Dynamical Heterogeneities and Cooperative Motion in Smectic Liquid Crystals

Using simulations of hard rods in smectic-A states, we find non-gaussian diffusion and heterogeneous dynamics due to the equilibrium periodic smectic density profiles, which give rise to permanent barriers for layer-to-layer diffusion. This relaxation behavior is surprisingly similar to that of non-equilibrium supercooled liquids, although there the particles are trapped in transient (instead of permanent) cages. Interestingly, we also find stringlike clusters of up to 10 inter-layer rods exhibiting dynamic cooperativity in this equilibrium state.Comment: 10 pages, 4 figure

Heterogeneous Dynamics in Columnar Liquid Crystals of Parallel Hard Rods

In the wake of previous studies on the rattling-and-jumping diffusion in smectic liquid crystal phases of colloidal rods, we analyze here for the first time the heterogeneous dynamics in columnar phases. More specifically, we perform computer simulations to investigate the relaxation dynamics of a binary mixture of perfectly aligned hard spherocylinders. We detect that the columnar arrangement of the system produces free-energy barriers the particles should overcome to jump from one column to another, thus determining a hopping-type diffusion. This phenomenon accounts for the non-Gaussian inter-column diffusion and shows a two-step structural relaxation which is remarkably analogous to that of out-of-equilibrium glass-forming systems and gels. Surprisingly enough, slight deviations from the behavior of simple liquids due to transient cages is also observed in the direction perpendicular to this plane, where the system is usually referred to as liquid-like.Comment: accepted by J Chem Phys; 10 pages, 10 figure

Phase diagrams of charged colloidal rods: can a uniaxial charge distribution break chiral symmetry?

We construct phase diagrams for charged rodlike colloids within the second-virial approximation as a function of rod concentration, salt concentration, and colloidal charge. Besides the expected isotropic-nematic transition, we also find parameter regimes with a coexistence between a nematic and a second, more highly aligned nematic phase including an isotropic-nematic-nematic triple point and a nematic-nematic critical point, which can all be explained in terms of the twisting effect. We compute the Frank elastic constants to see if the twist elastic constant can become negative, which would indicate the possibility of a cholesteric phase spontaneously forming. Although the twisting effect reduces the twist elastic constant, we find that it always remains positive. In addition, we find that for finite aspect-ratio rods the twist elastic constant is also always positive, such that there is no evidence of chiral symmetry breaking due to a uniaxial charge distribution.Comment: Added a reference to Sec. 4 and extended discussions in Secs. 4 and 7, results unchange

Анализ и моделирование макроэкономических процессов в переходной период

Рассматривается построение моделей процессов инфляции и трансформирования отношений собственности. На основании разработанных моделей поставлены задачи оптимального управления данными процессами, для решения которых применяется метод динамического моделирования. Получены аналитические выражения для оптимальных управляющих воздействий и оптимальные траектории реализации процессов инфляции и трансформирования отношений собственности.У статті розглядається побудова моделей процесів інфляції і трансформування власності. На підставі розроблених моделей поставлені задачі оптимального керування даними процесами, для рішення яких застосовується метод динамічного моделювання. Отримані аналітичні співвідношення для оптимальних керуючих впливів і оптимальні траєкторії реалізації процесів інфляції і трансформування власності.The paper is devoted to construction of mathematical models for inflation and transforming the property form or privatization. The models constructed are used for the optimal control problem statement aiming to compute optimal trajectories for the processes implementation. To solve the optimal control problem dynamic programming method is applied. As a result of the problem solving analytical expressions were derived for optimal inputs, and respective optimal trajectories were computed for various initial conditions

Fluids of platelike particles near a hard wall

Fluids consisting of hard platelike particles near a hard wall are investigated using density functional theory. The density and orientational profiles as well as the surface tension and the excess coverage are determined and compared with those of a fluid of rodlike particles. Even for low densities slight orientational packing effects are found for the platelet fluid due to larger intermolecular interactions between platelets as compared with those between rods. A net depletion of platelets near the wall is exhibited by the excess coverage, whereas a change of sign of the excess coverage of hard-rod fluids is found upon increasing the bulk density.Comment: 6 pages, 9 figure

