318 research outputs found

    Nonequilibrium process of self-gravitating N-body systems and quasi-equilibrium structure using normalized q-expectation values for Tsallis\u27 generalized entropy

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    金沢大学理工研究域機械工学系To clarify the nonequilibrium processes of self-gravitating systems, we examine a system enclosed in a spherical container with reflecting walls, by N-body simulations. To simulate nonequilibrium processes, we consider loss of energy through the reflecting wall, i.e., a particle reflected at a non-adiabatic wall is cooled to mimic energy loss. We also consider quasi-equilibrium structures of stellar polytropes to compare with the nonequilibrium process, where the quasi-equilibrium structure is obtained from an extremum-state of Tsallis\u27 entropy. Consequently, we numerically show that, with increasing cooling rates, the dependence of the temperature on energy, i.e., the - curve, varies from that of microcanonical ensembles (or isothermal spheres) to a common curve. The common curve appearing in the nonequilibrium process agrees well with an - curve for a quasi-equilibrium structure of the stellar polytrope, especially for the polytrope index n ∼ 5. In fact, for n > 5, the stellar polytrope within an adiabatic wall exhibits gravothermal instability [Taruya, Sakagami, Physica A, 322 (2003) 285]. The present study indicates that the stellar polytrope with n ∼ 5 likely plays an important role in quasi-attractors of the nonequilibrium process in self-gravitating systems with non-adiabatic walls. © 2010 IOP Publishing Ltd

    Transition of velocity distributions in collapsing self-gravitating N-body systems

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    By means of N-body simulations, we study the evolution of gravity-dominated systems from an early relaxation to a collapse, focusing on the velocity distributions and thermodynamic properties. To simulate the dynamical evolution, we consider self-gravitating small N-body systems enclosed in a spherical container with adiabatic or semipermeable walls. It is demonstrated that in the early relaxation process, the velocity distribution is non-Gaussian and q-Gaussian, since the system is in quasiequilibrium states (here q is the Tsallis entropic parameter). Thereafter, the velocity distribution undergoes higher non-Gaussian distributions, especially when the core forms rapidly in the collapse process; i.e., q tends to be larger than that for the quasiequilibrium state, since the velocity distribution further deviates from Gaussian. However, after the core forms sufficiently, the velocity distribution gradually relaxes toward a Gaussian-like distribution. Accordingly, the velocity distribution evolves from a non-Gaussian distribution through a higher non-Gaussian distribution to a Gaussian-like distribution; i.e., the velocity distribution does not monotonically relax toward a Gaussian-like distribution in our collapse simulations. We clearly show such a transition of the velocity distribution, based not only on the Tsallis entropic parameter but also on the ratio of velocity moments. We also find that a negative specific heat occurs in a collapse process with mass and energy loss (such as the escape of stars from globular clusters), even if the velocity distribution is Gaussian-like. © 2012 American Physical Society

    Negative specific heat in self-gravitating N -body systems enclosed in a spherical container with reflecting walls

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    金沢大学理工研究域機械工学系金沢大学環日本海域環境研究センターエコテクノロジー研究部門Gravity-dominated systems have a negative specific heat. We investigate the negative specific heat of self-gravitating systems enclosed in a spherical container with reflecting walls by means of N -body simulations. To simulate nonequilibrium processes, a particle reflected at a nonadiabatic wall is cooled to mimic energy loss by reflecting walls, while an adiabatic wall is employed for microcanonical ensembles. We show that a negative specific heat occurs not only in the microcanonical ensemble but also in certain nonequilibrium processes with the nonadiabatic wall. With increasing cooling rates, the dependence of temperature T on energy ε, i.e., the ε- T curve, gradually deviates from the microcanonical ensemble and approaches a certain common curve at a low-energy region. The common curve agrees with an ε- T curve for stellar polytropes, especially for the polytrope index of n∼5. We show that the stellar polytrope should be related to the present nonequilibrium process appearing in the self-gravitating system with the nonadiabatic wall. In the nonequilibrium process, a rapid change in velocity at the nonadiabatic wall significantly affects the velocity and density profiles. In particular, the greater the cooling rate, the greater the local velocity gradient at a low-energy region. © 2009 The American Physical Society

    Thermodynamic properties of an evaporation process in self-gravitating N -body systems

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    金沢大学理工研究域機械工学系By means of N -body simulations, we consider self-gravitating open systems enclosed in a spherical container with semipermeable reflecting walls, in order to investigate the thermodynamics of the evaporation process in self-gravitating N -body systems (such as the escape of stars from globular clusters). To simulate the evaporation process, when the energy of a particle exceeds a certain threshold value, the particle passes through the semipermeable reflecting wall freely. We show that the thermodynamic properties of the evaporation process, such as the dependence of the temperature on energy, agree well with those of stellar polytropes, if the system is in an approximate virial equilibrium state. However, in a lower-energy region or for a rapid evaporation process, the thermodynamic properties deviate from those for the stellar polytrope. Nevertheless, we found that a negative specific heat occurs even in the lower-energy region or for a rapid evaporation process. © 2010 The American Physical Society

    Numerical irreversibility in self-gravitating small N-body systems

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    金沢大学大学院自然科学研究科機能開発システムNumerical irreversibility due to round-off errors appearing in self-gravitating N-body systems is investigated by means of molecular dynamics methods. As a typical self-gravitating system, a closed spherical system consisting of N point-particles, which are interacting through the Plummer softened potential, is considered. In order to examine the numerical irreversibility, time-reversible simulations are executed: that is, a velocity inversion technique for a time-reversal operation is applied at a certain time during the evolution of the system. Through the simulations with various energy states, it is found that, under a restriction of constant initial potential energy, numerical irreversibility prevails more rapidly with decreasing initial kinetic energy. In other words, the lower the initial kinetic energy (or the lower the total energy), the earlier the memory of the initial conditions is lost. Moreover, an influence of integration step sizes (i.e., time increments Δ t) on numerical irreversibility is examined. As a result, even a small time increment could not improve reversibility of the present self-gravitating system, although the small time increment reduces global errors in total energy. © 2007 Elsevier Ltd. All rights reserved
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