A monopole mass filter with a hyperbolic V-shaped electrode

In this article we compare the classical monopole mass filter of von Zahn and the monopole mass filter with a hyperbolic V-shaped electrode. The experimental results and those of computer simulation for both mass spectrometers are presented. We show that the replacement of a conventional 90 degrees V-shaped electrode by an electrode with a hyperbolic profile substantially improves the peak shape of any given mass, and increases the mass resolution by a factor of 3-4 and the abundance sensitivity by a factor of 100. The potential of high analytical performance combined with electroforming techniques for electrode manufacture indicate future practical uses of such instruments. Copyright 1999 John Wiley & Sons, Ltd.     

Anharmonic magnetic deformation of self-assembled molecular nanocapsules

High magnetic fields were used to deform spherical nanocapsules, self-assembled from bolaamphiphilic sexithiophene molecules. At low fields the deformation--measured through linear birefringence-scales quadratically with the capsule radius and with the magnetic field strength. These data confirm a long standing theoretical prediction [W. Helfrich, Phys. Lett. A 43, 409 (1973)10.1016/0375-9601(73)90396-4], and permit the determination of the bending rigidity of the capsules as (2.6+/-0.8) x 10(-21) J. At high fields, an enhanced rigidity is found which cannot be explained within the Helfrich model. We propose a complete form of the free energy functional that accounts for this behavior, and allows discussion of the formation and stability of nanocapsules in solution.     

Non-spherical shapes of capsules within a fourth-order curvature model

We minimize a discrete version of the fourth-order curvature-based Landau free energy by extending Brakke's Surface Evolver. This model predicts spherical as well as non-spherical shapes with dimples, bumps and ridges to be the energy minimizers. Our results suggest that the buckling and faceting transitions, usually associated with crystalline matter, can also be an intrinsic property of non-crystalline membranes.     

Saddle-splay elasticity and field induced soliton in nematics

The symmetry breaking Fréedericksz transitions, when a uniformly aligned nematic state is replaced by a homogeneously or periodically distorted state, have been extensively studied before. Here we analyse the influence of the saddle-splay elasticity on the non-linear ground state of a nematic liquid crystal in the presence of a magnetic field above the Fréedericksz threshold. We identify the bifurcation point when the localized soliton-like state is linearly unstable with respect to the perturbations of the wavevector in the direction perpendicular to the initial plane of the soliton. This instability occurs only if the ratio of the saddle-splay elastic constant to the elastic modulus of nematics in the one-constant approximation is above the critical value K24/K\ ≥0.707     

Thin nematic films: Anchoring effects and stripe instability revisited

We study theoretically the formation of long-wavelength instability patterns observed at spreading of nematic droplets on liquid substrates. The role of surface-like elastic terms in nematic films of submicron thickness is (re)examined by extending our previous work to hybrid aligned nematics. We identify the upper threshold for the formation of stripes and compare our results with experimental observations. We find that the wavelength and the amplitude of the in-plane director undulations can be related to the small but finite azimuthal anchoring. Within a simplified model we analyse the possibility of non-planar base state below the Barbero–Barberi critical thickness.     

Justification of the Kirchhoff hypotheses and error estimation for two-dimensional models of anisotropic and inhomogeneous plates, including laminated plates

Asymptotic analysis of the problem describing deformation ofa thin cylindrical plate with clamped lateral side is performed.The problem is considered under the most general statement withthe plate being laminated and consisting of an arbitrary numberof nonhomogeneous and anisotropic (21 elastic moduli) layers.Explicit integral representations of the differential operatorswhich form the two-dimensional model of the plate are derived.In the case when the elastic moduli of each of the layers areconstant, these integral representations turn into algebraicones. The asymptotic procedure is justified with the help ofa weighted inequality of Korn's type. The error estimates obtainedgive a rigorous mathematical proof of both of Kirchhoff's hypotheses(kinematic and static) and shed light on the well-known intrinsicinconsistency of two of the hypotheses.