Twist-bend nematic phase in cyanobiphenyls and difluoroterphenyls bimesogens

The paper reviews assignment of the low-temperature nematic phase observed in simple bimesogenic or dimeric systems based on cyanobiphenyls and difluoroterphenyls to the twist-bend nematic phase, NTB, using a range of experimental techniques. These include DSC, X-rays, Polarising Microscopy, electro-optics, birefringence and measurements of the electroclinic effect arising from flexoelectricity. An emphasis is laid on the observations of the chiral domains of opposite handedness at zero field in an otherwise achiral liquid crystalline system in this phase. These observations are a direct consequence of the structure of the twist-bend phase predicted by Ivan Dozov for achiral bent core molecules. The paper reviews the electro-optic phenomena and the observed electroclinic effect and how these observations assign it as the NTB phase. Results of the nanoscale helical pitch measurements using freeze-fracture microscopy are reviewed and discussed briefly. Results of the measurements of elastic constants especially close to the N–NTB transition are also reviewed

Нетрадиційні кватерніони і пентаніони в задачах інерціальної орієнтації

The article considers the nonclassical quaternions and pentanions of helf-rotations of solidbody and their application in problems of control and orientation of moving objects. In contrast to classicalrationed Hamiltonian quaternions of complete rotations the nonclassical quaternions of helf-rotations maybe null, they have variable rates, depending on the angle of Euler finite rotationРассматрены неклассические кватернионы и пентанионы полувращений твердого тела и их применение в задачахуправления и ориентации движущихся объектов. В отличие от классических нормированных гамильтоновых кватернионов полных вращений неклассические кватернионы полувращений могут быть нулевыми, они имеют переменные нормы, зависящие от угла эйлерова конечного вращенияРозглянуто некласичні кватерніони і пентаніони напівобертання твердого тіла та їх застосування в задачах керування і орієнтації рухомих об’єктів. На відміну від класичних нормованих гамільтонових кватерніонів повних обертань некласичні кватерніони напівобертання можуть бути нульовими, вони мають змінні норми, що залежать від кута ейлерового кінцевого обертанн

Lattice Model for water-solute mixtures

A lattice model for the study of mixtures of associating liquids is proposed. Solvent and solute are modeled by adapting the associating lattice gas (ALG) model. The nature of interaction solute/solvent is controlled by tuning the energy interactions between the patches of ALG model. We have studied three set of parameters, resulting on, hydrophilic, inert and hydrophobic interactions. Extensive Monte Carlo simulations were carried out and the behavior of pure components and the excess properties of the mixtures have been studied. The pure components: water (solvent) and solute, have quite similar phase diagrams, presenting: gas, low density liquid, and high density liquid phases. In the case of solute, the regions of coexistence are substantially reduced when compared with both the water and the standard ALG models. A numerical procedure has been developed in order to attain series of results at constant pressure from simulations of the lattice gas model in the grand canonical ensemble. The excess properties of the mixtures: volume and enthalpy as the function of the solute fraction have been studied for different interaction parameters of the model. Our model is able to reproduce qualitatively well the excess volume and enthalpy for different aqueous solutions. For the hydrophilic case, we show that the model is able to reproduce the excess volume and enthalpy of mixtures of small alcohols and amines. The inert case reproduces the behavior of large alcohols such as, propanol, butanol and pentanol. For last case (hydrophobic), the excess properties reproduce the behavior of ionic liquids in aqueous solution.Comment: 28 pages, 13 figure

Optimization of large homogeneous air Cherenkov arrays and application to the design of a 1TeV-100TeV gamma-ray observatory

At the time large air Cherenkov arrays are being discussed for future gamma-ray observatories, we review the relationship between the targeted capabilities and the main design parameters taking into account construction costs. As an example application, we describe a telescope array optimized for observations between 1 TeV and a few 100 TeV and use detailed simulations to estimate its performances in comparison to science objectives.Comment: 23 pages, 16 figures, accepted for publication in Astroparticle Physic

Design and Investigation of de Vries Liquid Crystals Based on 5-Phenyl-Pyrimidine and (R,R)-2,3-Epoxyhexoxy backbone.

