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(873 citation statements)

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“…[23][24][25]). In two recent papers [26,27] we have discussed in detail how one can construct Langevin equations for relativistic Brownian motions (see Debbasch et al [28,29] and Zygadlo [30] for similar approaches, and also Dunkel and Ha¨nggi [31]).…”

confidence: 99%

“…[23][24][25]). In two recent papers [26,27] we have discussed in detail how one can construct Langevin equations for relativistic Brownian motions (see Debbasch et al [28,29] and Zygadlo [30] for similar approaches, and also Dunkel and Ha¨nggi [31]).…”

confidence: 99%

“…[26,27] we have analyzed the three most popular discretization rules for Langevin equations with multiplicative noise, namely, Ito's pre-point discretization rule [32,33], the Fisk-Stratonovich mid-point rule [34][35][36][37], and the Ha¨nggi-Klimontovich (HK) post-point rule [38][39][40][41]. As a main result it was found that only the HK interpretation of the Langevin equation yields a FPE, whose stationary solution coincides with the one-dimensional relativistic Ju¨ttner-Maxwell distribution, as known from Ju¨ttner's early work on the relativistic gas [42,43] and also from the relativistic kinetic theory [23,24]. Thus, in absence of other qualifying criteria, one may conclude that the post-point discretization rule is favorable.…”

confidence: 99%

“…In particular, the temperature jumps on two walls increase in accordance with the decrease in the temperature, because the representative relaxation rate [10] decreases in accordance with the decrease in the temperature, when Knudsen number is fixed. As a result, we cannot use the Rayleigh number as a parameter, which characterizes the transition of the thermal conduction to the thermal convection, under the transition regime between the rarefied and continuum regimes.…”

confidence: 98%

“…Provided that thermally relativistic fluids are composed of hard spherical partons with mass 7 m and diameter d, we obtain Ra using definitions of η and λ for hard spherical partons, which were calculated by Cercignani and Kremer on the basis of Israel-Stewart theory [10], as Ra = 256 45…”

confidence: 99%