Abstract:Nuclei undergo a phase transition in nuclear reactions according to a caloric curve determined by the amount of entropy. Here, the generation of entropy is studied in relation to the size of the nuclear system. * Universidad Autónoma Metropolitana. Unidad Azcapotzalco. Av. San Pablo 124, Col. Reynosa-Tamaulipas, Mexico City.
“…These results may prove useful to some of the large spectrum of physical and interdisciplinary topics where the percolation theory may be applied like forest fires spreading [20,28], immunology [29], liquid migration in porous media [30], econophysics [31], and sociophysics [32].…”
We report site percolation thresholds for square lattice with neighbor bonds at various increasing ranges. Using Monte Carlo techniques we found that nearest neighbors (NN), next-nearest neighbors (NNN), next-next-nearest neighbors (4N), and fifth-nearest neighbors (6N) yield the same pc = 0.592... . The fourth-nearest neighbors (5N) give pc = 0.298... . This equality is proved to be mathematically exact using symmetry argument. We then consider combinations of various kinds of neighborhoods with (NN+NNN), (NN+4N), (NN+NNN+4N), and (NN+5N). The calculated associated thresholds are respectively pc = 0.407..., 0.337..., 0.288..., and 0.234... . The existing Galam-Mauger universal formula for percolation thresholds does not reproduce the data showing dimension and coordination number are not sufficient to build a universal law which extends to complex lattices.
“…These results may prove useful to some of the large spectrum of physical and interdisciplinary topics where the percolation theory may be applied like forest fires spreading [20,28], immunology [29], liquid migration in porous media [30], econophysics [31], and sociophysics [32].…”
We report site percolation thresholds for square lattice with neighbor bonds at various increasing ranges. Using Monte Carlo techniques we found that nearest neighbors (NN), next-nearest neighbors (NNN), next-next-nearest neighbors (4N), and fifth-nearest neighbors (6N) yield the same pc = 0.592... . The fourth-nearest neighbors (5N) give pc = 0.298... . This equality is proved to be mathematically exact using symmetry argument. We then consider combinations of various kinds of neighborhoods with (NN+NNN), (NN+4N), (NN+NNN+4N), and (NN+5N). The calculated associated thresholds are respectively pc = 0.407..., 0.337..., 0.288..., and 0.234... . The existing Galam-Mauger universal formula for percolation thresholds does not reproduce the data showing dimension and coordination number are not sufficient to build a universal law which extends to complex lattices.
“…In that case fusion-multifragmention does not occur and the peaks re- veal the small proportion (0.15%) of events which undergo the fusion-evaporation process. Note that very recently higher order charge correlations were also studied for central Ni+Ni collisions simulated using LATINO semiclassical model [25]. A single source at 4.75 AMeV excitation energy was measured, which deexcites with an abnormal production of four equal sized fragments.…”
Section: Stochastic Mean-field Simulations and Spinodal Instabilitiesmentioning
Abnormal production of events with almost equal-sized fragments was theoretically proposed as a signature of spinodal instabilities responsible for nuclear multifragmentation. Many fragments correlations can be used to enlighten any extra production of events with specific fragment partitions. The high sensitivity of such correlation methods makes it particularly appropriate to look for small numbers of events as those expected to have kept a memory of spinodal decomposition properties and to reveal the dynamics of a first order phase transition for nuclear matter and nuclei. This section summarizes results obtained so far for both experimental and dynamical simulations data.
“…On the other hand, in spite of violating quantum principles, classical dynamics models (such as classical molecular dynamics) are capable of reproducing both the out-ofequilibrium and the equilibrium parts of a collision. Indeed, classical molecular dynamics (CMD) models are able to describe non-equilibrium dynamics, hydrodynamic flow, and changes of phase without adjustable parameters, neck fragmentation [10], phase transitions [11], critical phenomena [12,13], caloric curve [14,15], and isoscaling [16] in nuclear reactions, as well as in the formation of nuclear pasta in infinite systems [17][18][19].…”
This article presents a classical potential used to describe nucleon--nucleon interactions at intermediate energies. The potential depends on the relative momentum of the colliding nucleons and can be used to describe interactions at low momentum transfer mimicking the Pauli exclusion principle. We use the potential with molecular dynamics to study finite nuclei, their binding energy, radii, symmetry energy, and a case study of collisions.
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