软物质和分数阶导数建模

相对于一般的硬物质(如金属、半导体，陶瓷等)，软物质是介于理想固体和流体之间的复杂状态物质(又称复杂流体，软凝聚态物质)，如生命物质、聚合物、液晶、土壤、胶体、薄膜、颗粒物质、多孔岩层、石油等。软物质的物理性质主要由其介观(介于宏观和微观之间)尺度的大分子或基团的结构和性质决定，现有的物理和力学理论还不能很好地解释其运动规律和行为。本研究主要包括3个方面的内容：(1)以研究软物质的宏观力学行为为研究对象的软物质力学(唯象)；(2)描述软物质的介观量子力学理论；(3)软物质介观尺度的时空结构。另一方面，统称分数阶时间导数、LeVy稳态分布、分数布朗运动、Hurst指数、I/f能谱、分形等数学方法为分数阶数学。     

微液滴动力学特性的耗散粒子动力学模拟

对传统的耗散粒子动力学方法进行了改进.改进的耗散粒子动力学方法采用了包含远程吸引力和近距排斥力的保守力势函数,从而使得用耗散粒子动力学方法模拟多相流动成为可能.应用改进的耗散粒子动力学方法,对微尺度下液滴的形成及液滴在微重力下的大幅度振荡变形进行了数值模拟.计算结果表明,改进的耗散粒子动力学(DPD)方法能够有效地描述微尺度下液滴的动力学特性,对研究复杂流体多相流动有着重要的意义. 关键词： 多相流 微液滴 耗散粒子动力学(DPD)方法 保守力势函数     

带自由面流体的多体耗散粒子动力学模拟

利用多体耗散粒子动力学(MDPD)方法对介观尺度下液滴动力学进行了模拟分析,探讨了MDPD系统中液气共存界面的形成,并对表面张力进行了模拟研究,研究结果表明,MDPD方法形成的液气共存界面满足Laplace定律,通过改变不同的粒子间保守力作用参数,获得了液滴在固体壁面上不同的接触角,并研究了保守力作用参数与接触角之间的变化规律,进一步模拟了液滴在复杂微通道内的流动,研究结果有助于解释带自由面流体在粗糙表面上的运动行为。     

β-HMX基PBXs包覆行为的介观模拟

通过耗散粒子动力学方法研究了β-HMX(环四次甲基四硝基胺)基聚合物在室温下的介观结构. 并在此基础上,研究了不同温度时β-HMX与不同聚合物之间的排斥参数及β-HMX基PBXs的介观结构. 结果表明,β-HMX与偏氟乙烯、β-HMX与三氟氯乙烯及偏氟乙烯与三氟氯乙烯结构单元间的相溶性随着温度的升高不断增强. 温度及聚合物的摩尔比在其相互包覆行为中起着重要作用,且存在最佳的温度及摩尔比.     

耗散粒子动力学处理复杂固体壁面的一种有效方法

耗散粒子动力学(dissipative particle dynamics,DPD)作为一种介观尺度拉格朗日型粒子方法,已经成功地应用于微纳米流动和生化科技的研究中.复杂固体壁面的处理和壁面边界条件的实施一直是DPD方法发展及应用的一个障碍.提出了处理复杂固体壁面的一种新的方法.复杂固体区域通过冻结随机分布并且达到平衡状态的DPD粒子代表;所冻结的DPD粒子位于临近流动区域的一个截距内;在靠近固体壁面的流动区域中设置流动反弹层,当流动DPD粒子进入此流动层后反弹回流动区域.应用这种固体壁面处理方法对简单流动区域的Poiseuille流动和复杂多孔介质内的流动进行了分析.研究表明,这种新的固体壁面处理方法能够有效模拟复杂固体区域,准确实施壁面边界条件.     

棒状分子聚合物溶液的微宏观数值模拟

利用微宏观耦合方法模拟了棒状分子聚合物溶液在平板Couette流动中的复杂流变行为,其中微宏观模型通过非均匀Doi理论来描述.数值模拟中,应用有限体积方法耦合求解了介观尺度上的Smoluchowski方程和宏观尺度上的流场守恒方程.数值结果不仅得到了若干种典型的流动类型,而且还预测了另外两种新的复合瑕疵结构.数值试验表明：棒状分子聚合物的流变结构主要依赖于De数、分子相对尺度以及溶液浓度常数的取值;并且De数对分子指向矢的翻滚周期、随流取向角等微观特性也均有明显影响. 关键词： 棒状分子 聚合物溶液 微宏观模拟     

