Thermalization of electron–positron plasma with quantum degeneracy

The non-equilibrium electron–positron–photon plasma thermalization process is studied using relativistic Boltzmann solver, taking into account quantum corrections both in non-relativistic and relativistic cases. Collision integrals are computed from exact QED matrix elements for all binary and triple interactions in the plasma. It is shown that in non-relativistic case (temperatures $k_{B}T\le 0.3m_e{c}^2$) binary interaction rates dominate over triple ones, resulting in establishment of the kinetic equilibrium prior to final relaxation towards the thermal equilibrium, in agreement with the previous studies. On the contrary, in relativistic case (final temperatures $k_{B}T\ge 0.3m_e{c}^2$) triple interaction rates are fast enough to prevent the establishment of kinetic equilibrium. It is shown that thermalization process strongly depends on quantum degeneracy in initial state, but does not depend on plasma composition.     

Transient transition behaviors of fractional-order simplest chaotic circuit with bi-stable locally-active memristor and its ARM-based implementation

This paper proposes a fractional-order simplest chaotic system using a bi-stable locally-active memristor. The characteristics of the memristor and transient transition behaviors of the proposed system are analyzed, and this circuit is implemented digitally using ARM-based MCU. Firstly, the mathematical model of the memristor is designed, which is nonvolatile, locally-active and bi-stable. Secondly, the asymptotical stability of the fractional-order memristive chaotic system is investigated and some sufficient conditions of the stability are obtained. Thirdly, complex dynamics of the novel system are analyzed using phase diagram, Lyapunov exponential spectrum, bifurcation diagram, basin of attractor, and coexisting bifurcation, coexisting attractors are observed. All of these results indicate that this simple system contains the abundant dynamic characteristics. Moreover, transient transition behaviors of the system are analyzed, and it is found that the behaviors of transient chaotic and transient period transition alternately occur. Finally, the hardware implementation of the fractional-order bi-stable locally-active memristive chaotic system using ARM-based STM32F750 is carried out to verify the numerical simulation results.     

On the (N+1)-dimensional local fractional reduced differential transform method and its applications

In this paper, we generalize the (N+1)-dimensional local fractional reduced differential transform method (LFRDTM) within the local fractional derivative sense. First, we show some new properties, lemmas, theorems and corollariesfor the (N+1)-dimensional LFRDTM. Second, these new properties, lemmas and theorems can be proved immediately after. Thirdly, we used two examples to state that this approach is efficient and simple to find numerical solutions to higher dimensional local fractional partial differential equations. Finally, we can be seen that this work can be looked as an extension of the prior work.     

非齐度量测度空间上Morrey-Herz空间上的广义分数次积分算子及其交换子

设(χ,d,μ)是一个同时满足上双倍条件和几何双倍条件的非齐度量测度空间,对于引进的一类非齐度量测度空间上的Morrey-Herz空间,利用非齐度量测度空间的特征,证明了广义分数次积分算子及其交换子在非齐度量测度空间上MorreyHerz空间的有界性.     

Solutions with concentration for conservation laws with discontinuous flux and its applications to numerical schemes for hyperbolic systems

Measure-valued weak solutions for conservation laws with discontinuous flux are proposed and explicit formulae have been derived. We propose convergent discontinuous flux-based numerical schemes for the class of hyperbolic systems that admit nonclassical -shocks, by extending the theory of discontinuous flux for nonlinear conservation laws to scalar transport equation with a discontinuous coefficient. The article also discusses the concentration phenomenon of solutions along the line of discontinuity, for scalar transport equations with a discontinuous coefficient. The existence of the solutions for transport equation is shown using the vanishing viscosity approach and the asymptotic behavior of the solutions is also established. The performance of the numerical schemes for both scalar conservation laws and systems to capture the -shocks effectively is displayed through various numerical experiments.