Power-law expansion of the Universe from the bosonic Lorentzian type IIB matrix model

Recent studies on the Lorentzian version of the type IIB matrix model show that (3+1)D expanding universe emerges dynamically from (9+1)D space-time predicted by superstring theory. Here we study a bosonic matrix model obtained by omitting the fermionic matrices. With the adopted simplification and the usage of a large-scale parallel computer, we are able to perform Monte Carlo calculations with matrix size up to $N=512$, which is twenty times larger than that used previously for the studies of the original model. When the matrix size is larger than some critical value $N_{\rm c}\simeq 110$, we find that (3+1)D expanding universe emerges dynamically with a clear large-$N$ scaling property. Furthermore, at sufficiently late times, we observe a power-law behavior $t^{1/2}$ of the spatial extent with respect to time $t$, which is reminiscent of the expanding behavior of the Friedmann-Robertson-Walker universe in the radiation dominated era. We discuss possible implications of this result on the original model including fermionic matrices.Comment: 22 pages, 21 figures, 4 tables, (v2) typos correcte

Gravitational polarization of test-mass potential in equilibrium polytropic sheets with non-negative polytropic indexes

Gravitational polarization is examined for equilibrium self-gravitating polytropic sheets perturbed by gravitational field due to test mass sheet. We find equilibrium solutions to the corresponding perturbed Lane-Emden equations for non-negative polytropic indexes. It is shown that gravitational polarization may be observed even in a finite extent of self-gravitating systems in addition to previously discussed infinite systems. In the polytropic sheets, the maximum gravitational amplification gets greater with a higher polytropic index while the height at which the maximum amplification occurs gets lower. The ratio of height change to the original height increases with polytropic index. The last result constrains the linear approximation method used for the present perturbation method

アニオンの貯蔵・脱離反応を利用した炭素系正極に関する研究

京都大学新制・課程博士博士(工学)甲第24631号工博第5137号新制||工||1982(附属図書館)京都大学大学院工学研究科物質エネルギー化学専攻(主査)教授 安部 武志, 教授 阿部 竜, 教授 陰山 洋学位規則第4条第1項該当Doctor of Philosophy (Engineering)Kyoto UniversityDGA

Gravitational polarization of test-mass potential in the self-gravitating isothermal gases and a relation with gravitational instability

The present work analyzes perturbed potentials due to test mass that is added at the center of gravity of the non-singular equilibrium isothermal self-gravitating gases. We examine gravitational polarization in the infinite isothermal sheet, cylinder, and sphere, assuming that the systems are highly collisional and reach a new state of thermal equilibrium after perturbation. Under the assumptions, the isothermal sheet and cylinder amplify gravitational fields due to test sheet and line masses by 68 % and 53 % maximally. On the one hand, in the isothermal sphere, gravitational fields due to test point mass are amplified oscillatorily with radius and show a repulsive effect at large radii. Since the infinite isothermal sphere is gravitationally unstable, we confine it in a spherical wall in contact with a thermal bath. We find that only gravitational amplification occurs if the unperturbed finite sphere is gravitationally stable. The oscillatory amplification appears if the sphere is unstable, hence the repulsive effect is unrealistic in the canonical ensemble