Statistical Mechanics and Phase Transitions

马里兰州大学的迈克尔·费舍尔由理论和计算化学项目以及材料理论项目的资助共同资助，继续他在统计力学和物质状态，这些状态之间的相变以及相关临界现象的研究方面的基础理论研究。 具体研究的问题包括：1）在某些经历相分离的电解质中实验观察到的交叉临界行为的起源和性质; 2）对称性在连续流体和控制近临界热力学的线性标度场中的作用; 3）在Monte Carlo模拟中区分普适类的有限尺寸标度技术的改进; 4）对多组分离子球模型和一种新的可压缩胞气的精确分析：5）研究临界点附近界面张力与包含非经典临界指数的特殊自由能泛函之间的普遍关系; 6）利用自由能泛函方法计算了临界吸附和临界邻域密度分布的普适性; 7）利用新近发展的理论分析分子马达所施加的力;和8）发展处理分子马达模型所需的数学，该模型采用有偏的，线性的，周期随机游动的等待时间分布，包括分支和死亡过程。费舍尔的理论研究将进一步了解电解质各种物理条件下的溶液。 电解质溶液在许多工业和生物过程中是重要的。 这项研究的一个新的延伸是探索分子马达如何在细胞内沿着沿着运动，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.