Chamber basis of the Orlik-Solomon algebra and Aomoto complex

We introduce a basis of the Orlik-Solomon algebra labeled by chambers, so called chamber basis. We consider structure constants of the Orlik-Solomon algebra with respect to the chamber basis and prove that these structure constants recover D. Cohen's minimal complex from the Aomoto complex.Comment: 16 page

The Portevin-Le Chatelier Effect in Vanadium

In order to examine the temperature and strain-rate dependences of the Portevin-Le Chatelier (P-L) effect, tensile tests were carried out, using vanadium containing 170 p.p.m. of carbon and 42 p.p.m. of oxygen. The results obtained were as follows. 1. The P-L effect is observed in the temperature range from about 200℃ to 500℃ for a strain rate of 3.3×10^/sec. 2. The serrations observed after the initial Luders strain are classified into two types, relatively fine serrations (Type A) and coarser serrations (Type B) which appear intermittently and are observed clearly in the higher temperature region. 3. Type A serration is associated with a very high work-hardening rate, while the rate is smaller with Type B serration. 4. In the lower temperature region, the P-L effect is observed only when the deformation proceeds beyond some critical strain, and the serration increases in stress amplitude with strain, while, in the higher temperature region, Type A serration disappears abruptly at some critical strain. Type B serration remains for some time after Type A serration has disappeared. 5. The apparent activation energy is determined to be 27.9 kcal/mole from the critical conditions for the initiation of the P-L effect. This value agrees well with the activation energies for diffusion of carbon and oxygen in vanadium. A very large value of the energy, 76.7 kcal/mole, is found from the disappearing conditions of Type A serration. The results as to Type A serration accord with the mechanism of jerky motion of dislocations dragged by solute atmospheres (Yoshinaga and Morozumi 1971a), while those of Type B serration are understandable with the unlocking mechanism

Contraction of cross-linked actomyosin bundles

Cross-linked actomyosin bundles retract when severed in vivo by laser ablation, or when isolated from the cell and micromanipulated in vitro in the presence of ATP. We identify the time scale for contraction as a viscoelastic time tau, where the viscosity is due to (internal) protein friction. We obtain an estimate of the order of magnitude of the contraction time tau ~ 10-100 s, consistent with available experimental data for circumferential microfilament bundles and stress fibers. Our results are supported by an exactly solvable, hydrodynamic model of a retracting bundle as a cylinder of isotropic, active matter, from which the order of magnitude of the active stress is estimated.Comment: To be published in Physical Biolog

Dynamics of orbital degrees of freedom probed via isotope 121,123^{121,123} Sb nuclear quadrupole moments in Sb-substituted iron-pnictide superconductors

Isotope $^{121,123}$Sb nuclei with large electric quadrupole moments are applied to investigate the dynamics of orbital degrees of freedom in Sb-substituted iron(Fe)-based compounds. In the parent compound LaFe(As$_{0.6}$Sb$_{0.4}$)O, the nuclear spin relaxation rate $^{121,123}(T_{1}^{-1})$ at $^{121,123}$Sb sites was enhanced at structural transition temperature ($T_{s}\sim$ 135 K), which is higher than N\'eel temperature ($T_{\rm N}\sim$125 K). The isotope ratio $^{123}(T_{1}^{-1})/^{121}(T_{1}^{-1})$ indicates that the electric quadrupole relaxation due to the dynamical electric field gradient at Sb site increases significantly toward $T_{s}$. It is attributed to the critically enhanced nematic fluctuations of stripe-type arrangement of Fe-$3d_{xz}$ (or $3d_{yz}$) orbitals. In the lightly electron-doped superconducting (SC) compound LaFe(As$_{0.7}$Sb$_{0.3}$)(O$_{0.9}$F$_{0.1}$), the nematic fluctuations are largely suppressed in comparison with the case of the parent compound, however, it remains a small enhancement below 80 K down to the $T_c$($\sim$ 20 K). The results indicate that the fluctuations from both the spin and orbital degrees of freedom on the $3d_{xz}$(or $3d_{yz}$) orbitals can be seen in lightly electron-doped SC state of LaFeAsO-based compounds. We emphasize that isotope $^{121,123}$Sb quadrupole moments are sensitive local probe to identify the dynamics of orbital degrees of freedom in Fe-pnictides, which provides with a new opportunity to discuss the microscopic correlation between the superconductivity and both nematic and spin fluctuations simultaneously even in the polycrystalline samples.Comment: 7 pages, 4 figures and 1 supplemental fil

Collective dynamics of two-mode stochastic oscillators

We study a system of two-mode stochastic oscillators coupled through their collective output. As a function of a relevant parameter four qualitatively distinct regimes of collective behavior are observed. In an extended region of the parameter space the periodicity of the collective output is enhanced by the considered coupling. This system can be used as a new model to describe synchronization-like phenomena in systems of units with two or more oscillation modes. The model can also explain how periodic dynamics can be generated by coupling largely stochastic units. Similar systems could be responsible for the emergence of rhythmic behavior in complex biological or sociological systems.Comment: 4 pages, RevTex, 5 figure