Интеграционные процессы в условиях международной глобализации экономики

We present a double-charge model for the interaction between parallel polarizable hard spherocylinders subject to an external electric field. Using Monte Carlo simulations and free-energy calculations, we predict the phase behaviour for this model as a function of the density and electric field strength, at a fixed length-to-diameter ratio L/D = 5. The resulting phase diagram contains, in addition to the well-known nematic, smectic A, ABC crystal, and columnar phases, a smectic C phase, and a low temperature crystal X phase. We also find a string fluid at low densities and field strengths, resembling results found for dipolar spheres

Demixing and orientational ordering in mixtures of rectangular particles

Using scaled-particle theory for binary mixtures of two-dimensional hard particles with rotational freedom, we analyse the stability of nematic phases and the demixing phase behaviour of a variety of mixtures, focussing on cases where at least one of the components consists of hard rectangles or hard squares. A pure fluid of hard rectangles may exhibit, aside from the usual uniaxial nematic phase, an additional (tetratic) oriented phase, possessing two directors, which is the analogue of the biaxial or cubatic phases in three- dimensional fluids. There is computer simulation evidence that the tetratic phase might be stable with respect to phases with spatial order for rectangles with low aspect ratios. As hard rectangles are mixed with other particles not possessing stable tetratic order by themselves, the tetratic phase is destabilised, via a first- or second-order phase transition, to uniaxial nematic or isotropic phases; for hard rectangles of low aspect ratio tetratic order persists in a relatively large range of volume fractions. The order of these transitions depends on the particle geometry, dimensions and thermodynamic conditions of the mixture. The second component of the mixture has been chosen to be hard discs or disco-rectangles, the geometry of which is different from that of rectangles, leading to packing frustration and demixing behaviour, or simply rectangles of different aspect ratio. These mixtures may be good candidates for observing thermodynamically stable tetratic phases in monolayers of hard particles. Finally, demixing between fluid (isotropic--tetratic or tetratic--tetratic) phases is seen to occur in mixtures of hard squares of different sizes when the size ratio is sufficiently large.Comment: 27 pages, 9 figure

"Blue energy" from ion adsorption and electrode charging in sea- and river water

A huge amount of entropy is produced at places where fresh water and seawater mix, for example at river mouths. This mixing process is a potentially enormous source of sustainable energy, provided it is harnessed properly, for instance by a cyclic charging and discharging process of porous electrodes immersed in salt and fresh water, respectively [D. Brogioli, Phys. Rev. Lett. 103, 058501 (2009)]. Here we employ a modified Poisson-Boltzmann free-energy density functional to calculate the ionic adsorption and desorption onto and from the charged electrodes, from which the electric work of a cycle is deduced. We propose optimal (most efficient) cycles for two given salt baths involving two canonical and two grand-canonical (dis)charging paths, in analogy to the well-known Carnot cycle for heat-to-work conversion from two heat baths involving two isothermal and two adiabatic paths. We also suggest a slightly modified cycle which can be applied in cases that the stream of fresh water is limited.Comment: 7 Figure

Orientational order in dipolar fluids consisting of nonspherical hard particles

We investigate fluids of dipolar hard particles by a certain variant of density-functional theory. The proper treatment of the long range of the dipolar interactions yields a contribution to the free energy which favors ferromagnetic order. This corrects previous theoretical analyses. We determine phase diagrams for dipolar ellipsoids and spherocylinders as a function of the aspect ratio of the particles and their dipole moment. In the nonpolar limit the results for the phase boundary between the isotropic and nematic phase agree well with simulation data. Adding a longitudinal dipole moment favors the nematic phase. For oblate or slightly elongated particles we find a ferromagnetic liquid phase, which has also been detected in computer simulations of fluids consisting of spherical dipolar particles. The detailed structure of the phase diagram and its evolution upon changing the aspect ratio are discussed in detail.Comment: 35 pages LaTeX with epsf style, 11 figures in eps format, submitted to Phys. Rev.