「博士論文」 アブストラクト
氏名： 礒部 雅晴（いそべ まさはる）
所属： 名古屋工業大学工学部
審査年： 2000年度（九州大学）
タイトル：
Phase Changes in an Inelastic Hard Disk System with a Heat Bath under Weak Gravity for Granular Fluidization
アブストラクト：
In this thesis, the numerical study on the dynamics of granular fluidization in a simple model is presented.
The model consists of two-dimensional hard
disks, which undergo inelastic collisions; the system is under the uniform
external gravity and is driven by the heat bath. The competition between the
two effects, namely, the gravitational force and the heat bath, is carefully
studied.
In the simulation, the event driven method is employed. By improving the
various techniques, we succeed in developing the fast algorithm; its complexity
is O(log N) with N being the number of particles. This is the same with the
existing algorithm but its coefficient is somewhat smaller than the previously
published one. This algorithm allows us to perform the simulation over a wide
range of parameter region.
From the numerical simulations, we found the system shows three phases upon
increasing the external driving, which is described by the ratio of the heat
bath to the gravitational force. These phases are named the condensed phase,
the locally fluidized phase, and the granular turbulent phase. In the condensed
phase, most of the particles are aggregated around the bottom of the system
with an almost closed packed density, and the state of a dense packing layer is
relatively stable, which means the potential energy is dominant and the system
is in weakly excited states. In the locally fluidized phase, the dense packing
layer is locally broken by excitation of the heat bath. The high-speed
particles are blown upward from the holes in the layer. The location of holes
is fairly stable. In the granular turbulent phase, the positions of the hole
become unstable in time. The average density is quite low, but it is different
from the ordinary molecular gas phase. The density fluctuation is large and
this fluctuation causes turbulent motion due to the gravity. The holes become
dynamically unstable, and the condensed layer, appears only temporally.
Over the whole region, the flatness f(y)=<vx4>/<vx2>2 at the height of the
maximum packing fraction layer is different from 3, which means the velocity
distribution deviates from the Gaussian. It is remarkable that f becomes very
large, as large as 20, in the locally fluidized phase. The transition from the
condensed phase to the locally fluidized phase is distinguished by the
existence of fluidized holes. On the other hand the transition from the locally
fluidized phase to the granular turbulent phase is understood by the
destabilization transition of the fluidized holes due to the mutual
interference.
リンク： 論文ダウンロード（gzip圧縮,2.7Mbytes）
氏名： 藤田 伸尚（ふじた のぶひさ）
審査年： 1999年度（平成11年度） 東北大学
タイトル：
Theoretical study on electronic localization properties of a one-dimensional
quasiperiodic system
アブストラクト：
Quasiperiodic structures have attracted much attention through various areas of
science and engineering since Schechtman and coworkers found by chance an
unexpected five-fold electron diffraction pattern from a rapidly quenched Al-Mn
alloy sample; the sharp diffraction spots with icosahedral symmetry have
suggested that the structure is non-periodic but is long-range ordered. Today,
it is well accepted that there is a category of materials with quasiperiodic
long-range order, called quasicrystals (QCs).
A notable fact is that several kinds of QCs are thermodynamically stable;
that is, their structural quality improves through annealing. Many authors have
reported measurements of various physical quantities, and revealed unique
physical properties of stable QCs. In order to understand these properties, it
is important to investigate theoretically the relation between the
quasiperiodicity of the structure and resultant physical properties.
The main motivation of the present thesis is to understand the connection
between the quasiperiodicity of structure and electronic properties. Since
early eighties, a few one-dimensional quasiperiodic models have attracted much
effort and have exhibited many remarkable properties. One of the most
interesting models is the Fibonacci chain (FC), whose one-electron energy
spectrum turned out to be purely singular continuous and the eigenfunctions to
be critical. The energy spectrum is also known to possess locally a fractional
dimension (0 < α <1) and to be globally a multifractal.
There exist, however, a number of quasiperiodic models whose structural
characters are essentially different from that of the FC. Among them, there are
several one-dimensional models which have not yet been studied thoroughly, but
are important to understand properties beyond the ``peculiarity of the FC''.
In this thesis, we discuss electronic properties of a simple quasiperiodic
chain which is generated by a circle map. The chain is expected to be beyond
the universality class of the FC, because its structural properties are
essentially different from that of the FC.
To be specific, we thoroughly analyse the scaling properties of the energy
spectrum and the eigenfunctions of the chain. We show numerically that there
is a subset of the energy spectrum, including that of the ground state level,
which exhibits a new type of local scaling; the relevant local dimension α is 0.
The eigenfunctions for these levels consist of strongly isolated peaks showing
no self-similarity, and their character is quite close to that of localized
ones. Nevertheless, these states are still critical because they are not
normalizable in the infinite system. This type of eigenstates is called
marginal critical states in this thesis. We analyse such unusual scaling
behavior with the real-space renormalization-group approach and derive an
explicit form of the asymptotic scaling law: w \sim exp[-(L/ξ)ν], where w is
the relevant band width and L the system size. ξ denotes some
characteristic length depending on the level and the system parameters. The
exponent ν \approx 0.6105 is determined by the asymptotic structure of the
renormalization-group equation and is related to the self-similarity of the
model.
On the other hand, other levels still show the power-law scaling and each of
them corresponds to a critical eigenfunction in the usual meaning.
In particular, one of these levels is related to a four-cycle fixed point of
the trace map, exhibiting a self-similar eigenfunction. We derive an exact
expression for the scaling exponent related to the fixed point.
