Modeling complex systems macroscopically: Case/agent-based modeling,synergetics, and the continuity equation

Recently, the continuity equation (also known as the advection equation) has been used to study stability properties of dynamical systems, where a linear transfer operator approach was used to examine the stability of a nonlinear equation both in continuous and discrete time (Vaidya and Mehta, IEEE Trans Autom Control 2008, 53, 307–323; Rajaram et al., J Math Anal Appl 2010, 368, 144–156). Our study, which conducts a series of simulations on residential patterns, demonstrates that this usage of the continuity equation can advance Haken's synergetic approach to modeling certain types of complex, self-organizing social systems macroscopically. The key to this advancement comes from employing a case-based approach that (1) treats complex systems as a set of cases and (2) treats cases as dynamical vsystems which, at the microscopic level, can be conceptualized as k dimensional row vectors; and, at the macroscopic level, as vectors with magnitude and direction, which can be modeled as population densities. Our case-based employment of the continuity equation has four benefits for agent-based and case-based modeling and, more broadly, the social scientific study of complex systems where transport or spatial mobility issues are of interest: it (1) links microscopic (agent-based) and macroscopic (structural) modeling; (2) transforms the dynamics of highly nonlinear vector fields into the linear motion of densities; (3) allows predictions to be made about future states of a complex system; and (4) mathematically formalizes the structural dynamics of these types of complex social systems.     

Percolation in two-scale porous media

Two-scale porous media are generated by filtering a Gaussian random correlated field with a random correlated threshold field. The percolation threshold and the critical exponent ν are derived with the help of a finite-size scaling method. The percolation threshold for the three-dimensional media is a decreasing function of the variance and correlation length of the threshold field. A simplified model predicts these trends in 3d; moreover, it suggested some effects in 2d which were all numerically verified. Received 17 August 2000     

Effects of Arbitrarily Directed Field on Spin Phase Oscillations in Biaxial Molecular Magnets

Quantum phase interference and spin-parity effects are studied in biaxial molecular magnets in a magnetic field at an arbitrarily directed angle.The calculations of the ground-state tunnel splitting are performed on the basis of the instanton technique in the spin-coherent-state path-integral representation,and complemented by exactly numerical diagonalization.Both the Wentzel-Kramers-Brillouin exponent and the pre-exponential factor are obtained for the entire region of the direction of the field.Our results show that the tunnel splitting oscillates with the field for the small field angle,while for the large field angle the oscillation is completely suppressed.This distinct angular dependence,together with the dependence of the tunnel splitting on the field strength,provides an independent test for spin-parity effects in biaxial molexular magnets.The analytical results for the molecular Fes magnet are found to be in good agreement with the numerical simulations,which suggests that even the molecular magnet with total spin S=10 is large enough to be treated as a giant spin system.     

Structure of gels and aggregates of disk-like colloids

The static structure factor (S(q)) of dispersions and gels of disk-like mineral colloids (Laponite) was investigated using time- and ensemble-averaged light scattering. The evolution of S(q) in time after increasing the ionic strength of well-dispersed Laponite suspensions shows that Laponite aggregates and forms fractal clusters. The structure of the aggregates does not depend on the ionic strength, but the rate of growth increases very strongly with the ionic strength. At concentrations below about 3 g/l (0.12% v/v) the aggregates sediment while at higher concentrations space-filling gels are formed. The gels are homogeneous on length scales larger than the correlation length which decreases strongly with decreasing ionic strength and increasing concentration. However, the local structure is the same, independent of the concentration and the ionic strength. Received 6 August 2000 and Received in final form 16 March 2001     

Chirality-asymmetry force between ɑ-quartz and copper block

The chirality-asymmetry macroscopic force mediated by light pseudoscalar particles between α -quartz and some achiral matter is studied. If this force between achiral source mass and α -quartz with some chirality is attractive, it will become repulsive when the chirality of the α -quartz crystal is changed. According to the tested limits of the coupling constant g_s g_p /\hbar c< 1.5× 10^-24 at the Compton wavelength λ = 10^-3 m, the force (F) between a 0.08× 0.08× 0.002 m³ block of α -quartz and a 0.08× 0.08× 0.01 m³ copper block with a separation being 0.5× 10^-3 \mbox{m} in between, is estimated from the published data at less than 4.64× 10^-24 N, i.e. F < 4.64× 10^-24 N.     