基于活性网络模型的细胞组织模拟（英文）

在过去的十年中,由于细胞生物学的进步,将细胞组织作为活性物质的理论研究已经成为软物质物理学的一个新领域。本文综述了近年来基于细胞组织活性网络（AN）模型的理论进展。在介观尺度上,细胞组织的非平衡动力学主要由细胞的自我推进和其他非推进活动驱动,如主动收缩力或细胞张力/体积振荡。自推进细胞的AN模型可以再现体内细胞组织的复杂动力学,如活性/黏附驱动的固液转变、集群和活性湍流。结合细胞张力波动的AN模型还可以模拟果蝇胚胎细胞中的体积振荡波,并预测张力波动驱动的细胞组织固液转变。利用AN模型研究细胞组织的结构相变和密度涨落,加深了我们对这一独特的非平衡软物质系统的认识。     

适用复杂几何壁面的耗散粒子动力学边界条件

耗散粒子动力学(DPD)是一种针对介观流体的高效的粒子模拟方法,经过二十多年发展已经在诸如聚合物、红细胞、液滴浸润性等方面有了很多研究应用.但是因为其边界处理手段的不完善,耗散粒子动力学模拟仍局限于相对简单的几何边界问题中.本文提出一种能自适应各种复杂几何边界的处理方法,并能同时满足三大边界要求:流体粒子不穿透壁面、边界处速度无滑移、边界处密度和温度波动小.具体地,通过给每个壁面粒子赋予一个新的矢量属性—局部壁面法向量,该属性通过加权计算周围壁面粒子的位置得到;然后通过定义周围固体占比概念,仅提取固体壁面的表层粒子参与模拟计算,减少了模拟中无效的粒子;最后在运行中,实时计算每个流体粒子周围固体粒子占比,判断是否进入固体壁面内,如果进入则修正速度和位置.我们将这种方法应用于Poiseuille流动,验证了该方法符合各项要求,随后还在复杂血管网络和结构化固体壁面上展示了该边界处理方法的应用.这种方法使得DPD模拟不再局限于简单函数描述的壁面曲线,而是可以直接从各种设计图纸和实验扫描影像中提取壁面,极大地拓展了DPD的应用范围.     

带电粒子形成胶体晶体的有效硬球模型判据的计算机模拟验证

在对胶体晶体的研究中,带电粒子胶体晶体的形成机理比硬球胶体晶体更加复杂,对其形成条件目前还缺少有效的判断依据. 有效硬球模型判据提出以有效直径作为判断参数. 为了验证该判据的有效性,利用布朗动力学模拟研究了不同有效直径下带电粒子胶体晶体的特性. 为了更加定量地研究单因素对带电胶体晶体形成的影响,取有效直径为2.8至0.8,并对一定的有效直径,研究了粒子几何直径和排斥力不同情况下的结晶行为. 在布朗动力学模拟过程中,采用径向分布函数和键序参数方法检测体系的结构变化,并分析所形成的晶体结构. 结果表明,在判断带电粒子胶体体系能否形成有序结构方面,有效硬球模型判据有一定的合理性. 但是,并不能将有效直径作为唯一的判别参数,而是需要综合其他参数的影响,这显示出该判据的片面性. 关键词： 布朗动力学模拟 带电胶体晶体 有效硬球模型     

软凝聚态物质物理学

软物质是指其某种物理性质在小的外力作用下能产生很大变化的凝聚态物,典型的例子包括液晶、高分子体系、胶体、微乳液等。软物质的结构和性质主要不是由内能,而是由熵来决定,较通俗地介绍了软物质的概念,仔细分析了熵在软物质中所起的作用,同时详细介绍了聚合物体系、胶体及生物膜等几种典型的软物质,通过硫化橡胶和无管虹吸等十分有趣的例子。说明了聚合物对流变性质的影响;通过分析硬球胶体的相变及相分离等行为说明了熵力的概念;仔细分仔了电稳定胶体的相互作用,并介绍了DLVO理论以及近年来发现的对这一理论的偏离,特别是约束条件下同号带电胶球的长程吸引相互作用及其对此现象的一些解释;对生物膜也作了初步介绍。人们对软物质的研究和理解目前还处于一个非常原始的阶段,深入研究和理解软物质的各种性质必将促进人类对自然和人类自身的认识。     

凝聚态物理学中的基本概念

本文首先根据物质世界的层次化来说明凝聚态物理学在当今物理学中所处的地位,并阐述了复杂与简单的辨证关系,来说明为何这一学科至今仍然富有生命力;进而对这一学科的范围进行了讨论,强调了位形空间和动量空间中都存在多种类型的凝聚现象,而相应的凝聚体构成了这一学科的研究对象;还探讨了处理凝聚态理论问题的量子物理与经典物理方法有效领域的界限与分野;最终对此学科的发展历史进行回顾,并追溯和剖析了其概念全系的演变,     

Construct order parameters from the reduced density matrix spectra

In this paper, we try to establish a connection between a quantum information concept, i.e., the mutual information, and the conventional order parameter in condensed matter physics. We show that non-vanishing mutual information between two subsystems separated by a long distance means the existence of long-range orders in the system. By analyzing the spectra of the reduced density matrices that are used to calculate the mutual information, we show how to derive the local order operators that identify various ordered phases in condensed matter physics.     