We discuss further the generalization of our model as well as the implication
of the existence of marginal critical states in a certain type of QCs.
公表論文リスト：
-
Electronic Properties of a Generalized Fibonacci Model,
N. FUJITA and K. NIIZEKI, Proceedings of the 6th International
Conference on Quasicrystals (World Scientific, 26-30 May 1997), p. 172.
-
Localization properties of electronic wave functions of the Hubbard model on
the Fibonacci lattice, Nobuhisa Fujita and Komajiro Niizeki,
to appear in Materials Science and Engineering: A, 294-296, 560 (2000).
-
New classes of quasicrystals and marginal critical states,
Nobuhisa Fujita and Komajiro Niizeki,
Report No. cond-mat/0004233, Phys. Rev. Lett. 85, 4924 (2000).
-
Classification of one-dimensional quasilattices into mutual local-derivability
classes, Komajiro Niizeki and Nobuhisa Fujita,
Report No. cond-mat/0009422, submitted to Phys. Rev. B.
氏名： 市來 健吾（いちき けんご）
審査年： 1996年度（平成 8 年度） 東北大学
タイトル：
「粉体流動層の粒子ダイナミックス」
アブストラクト：
本研究では粉体流動層の数値解析を行う。本研究の特徴は、これまでに開発されて来
た手法のほとんどが現象論的に流体と粒子の相互作用を導入したのに対し、この流体
力学的相互作用を正確に扱いモデルの構成を行った点である。このようなモデルを構
成する為に、粒子集団を連続体近似で扱うのではなく、個々の粒子の運動を直接扱う。
また現実の流動層から最小限の基本的なメカニズムのみを取り出して「理想流動層」
を定義し、この系をモデル化する。これは、現実の粉体流動層は一般に粒子の大きさ
や系に流し込む流体の流速の範囲が広く、これら全てを包括的に記述する第一原理的
なモデルの構成は不可能である為である。
粒子と流体の相互作用は本来流体の粘性による摩擦の効果である為、理想流動層では
粘性が支配的な低レイノルズ数の極限で流体を記述する。粒子間の直接相互作用は剛
体的で、衝突は弾性とした。また粒子は全て同じ大きさの球とし、粒径や質量、形状
の分布は無視した。低レイノルズ数を仮定している為、流入流速が大きな場合の挙動、
例えば希薄流動状態や輸送状態などを記述するのは不可能である。従って現実の流動
層の示す現象の中でも静止状態から流動状態への流動化現象と、気泡流動状態を含む
比較的穏やかな流動状態が直接の考察対象となる。
モデル化で最も重要な低レイノルズ数での粒子間相互作用は、支配方程式の線形成の
為に、粒子速度と流体に及ぼす力とを関係づける行列によって表される。この行列は
粒子濃度が希薄な場合や２粒子のみの場合は求められている。今考察しようとする粒
子濃度が高く多くの粒子が存在する場合は、希薄な場合と２粒子の場合の解をセルフ
コンシステントに結合する方法が良い結果を示す事が、コロイド粒子系の数値シミュ
レーションに於いて示された。本研究ではこの近似の正当性を確認する意味から、沈
澱現象での平均沈降速度の解析にこの近似を用い、既存の解析が改善される事を示す。
粉体はコロイド粒子と異なり粒子の慣性が重要となる。しかし低レイノルズ数での粒
子間相互作用を用いると、この相互作用の近接効果の持つ特異性(抵抗の発散)の為に、
モデルに有効に慣性を導入できないことが分かる。本研究ではこの特異性を繰り込ん
だ慣性を用いる事でモデルを構成した。この繰り込みが現実の系の振舞を良く再現す
る事は、現実の系では流体の連続性の限界や粒子表面での凹凸などにより流体力学的
相互作用の特異性が隠されることを意味する。
このモデルを特徴付けるパラメータは、流入速度と無次元化された粒子質量であるス
トークス数である。このパラメータ空間で系統的に数値シミュレーションを行う。こ
の結果、流入速度に流動化相転移が生じる臨界流速が存在する事が分かる。流動層の
膨張率と流入速度の関係も実験結果を定性的に再現する。また流動状態はチャンネル
状態と気泡状態の２種類があり、ストークス数がこれらの状態を特徴付けることが分
かる。
粒子の運動エネルギーの振舞から、流入速度が「温度」の役割を持つ事が示唆される。
この「温度」を用いて揺動散逸定理(アインシュタインの関係)を理想流動層に適用し、
自己拡散係数から有効粘性率を定義する。この有効粘性の流入速度依存性が、現実の
実験結果と無矛盾である事が示される。また有効粘性率はストークス数依存性を含め
て速度分布の非ガウス性の強さと極めて良く一致している事が分かる。
これらの結果は液体論で用いられる空孔模型で説明する事が出来る。つまり理想流動
層の定常状態と液体の間に強い類似性が示される。
氏名：小林 一昭
所属： 物質・材料研究機構
審査年： 1990年度（東大）
タイトル：
The electronic properties and optimized structures of the alkali adsorbed
Si(001) surface by using the first principles molecular dynamics
アブストラクト：
The purpose of this thesis is a clarification of the calculational process for
optimizeation of structure and analizing the Si(001) clean and alkali adsorbed
surfaces. This process is performed by using the new method `Car-Parrinellow
method'. This work will be continued up to design and reserch the unknow
practical materials in near future.
リンク： 論文
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