296 research outputs found
Microscopic Deterministic Dynamics and Persistence Exponent
Numerically we solve the microscopic deterministic equations of motion with
random initial states for the two-dimensional theory. Scaling behavior
of the persistence probability at criticality is systematically investigated
and the persistence exponent is estimated.Comment: to appear in Mod. Phys. Lett.
Phase Ordering Dynamics of Theory with Hamiltonian Equations of Motion
Phase ordering dynamics of the (2+1)- and (3+1)-dimensional theory
with Hamiltonian equations of motion is investigated numerically. Dynamic
scaling is confirmed. The dynamic exponent is different from that of the
Ising model with dynamics of model A, while the exponent is the same.Comment: to appear in Int. J. Mod. Phys.
Topological origin of the phase transition in a mean-field model
We argue that the phase transition in the mean-field XY model is related to a
particular change in the topology of its configuration space. The nature of
this topological transition can be discussed on the basis of elementary Morse
theory using the potential energy per particle V as a Morse function. The value
of V where such a topological transition occurs equals the thermodynamic value
of V at the phase transition and the number of (Morse) critical points grows
very fast with the number of particles N. Furthermore, as in statistical
mechanics, also in topology the way the thermodynamic limit is taken is
crucial.Comment: REVTeX, 5 pages, with 1 eps figure included. Some changes in the
text. To appear in Physical Review Letter
Topological aspects of geometrical signatures of phase transitions
Certain geometric properties of submanifolds of configuration space are
numerically investigated for classical lattice phi^4 models in one and two
dimensions. Peculiar behaviors of the computed geometric quantities are found
only in the two-dimensional case, when a phase transition is present. The
observed phenomenology strongly supports, though in an indirect way, a recently
proposed topological conjecture about a topology change of the configuration
space submanifolds as counterpart of a phase transition.Comment: REVTEX file, 4 pages, 5 figure
Topology and phase transitions: a paradigmatic evidence
We report upon the numerical computation of the Euler characteristic \chi (a
topologic invariant) of the equipotential hypersurfaces \Sigma_v of the
configuration space of the two-dimensional lattice model. The pattern
\chi(\Sigma_v) vs. v (potential energy) reveals that a major topology change in
the family {\Sigma_v}_{v\in R} is at the origin of the phase transition in the
model considered. The direct evidence given here - of the relevance of topology
for phase transitions - is obtained through a general method that can be
applied to any other model.Comment: 4 pages, 4 figure
Comment on ``Deterministic equations of motion and phase ordering dynamics''
Zheng [Phys. Rev. E {\bf 61}, 153 (2000), cond-mat/9909324] claims that phase
ordering dynamics in the microcanonical model displays unusual scaling
laws. We show here, performing more careful numerical investigations, that
Zheng only observed transient dynamics mostly due to the corrections to scaling
introduced by lattice effects, and that Ising-like (model A) phase ordering
actually takes place at late times. Moreover, we argue that energy conservation
manifests itself in different corrections to scaling.Comment: 5 pages, 4 figure
Land use influence on ambient PM2.5 and ammonia concentrations: Correlation analyses in the Lombardy region, Italy
Air pollution is identified as the primary environmental risk to health worldwide. Although most of the anthropic emissions are due to combustion processes, intensive farming activities may also contribute significantly, especially as a source of particulate matter 2.5 and ammonia. Investigations on particulate matter and precursors dynamics, identifying the most relevant environmental factors influencing their emissions, are critical to improving local and regional air quality policies. This work presents an analysis of the correlation between particulate matter 2.5 and ammonia concentrations, obtained from the Copernicus Atmosphere Monitoring Service, and local land use characteristics, to investigate the influence of agricultural activities on the space-time pollutant concentration patterns. The selected study area is the Lombardy region, northern Italy. Correlation is evaluated through Spearman’s coefficient. Agricultural areas resulted in a significant factor for high ammonia concentrations, while particulate matter 2.5 was strongly correlated with built-up areas. Natural areas resulted instead a protective factor for both pollutants. Results provide data-driven evidence of the land use effect on air quality, also quantifying such effects in terms of correlation coefficients magnitude
Hamiltonian dynamics of the two-dimensional lattice phi^4 model
The Hamiltonian dynamics of the classical model on a two-dimensional
square lattice is investigated by means of numerical simulations. The
macroscopic observables are computed as time averages. The results clearly
reveal the presence of the continuous phase transition at a finite energy
density and are consistent both qualitatively and quantitatively with the
predictions of equilibrium statistical mechanics. The Hamiltonian microscopic
dynamics also exhibits critical slowing down close to the transition. Moreover,
the relationship between chaos and the phase transition is considered, and
interpreted in the light of a geometrization of dynamics.Comment: REVTeX, 24 pages with 20 PostScript figure
Hamiltonian equation of motion and depinning phase transition in two-dimensional magnets
Based on the Hamiltonian equation of motion of the theory with
quenched disorder, we investigate the depinning phase transition of the
domain-wall motion in two-dimensional magnets. With the short-time dynamic
approach, we numerically determine the transition field, and the static and
dynamic critical exponents. The results show that the fundamental Hamiltonian
equation of motion belongs to a universality class very different from those
effective equations of motion.Comment: 6 pages, 7 figures, have been accept by EP
Phase transitions as topology changes in configuration space: an exact result
The phase transition in the mean-field XY model is shown analytically to be
related to a topological change in its configuration space. Such a topology
change is completely described by means of Morse theory allowing a computation
of the Euler characteristic--of suitable submanifolds of configuration
space--which shows a sharp discontinuity at the phase transition point, also at
finite N. The present analytic result provides, with previous work, a new key
to a possible connection of topological changes in configuration space as the
origin of phase transitions in a variety of systems.Comment: REVTeX file, 5 pages, 1 PostScript figur
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