293 research outputs found

    Microscopic Deterministic Dynamics and Persistence Exponent

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    Numerically we solve the microscopic deterministic equations of motion with random initial states for the two-dimensional Ï•4\phi^4 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 Ï•4\phi^4 Theory with Hamiltonian Equations of Motion

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    Phase ordering dynamics of the (2+1)- and (3+1)-dimensional ϕ4\phi^4 theory with Hamiltonian equations of motion is investigated numerically. Dynamic scaling is confirmed. The dynamic exponent zz is different from that of the Ising model with dynamics of model A, while the exponent λ\lambda is the same.Comment: to appear in Int. J. Mod. Phys.

    Topological origin of the phase transition in a mean-field model

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    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

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    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

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    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 Ï•4\phi^4 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''

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    Zheng [Phys. Rev. E {\bf 61}, 153 (2000), cond-mat/9909324] claims that phase ordering dynamics in the microcanonical Ï•4\phi^4 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

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    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

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    The Hamiltonian dynamics of the classical Ï•4\phi^4 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

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    Based on the Hamiltonian equation of motion of the Ï•4\phi^4 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

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    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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