Strain Hardening and Recovery in High-Temperature Deformation by Pure-Metal Mode

By a new method using the stress relaxation test, the coefficient of strain hardening without recovery (h) and the rate of recovery without strain hardening (r) are estimated in high-temperature deformation of fcc aluminum and b c c iron, where the internal stress is confirmed to be nearly 100% of the flow stress. Both h and r are dependent on applied stress σ and temperature T in a steady-state deformation, and are represented by h=h_0(σ/E)^m exp(-Q_h/RT) and r=r_0 (σ/E)^l exp (-Q_r/RT), where h_0 and r_0 are constants, E is Young\u27s modulus and m=-0.88(-1.5), l=4.3(3.2), Q_h=-22(-76) kJ/mol, Q_r=88(132) kJ/mol for aluminum(iron). During a transient state of tensile deformation in the constant strain-rate test, h and r are nearly independent of strain. The activation energy for recovery (Q_r) is found to be appreciably smaller than that of self-diffusion, and then possible roles of pipe-diffusion and strain-enhanced diffusion in dynamic recovery are discussed

Nonextensive thermodynamics of the two-site Hubbard model

Thermodynamical properties of canonical and grand-canonical ensembles of the half-filled two-site Hubbard model have been discussed within the framework of the nonextensive statistics (NES). For relating the physical temperature $T$ to the Lagrange multiplier $\beta$, two methods have been adopted: $T=1/k_B \beta$ in the method A [Tsallis {\it et al.} Physica A {\bf 261} (1998) 534], and $T=c_q/k_B \beta$ in the method B [Abe {\it et al.} Phys. Lett. A {\bf 281} (2001) 126], where $k_B$ denotes the Boltzman constant, $c_q= \sum_i p_i^q$, $p_i$ the probability distribution of the $i$th state, and $q$ the entropic index. Temperature dependences of specific heat and magnetic susceptibility have been calculated for 1 \lleq q \lleq 2, the conventional Boltzman-Gibbs statistics being recovered in the limit of $q = 1$. The Curie constant $\Gamma_q$ of the susceptibility in the atomic and low-temperature limits ($t/U \to 0, T/U \to 0$) is shown to be given by $\Gamma_q=2 q 2^{2(q-1)}$ in the method A, and $\Gamma_q=2 q$ in the method B, where $t$ stands for electron hoppings and $U$ intra-atomic interaction in the Hubbard model. These expressions for $\Gamma_q$ are shown to agree with the results of a free spin model which has been studied also by the NES with the methods A and B. A comparison has been made between the results for canonical and grand-canonical ensembles of the model.Comment: 22 pages, 7 figures, accepted in Physica A with minor change

Contributing Processes to Arctic Temperature Amplification for a Range of Forcing in MIROC GCM

第3回極域科学シンポジウム/第35回極域気水圏シンポジウム 11月30日（金） 国立国語研究所 ２階多目的

Thermal entanglement of Hubbard dimers in the nonextensive statistics

The thermal entanglement of the Hubbard dimer (two-site Hubbard model) has been studied with the nonextensive statistics. We have calculated the auto-correlation ($O_q$), pair correlation ($L_q$), concurrence ($\Gamma_q$) and conditional entropy ($R_q$) as functions of entropic index $q$ and the temperature $T$. The thermal entanglement is shown to considerably depend on the entropic index. For $q < 1.0$, the threshold temperature where $\Gamma_q$ vanishes or $R_q$ changes its sign is more increased and the entanglement may survive at higher temperatures than for $q=1.0$. Relations among $L_q$, $\Gamma_q$ and $R_q$ are investigated. The physical meaning of the entropic index $q$ is discussed with the microcanonical and superstatistical approaches. The nonextensive statistics is applied also to Heisenberg dimers.Comment: 28 pages, 6 figures; the final version accepted in Physica