Calamitic liquid crystals based on 5-phenyl-pyrimidine derivatives have been designed, synthesized, and characterized. The 5-phenyl pyrimidine core was functionalized with a chiral (R,R)-2,3-epoxyhexoxy chain on one side and either siloxane or perfluoro terminated chains on the opposite side. The one involving a perfluorinated chain shows SmA^{*} phase over a wide temperature range of 82 °C, whereas the siloxane analog exhibits both SmA^{*} and SmC^{*} phases over a broad range of temperatures, and a weak first-order SmA^{*}-SmC^{*} transition is observed. For the siloxane analog, the reduction factor for the layer shrinkage R (relative to its thickness at the SmA^{*}-SmC^{*} transition temperature, T_{AC}) is ∼0.373, and layer shrinkage is 1.7% at a temperature of 13 °C below the T_{AC}. This compound is considered to have de Vries smectic characteristics with the de Vries coefficient C_{deVries} of ∼0.86 on the scale of zero (maximum-layer shrinkage) to 1 (zero-layer shrinkage). A three-parameter mean-field model is introduced for the orientational distribution function (ODF) to reproduce the electro-optic properties. This model explains the experimental results and leads to the ODF, which exhibits a crossover from the sugar-loaf to diffuse-cone ODF some 3 °C above T_{AC}

Coulomb singularity effects in tunnelling spectroscopy of individual impurities

Non-equilibrium Coulomb effects in resonant tunnelling processes through deep impurity states are analyzed. It is shown that Coulomb vertex corrections to the tunnelling transfer amplitude lead to a power-law singularity in current- voltage characteristicsComment: 7 pages, 2 figure

Nematic twist-bend phase with nanoscale modulation of molecular orientation

A state of matter in which molecules show a long-range orientational order and no positional order is called a nematic liquid crystal. The best known and most widely used (for example, in modern displays) is the uniaxial nematic, with the rod-like molecules aligned along a single axis, called the director. When the molecules are chiral, the director twists in space, drawing a right-angle helicoid and remaining perpendicular to the helix axis; the structure is called a chiral nematic. Here using transmission electron and optical microscopy, we experimentally demonstrate a new nematic order, formed by achiral molecules, in which the director follows an oblique helicoid, maintaining a constant oblique angle with the helix axis and experiencing twist and bend. The oblique helicoids have a nanoscale pitch. The new twist-bend nematic represents a structural link between the uniaxial nematic (no tilt) and a chiral nematic (helicoids with right-angle tilt)

A theory of L1L^1-dissipative solvers for scalar conservation laws with discontinuous flux

We propose a general framework for the study of $L^1$ contractive semigroups of solutions to conservation laws with discontinuous flux. Developing the ideas of a number of preceding works we claim that the whole admissibility issue is reduced to the selection of a family of "elementary solutions", which are certain piecewise constant stationary weak solutions. We refer to such a family as a "germ". It is well known that (CL) admits many different $L^1$ contractive semigroups, some of which reflects different physical applications. We revisit a number of the existing admissibility (or entropy) conditions and identify the germs that underly these conditions. We devote specific attention to the anishing viscosity" germ, which is a way to express the "$\Gamma$-condition" of Diehl. For any given germ, we formulate "germ-based" admissibility conditions in the form of a trace condition on the flux discontinuity line $x=0$ (in the spirit of Vol'pert) and in the form of a family of global entropy inequalities (following Kruzhkov and Carrillo). We characterize those germs that lead to the $L^1$-contraction property for the associated admissible solutions. Our approach offers a streamlined and unifying perspective on many of the known entropy conditions, making it possible to recover earlier uniqueness results under weaker conditions than before, and to provide new results for other less studied problems. Several strategies for proving the existence of admissible solutions are discussed, and existence results are given for fluxes satisfying some additional conditions. These are based on convergence results either for the vanishing viscosity method (with standard viscosity or with specific viscosities "adapted" to the choice of a germ), or for specific germ-adapted finite volume schemes