodomain transition. The results for different materials show the
universal ultra-slow logarithmic behaviour, especially pronounced in the region
of the transition. The data is approximated very well by an equation Sigma(t) ~
Sigma_{eq} + A/(1+ Alpha Log[t]). We propose a theoretical model based on the
concept of cooperative mechanical resistance for the re-orientation of each
domain, attempting to follow the soft-deformation pathway. The exact model
solution can be approximated by compact analytical expressions valid at short
and at long times of relaxation, with two model parameters determined from the
data.Comment: 4 pages (two-column), 5 EPS figures (included via epsfig
First order phase transition in a 1+1-dimensional nonequilibrium wetting process
A model for nonequilibrium wetting in 1+1 dimensions is introduced. It
comprises adsorption and desorption processes with a dynamics which generically
does not obey detailed balance. Depending on the rates of the dynamical
processes the wetting transition is either of first or second order. It is
found that the wet (unbound) and the non-wet (pinned) states coexist and are
both thermodynamically stable in a domain of the dynamical parameters which
define the model. This is in contrast with equilibrium transitions where
coexistence of thermodynamically stable states takes place only on the
transition line.Comment: 4 pages, RevTeX, including 4 eps figure