Plasma scalding is one of the most typical laser damage morphologies induced by a nanosecond laser with a wavelength of 1053 nm in HfO(2)/SiO(2) multilayer films. In this paper, the characteristics of plasma scalds are systematically investigated with multiple methods. The scalding behaves as surface discoloration under a microscope. The shape is nearly circular when the laser incidence angle is close to normal incidence and is elliptical at oblique incidence. The nodular-ejection pit is in the center of the scalding region when the laser irradiates at the incidence angle close to normal incidence and in the right of the scalding region when the laser irradiates from left to right at oblique incidence. The maximum damage size of the scalding increases with laser energy. The edge of the scalding is high compared with the unirradiated film surface, and the region tending to the center is concave. Plasma scald is proved to be surface damage. The maximum depth of a scald increases with its size. Tiny pits of nanometer scale can be seen in the scalding film under a scanning electronic microscope at a higher magnification. The absorptions of the surface plasma scalds tend to be approximately the same as the lower absorptions of test sites without laser irradiation. Scalds do not grow during further illumination pulses until 65 J/cm(2). The formation of surface plasma scalding may be related to the occurrence of the laser-supported detonation wave.
Emergence refers to the existence or formation of collective behaviors in complex systems. Here, we develop a theoretical framework based on the eigen microstate theory to analyze the emerging phenomena and dynamic evolution of complex system. In this framework, the statistical ensemble composed of M microstates of a complex system with N agents is defined by the normalized N × M matrix A , whose columns represent microstates and order of row is consist with the time. The ensemble matrix A can be decomposed as A = ∑ I = 1 r σ I U I ⨂ V I , where r = min ( N , M ) , eigenvalue σ I behaves as the probability amplitude of the eigen microstate U I so that ∑ I = 1 r σ I 2 = 1 and U I evolves following V I . In a disorder complex system, there is no dominant eigenvalue and eigen microstate. When a probability amplitude σ I becomes finite in the thermodynamic limit, there is a condensation of the eigen microstate U I in analogy to the Bose–Einstein condensation of Bose gases. This indicates the emergence of U I and a phase transition in complex system. Our framework has been applied successfully to equilibrium three-dimensional Ising model, climate system and stock markets. We anticipate that our eigen microstate method can be used to study non-equilibrium complex systems with unknown order-parameters, such as phase transitions of collective motion and tipping points in climate systems and ecosystems.
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