相变

In the half-filled case, a dimerized lattice will be formed and its ground state is at an insulating phase.

在一维电-声子体系中，电声相互作用使得金属相总是不稳定的，这就是Peierls相变。

Based on the electron-lattice interaction,Frohlich Hamiltonian and quantization theory are used to deduce the dimerized energy gap and phase transition temperature of carbon nanotube.

依据碳纳米管中电子-声子相互作用的原理，采用哈密顿量、量子化理论推导了二聚化对应能隙和相变温度，在紧束缚近似、量子理论和能带理论的基础上，利用周期性边界条件对碳纳米管Π电子进行了分析，讨论了碳纳米管的导电性，预测了室温下碳纳米管碳管中载流子输运方向

The spin-1/2 dimerized antiferromagnetic system is related to spin-Peierls tran-sition.There are still some discrepancy on the behavior of the ground energy densityand energy gap,such as pure power-law,logarithmic correction to the pure power-law in the uniform,integer powers in the dimerized limit,etc.

自旋S-1/2的二聚化反铁磁链与spin-Peierls相变有关，在对其基态能和激发能隙的临界行为描述上仍存在一些不完全一致的观点：如均匀极限的纯幂级数律，纯幂级数律的对数修正；二聚化极限的整数幂级数行为等。

By employing the Jordan-Wigner transformation and a modified mean field method, we are able to determine its ground-state quantum phase diagram approximately. The chapter IV is the main part of this Thesis. It contains the main innovations in our work. We propose and study in detail a S=1 Ising chain with the interplay of single-ion anisotropy and dimerization. The main results and innovations are the following: We show that the total number of the zero-component of spins at each site is a conserved quantity. This quantity, which may intuitively called as hole's quantum number, is hidden in the system. We show further that the hole's number in the ground-state is zero; By using the Jordan-Wigner transformation, we map this model onto a series of subsystems described by the spin 1/2 dimerized transverse Ising model. We solve the subsystems exactly, by presenting the exact wave functions and spectra;We show that this system exhibits a series of quantum phase transitions by varying the dimerization strength. We determine the quantum critical points exactly. We also show that the criticality is the same as that of the uniform S = 1/2 transverse Ising chain.

第四章是本文的重点及主要创新内容，我们具体研究了自旋为1的在横向单离子晶格场中的一维二聚化Ising链，我们得到的主要结果和创新之处是：(1)证明了这一模型具有一种隐藏的对称性，即自旋第三分量为零的格点数目是一个守恒量，并证明基态出现在空穴数目为零的子空间中；(2)利用Jordan-Wigner 变换将此模型变换到一系列自旋为1/2的横磁场中的二聚化Ising 模型，并给出了相应严格的波函数及能谱；(3)我们发现系统的基态随着二聚化强度的变化将呈现出一系列量子相变，我们得到了量子临界点的精确位置，并证明其临界性质与自旋为1/2的横磁场中的均匀Ising 链中的临界行为属于同一普适类。

The transition point of the bilayer antiferromagnet is also determined by bond-operatormean-field theory and the result is consistent with the strong coupling expansion.

此外，本文还采用键算符平均场理论计算了反铁磁双层Heisenberg模型中相变的临界点，计算结果与微扰论一致。

For the second part, the damping behavior of Mg matrix composite was studied. It is found that the graphite fiber achieves better damping capacity than other reinforcements. The phase transformation happened in the Mg matrix can improve damping capacity and with the increase of reinforcement damping capacity can also be improved at high temperature.

其次，对镁基复合材料的阻尼行为的研究，发现石墨纤维比其它增强物具有更好的阻尼效果，基体镁合金的相变过程能提高复合材料的阻尼性能，增加增强物含量能增加复合材料的阻尼且高温下的效果更好。

In particular, a great deal of attention has be.en paid to critical behaviors of fractals.

尤其是分形系统丰富的相变与临界现象引起人们极大的研究兴趣。

These influences can be divided into two states: friction and block interference. Based on the data of interference of bicycles on vehicles' driving in typical road section in Beijing, this paper quantitatively analyzes the velocity changing tendency of vehicles under different interference, velocity distribution frequency, and critical transformation of different interference state. The friction and block interference coefficients are also worked out, which are useful to compare interference degrees under different road conditions.

文章将自行车对机动车的影响划分摩擦干扰和阻滞干扰两种状态，通过采集北京市三个典型路段的混合交通干扰数据，定量分析了不同自行车干扰状态下机动车速度的变化趋势，以及速度分布频率，定义并计算了干扰状态相变的临界点：干扰变化阀值，进一步计算了可对不同道路条件下干扰程度进行比较的摩擦干扰系数和阻滞干扰系数。

All these provide very important vaules and fundaments to futher study and understand glass transition and nonequilibrium phase transformations.

这些都为进一步研究和理解玻璃转变及非平衡相变过程而提供了有价值的参考和基础。

Since Garvie, an Australia scientist, firstly used zirconia as transformation toughening materials from 1975, its exploitation, investigation and application bring the greatly attention of all the countries in the word. It not only further promotes the study upsurge in scientific research field, but also accelerates the application in industrial and technical field.

自从1975年澳大利亚科学家Garvie首先发明利用氧化锆相变增韧陶瓷材料以来，它的开发、研究与应用，更是引起世界各国的高度重视，这不仅进一步促进了其在科研领域的研究热潮，而且更是促进了其在各工业及技术领域的广泛应用。

The labia have now been sutured together almost completely.The drains and the Foley catheter come out at the top.

此刻阴唇已经几乎完全的缝在一起了，排除多余淤血体液的管子和Foley导管从顶端冒出来。

To get the business done, I suggest we split the difference in price.

为了做成这笔生意，我建议我们在价格上大家各让一半。