凝聚态物理与量子力学

文章扼要地回顾了量子力学在奠定凝聚态物理基础中所起的关键作用;并讨论了当今凝聚态物理发展的主要动向;进而阐明了为何凝聚态物理,不论在基础研究,还是促进技术发展,抑或推动学科交叉方面,尚大有可为。     

Superfluid analogies of cosmological phenomena

In a modern viewpoint relativistic quantum field theory is an emergent phenomenon arising in the low-energy corner of the physical fermionic vacuum – the medium, whose nature remains unknown. The same phenomenon occurs in condensed matter systems: In the extreme limit of low-energy condensed matter systems of special universality class acquire all the symmetries, which we know today in high-energy physics: Lorentz invariance, gauge invariance, general covariance, etc. The chiral fermions as well as gauge bosons and gravity field arise as fermionic and bosonic collective modes of the system. Inhomogeneous states of the condensed matter ground state – vacuum – induce nontrivial effective metrics of the space, where the free quasiparticles move along geodesics. This conceptual similarity between condensed matter and the quantum vacuum allows us to simulate many phenomena in high-energy physics and cosmology, including the axial anomaly, baryoproduction and magnetogenesis, event horizon and Hawking radiation, cosmological constant and rotating vacuum, etc., probing these phenomena in ultra-low-temperature superfluid helium, atomic Bose condensates and superconductors. Some of the experiments have been already conducted.     

Nonexponential decay in relaxation phenomena

A variety of considerations from different points of view including non-Markovian stochastic processes, basic quantum mechanics, and a mechanism based on condensed matter physics, all lead to the fractional exponential decay at long times in relaxation processes. Implications of this decay law and its verifiable predictions in a broad range of phenomena in condensed matter physics are pointed out.     

Graphene-like physics in optical lattices

Graphene has attracted enormous attention over the past years in condensed matter physics. The most interesting feature of graphene is that its low-energy excitations are relativistic Dirac fermions. Such feature is the origin of many topological properties in graphene-like physics. On the other hand, ultracold quantum gas trapped in an optical lattice has become a unique setting for quantum simulation of condensed matter physics. Here, we mainly review our recent work on quantum simulation of graphene-like physics with ultracold atoms trapped in a honeycomb or square optical lattice, including the simulation of Dirac fermions and quantum Hall effect with and without Landau levels. We also present the related experimental advances.     

Deconstructing the glass transition through critical experiments on colloids

The glass transition is the most enduring grand-challenge problem in contemporary condensed matter physics. Here, we review the contribution of colloid experiments to our understanding of this problem. First, we briefly outline the success of colloidal systems in yielding microscopic insights into a wide range of condensed matter phenomena. In the context of the glass transition, we demonstrate their utility in revealing the nature of spatial and temporal dynamical heterogeneity. We then discuss the evidence from colloid experiments in favor of various theories of glass formation that has accumulated over the last two decades. In the next section, we expound on the recent paradigm shift in colloid experiments from an exploratory approach to a critical one aimed at distinguishing between predictions of competing frameworks. We demonstrate how this critical approach is aided by the discovery of novel dynamical crossovers within the range accessible to colloid experiments. We also highlight the impact of alternate routes to glass formation such as random pinning, trajectory space phase transitions and replica coupling on current and future research on the glass transition. We conclude our review by listing some key open challenges in glass physics such as the comparison of growing static length scales and the preparation of ultrastable glasses that can be addressed using colloid experiments.     

Geometry of the Parameter Space of a Quantum System: Classical Point of View

The local geometry of the parameter space of a quantum system is described by the quantum metric tensor and the Berry curvature, which are two fundamental objects that play a crucial role in understanding geometrical aspects of condensed matter physics. Classical integrable systems are considered and a new approach is reported to obtain the classical analogs of the quantum metric tensor and the Berry curvature. An advantage of this approach is that it can be applied to a wide variety of classical systems corresponding to quantum systems with bosonic and fermionic degrees of freedom. The approach used arises from the semiclassical approximation of the Berry curvature and the quantum metric tensor in the Lagrangian formalism. This semiclassical approximation is exploited to establish, for the first time, the relation between the quantum metric tensor and its classical counterpart. The approach described is illustrated and validated by applying it to five systems: the generalized harmonic oscillator, the symmetric and linearly coupled harmonic oscillators, the singular Euclidean oscillator, and a spin-half particle in a magnetic field. Finally, some potential applications of this approach and possible generalizations that can be of interest in the field of condensed matter physics are mentioned.     

凝聚态物理学的新进展Ⅲ

本文综述凝聚态物理学近几年来的重要进展,列举了一些事例予以阐述。在第Ⅲ部分中涉及的主题为细小体系及凝聚态中的非线性现象。讨论的问题包括:介观系统中的量子相干性和电子输运,团簇的幻数和壳层结构,离子阱中库仑团簇的类相变行为,魔梯,自组织临界性和非平衡态流体中空时图样的形成与演化。