Fluctuating Elastic Rings: Statics and Dynamics

We study the effects of thermal fluctuations on elastic rings. Analytical expressions are derived for correlation functions of Euler angles, mean square distance between points on the ring contour, radius of gyration, and probability distribution of writhe fluctuations. Since fluctuation amplitudes diverge in the limit of vanishing twist rigidity, twist elasticity is essential for the description of fluctuating rings. We find a crossover from a small scale regime in which the filament behaves as a straight rod, to a large scale regime in which spontaneous curvature is important and twist rigidity affects the spatial configurations of the ring. The fluctuation-dissipation relation between correlation functions of Euler angles and response functions, is used to study the deformation of the ring by external forces. The effects of inertia and dissipation on the relaxation of temporal correlations of writhe fluctuations, are analyzed using Langevin dynamics.Comment: 43 pages, 9 Figure

Structure influence on mechanical properties of Ti-W-B system nanocrystalline coatings

The effect of structure on nano-hardness and elastic modulus of Ti-W-B nanocrystalline coatings prepared by triode sputtering has been studied. The material structure state has been found to change from cluster-crystalline (at low sputtering potentials U = 0.6 to 1.0 kV) to preferentially oriented-crystalline (at U > 2.2 kV). The texture perfection improvement with increasing U results in increased hardness and elastic modulus of the condensates. The maximum values were attained at U = 3.2 kV and amounted Н = 19.9 GPa and Е = 205 GPa for the cubic phase and Н = 37.9 GPa, Е = 389 GPa for the hexagonal phase, respectively.Исследовано влияние структуры нанокристаллических Ti-W-B покрытий, полученных триодным распылением, на их нанотвердость и модуль упругости. Выявлено изменение структурного состояния материала от кластерно-кристаллического при низких значениях распыляющего напряжения U = 0,6...1,0 кB до преимущественно ориентированного-кристаллического при U > 2,2 кВ. Рост совершенства текстуры с увеличением U приводит к повышению твердости и модуля упругости конденсатов. Максимальные значения были достигнуты при U = 3,2 кB и составляют для фазы с кубической решеткой: твердость Н = 19,9 ГПа, модуль упругости Е = 205 ГПа, а для фазы с гексагональной решеткой: Н = 37,9 ГПа, Е = 389 ГПа.Дослiджено вплив структури нанокристалiчних Ti-W-B iонно-плазмових (трiодна схема) покриттiв на їх нанотвердiсть та модуль пружностi. Виявлено змiни структурного стану матерiалу вiд кластерно-кристалiчного при низьких значеннях U = 0,6...1,0 кВ до переважно орiєнтованого кристалiчного при U > 2,2 кВ. 3ростання досконалостi текстури зi збiльшенням U призводить до зростання твердостi та модулю пружностi конденсатiв. Максимальнi значення досягнуто при U = 3,2 кВ i складають для фази з кубiчною граткою: твердiсть Н = 19,9 ГПа, модуль пружностi Е = 205 ГПа, а для фази з гексагональною граткою: Н = 37,9 ГПа, Е = 389 ГПа

Peculiarities of structure state and mechanical characteristics in ion-plasma condensates of quasibinary system borides W2B5-TiB2

In order to create high-durable, wear-resistant materials for a wide range of functional applications, comparative investigations of the structure and mechanical characteristics of ion-plasma Ti-W-B nano-crystalline condensates were carried out. The range of condensation rates 0.11÷0.25nm/s was found to be critical for the coatings obtained from the target with 80 vol% W2B5-20 vol% TiB2. Below this, a phase with a cubic lattice (W,Ti)B0.7…1.2(O,N,C)0.3…0.2 formed, while over this range, a solid solution (W,Ti)B2 with a hexagonal lattice and element composition close to the sputtered target was observed. The structure state of the material changed from cluster-crystalline (under low sputter potentials U=0.6…1.0 kV) to textured- crystalline (under U>2.2 kV). Structure perfection improvement with U increase results in higher hardness and elastic modulus of condensates. The conditions of cluster component formation and its effect on hardness and elastic modulus of condensates are discussed.