氟硼铍酸钾晶体的生长、表面形貌和缺陷

采用自发成核方法,以KF-B2O3为助溶剂,在KBBF∶KF∶B2O3为1.5∶5.0∶0.8的体系中,较为重复地生长了尺寸较大的KBBF晶体,从中可加工出10mm×10mm×1.5mm的样品供测试和非线性谐波输出应用.晶体的理想外形由{0001}、{1010}、和{1011}三组单形构成.其宏观缺陷主要为连生、孪生、包裹体,宏观生长台阶和条纹、开裂等.并观察了晶体的表面形貌.     

Efficient modification with flexible spacing coating for in situ reversible assembly of semirigid macroscopic objects through hierarchical metal coordination

Macroscopic supramolecular assembly plays a key role to bridge the fundamental researches on molecular recognition to the potential applications as supramolecular materials. However, the challenge remains to promote the research from soft hydrogel system to semirigid objects or building blocks. Herein, the concept of flexible spacing coating was employed to modify the model polydimethylsiloxane building blocks, and reversible macroscopic assembly was successfully realized through introducing highly directional, dynamic, and reversible coordinate interactions as driving forces. The driving force for the macroscopic assembly was confirmed by introducing highly competitive ethylene diamine tetra acetic acid solution as an orthodox system to disassemble the assembled blocks. Moreover, the coordinate interaction was further understood through unique in situ measurements of binding forces between building blocks during assembly process. This work of macroscopic supramolecular assembly provides an in situ visible platform, which is significant to clarify the highly fascinating and facile coordinate interactions on the macroscopic assembly behavior.     

Precise Macroscopic Supramolecular Assemblies: Strategies and Applications

Macroscopic supramolecular assembly (MSA) is a new concept in supramolecular science with a focus on interfacial assembly of macroscopic building blocks, which has largely extended the applicable materials of supramolecular assembly and provided new solutions to fabricating tissue scaffolds, soft devices, etc. The precision of the assembled structures is of great interest; unlike molecular assemblies, MSA precision is highly dependent on the matching degree of assembled surfaces because of the large interactive area and group number, which result in remarkably increased kinetic possibilities and metastable assemblies. This Concept introduces the principle, history, and development of MSA, elaborates the low-precision challenge in MSA, summarizes the strategies for precise MSA based on the different thermodynamic stability of precise/imprecise structures and control over assembly kinetics, and finally demonstrates the applications of precise MSA structures in advanced manufacture such as tissue scaffolds.     

AUTOMATIC IDENTIFICATION OF MESOSCOPIC PARAMETERS OF DISCRETE ELEMENTS OF SAND MATERIAL 1)

本文依照四川大学某理论力学教学班实际教学改革的经验,通过具体举例说明计算机技术在理论力学教学中尚未开发的巨大潜力,减小数学运算使学生重点关注理论力学基本原理,批量求解使学生提前接触实际应用案例,普适性求解使学生深化对处理多变量问题的认识。同时本文还探讨了理论力学教学改革的方向和目的,即把教学重点放在普适的教学方法上,借助计算机求解多刚体、多变量问题,以期有助于理论力学教材更好地适应时代发展。     

Shell structure in deformed nuclei and nuclear fission

Some new aspects in the theory of heavy nuclei emerging from studies of nuclear shell structure in the nuclear-fission process are described. Specific subjects cover general understanding of shell structure, the significance of macroscopic modes and the droplet model.