Statistical Mechanics and Phase Transitions

马里兰大学的Michael Fisher得到了理论与计算化学计划和材料理论计划的共同资助，继续他在统计力学方面的基础理论研究，以及物质状态、这些状态之间的相变和相关关键现象的研究。需要研究的具体问题包括：1)实验观察到的在某些电解质中发生相分离的交叉临界行为的起源和性质；2)对称性在连续流体中的作用以及控制近临界热力学的线性标度场；3)改进了蒙特卡罗模拟中区分通用性类的有限尺度技术；4)多组分离子球形模型和新型可压缩电池气体的精确分析；5)临界端点附近的界面张力与容纳非经典临界指数的特殊自由能泛函之间的普遍关系的研究；6)利用这种自由能泛函方法计算临界邻域的通用临界吸附和密度曲线；7)用最新发展的理论分析分子马达所施加的力；8)发展了处理分子运动模型所需的数学，这些模型采用有偏差的、线性的、具有等待时间分布（包括分支和死亡过程）的周期性随机行走。费雪的理论研究将进一步加深对各种物理条件下电解质溶液的认识。电解质溶液在许多工业和生物过程中都很重要。这项研究的一个新的延伸是探索分子马达如何沿着细胞内的线性轨迹运动，以执行对生物体生命至关重要的功能。

Michael Fisher of the University of Maryland is cofunded by a grant from the Theoretical and Computational Chemistry Program and the Materials Theory Program to continue his basic theoretical research in statistical mechanics and the study of states of matter, phase transitions between these states, and related critical phenomena. Specific problems to be studied include: 1) the origin and nature of crossover critical behavior observed experimentally in certain electrolytes that undergo a phase separation; 2) the role of symmetry in continuum fluids and the linear scaling fields that govern near-critical thermodynamics; 3) the refinement of finite-size scaling techniques for discriminating between universality classes in Monte Carlo simulations; 4) the exact analysis of multi-species ionic spherical models and of a novel compressible cell gas; 5) the study of universal relations between interfacial tension near a critical endpoint and special free energy functional that accommodate non-classical critical exponents; 6) the use of this free energy functional approach to compute universal critical adsorption and density profiles in the critical neighborhood; 7) the analysis of the forces exerted by molecular motors using a recently developed theory; and 8) the development of the mathematics needed for the treatment of molecular motor models that employs biased, linear, periodic random walks with waiting time distributions including branching and death processes.Fisher's theoretical research will further the understanding of electrolyte solutions under various physical conditions. Electrolyte solutions are important in many industrial and biological processes. A novel extension of this research is the probing of how molecular motors move along linear tracks within cells to perform functions vital to the life of the organism.