Phase transitions of a polymer threading a membrane coupled to coil-globule transitions

We theoretically study phase transitions of a polymer threading through a pore imbedded in a membrane. We focus on the coupling between a partition of the polymer segments through the membrane and a coil-globule transition of the single polymer chain. Based on the Flory model for collapse transitions of a polymer chain, we calculate the fraction of polymer segments and the expansion factor of a polymer coil on each side of the membrane. We predict a first-order phase transition of a polymer threading a membrane; polymer segments in one side are discontinuously translocated into the other side, depending on solvent conditions and molecular weight of the polymer. We also discuss the equilibrium conformation of the polymer chain on each side of the membrane

Kinetics of polymer translocation through a pore

We theoretically study kinetics of a polymer threading through a pore embedded in a flat membrane. We numerically solve three coupled kinetic equations for the number n1 of polymer segments in one side of the membrane and expansion factors of the polymer chain in each side of the membrane. We find the time evolution n1t1/(1 + ) at late stages and the translocation time t is scaled as tn1 + for large number n of the polymer segments, where is the effective size exponent of the radius of gyration of the polymer. When the polymer is translocated into a region with a good solvent condition (= 3/5), we obtain n1t5/8 and tn8/

Discontinuous elongation of nematic gels by a magnetic field

The effects of a magnetic field on the swelling of a nematic gel immersed in a low molecular weight liquid crystal solvent are examined by using a mean field theory. The nematic-isotropic (paranematic) phase transition temperature of the gel and the solvent is controlled by the external field. As a result of an anisotropic coupling between the gel and solvent, the shape of the gel is discontinuously (or continuously) elongated with increasing the strength of the external field. We examine the condition for a first- and second-order volume phase transition of the gel under a magnetic field

Orientation fluctuation-induced spinodal decomposition in polymer–liquid-crystal mixtures

We study the early stages of spinodal decomposition (SD) in polymer–liquid-crystal mixtures by solving linearized time-dependent Landau-Ginzburg equations for concentration (conserved order parameter) and orientation (nonconserved order parameter). The theory takes into account a cross term between concentration and orientation gradients, which becomes an important factor for phase separation kinetics. We calculate structure factors for concentration and for orientation, depending on a quench temperature and concentration. We find a new SD process driven by instability of the orientational order parameter. In this case, the average domain size initially grows as a nontrivial and evolving power of time, which starts as t1/3 in our minimal model. The domain growth is advanced by the coupling between the two order parameters

Helical inversions and phase separations in binary mixtures of cholesteric liquid crystalline molecules

A mean field theory is introduced to describe a helical inversion in nematic-cholesteric mixtures and binary cholesteric mixtures. Taking into account a chiral coupling between unlike molecules, the helical pitch is derived as a function of orientational order parameters and concentration. We find the conditions of helical inversions for the mixtures and derive the concentration of the helical inversions, depending on the chiral interaction. The numerical results are in agreement with the experimental results. We also examine phase separations on the temperature-concentration plane, including the helical inversions. A large variety of phase separations, such as the two-phase coexistence between a right-handed rich and a left-handed rich phase, etc., are predicted

An Approach to Equilibrium Selection

We consider equilibrium selection in 2x2 bimatrix (both symmetric and asymmetric) games with two strict Nash equilibria by embedding it in a dynamic random matching game played by a continuum of anonymous agents. Unlike in the evolutionary game literature, we assume that the players are rational, seeking to maximize the expected discounted payoffs; but they are instead restricted to make a short run commitment when choosing actions. Modeling the friction this way yields the equilibrium dynamics, whose stationary states correspond to the Nash outcomes of the original game. Our selection is based on differential stability properties of the stationary states. It is shown that, as friction becomes arbitrarily small, a strict Nash outcome becomes uniquely absorbing and globally accessible if and only if it satisfies the Harsanyi and Selton (1988) notion of risk-dominance criterion. Our approach thus supplies another support for risk-dominance in addition to those given in literature.Equilibrium Selection, Random Matching Games, Risk-dominance

An Approach to Equilibrium Selection

We consider equilibrium selection in 2x2 bimatrix games with two strict Nash equilibria in a random matching framework. The players seek to maximize the discounted payoffs, but are restricted to make a short run commitment. Modeling the friction this way yields equilibrium dynamics of the behavior patters in the society. We define and characterize an absorbing and globally attractive state in this dynamics. It is shown that, as friction becomes arbitrarily small, a strict Nash equilibrium outcome becomes unique absorbing and globally attractive if and only if it satisfies the Harsanyi/Selton notion of risk-dominance criterion.Equilibrim Selection, Random Matching Games, risk-dominance

Development of a glue-free bimorph mirror for use in vacuum chambers

PZT (lead zirconate titanate)-glued bimorph deformable mirrors are widely used in hard X-ray regimes; however, they have not yet been used in soft X-ray regimes because they are less compatible for usage under high vacuum. In this study, we developed a glue-free bimorph deformable mirror, in which silver nano-particles were employed to bond PZT actuators to mirror substrates. Under an appropriate bonding condition, the bonding layer was confirmed to be uniform and the mirror's bending characteristics were demonstrated to be sufficiently stable; its gas emission rate was also shown to be acceptable. Piezo responses before and after additional heating at 200 °C showed the thermal stability of its bonding and bending properties.Yoshio Ichii, Hiromi Okada, Hiroki Nakamori, Akihiko Ueda, Hiroyuki Yamaguchi, Satoshi Matsuyama, and Kazuto Yamauchi, "Development of a glue-free bimorph mirror for use in vacuum chambers", Review of Scientific Instruments 90, 021702 (2019), https://doi.org/10.1063/1.5066105