Rigidity and flexibility of virtual polytopes

All 3-dimensional convex polytopes are known to be rigid. Still their Minkowski differences (virtual polytopes) can be flexible with any finite freedom degree. We derive some sufficient rigidity conditions for virtual polytopes and present some examples of flexible ones. For example, Bricard's first and second flexible octahedra can be supplied by the structure of a virtual polytope.     

Phase separation in blends of two homopolymers and a diblock copolymer during film casting

Demixing during film casting of blends of polystyrene, polymethylmethacrylate, and a symmetric diblock copolymer of styrene and methylmethacrylate is discussed. The concentration fluctuations in the homogeneous solutions were calculated in mean field approximation. The structures in the homogeneous and demixed solutions and in the dry films were measured by small-angle x-ray scattering, and the morphologies of the dry films were characterized by transmission electron microscopy. The structure of the dry blends is evidently already pre-formed in solution.     

Viscoelastic properties of amorphous polymers 3: low molecular weight poly(methylphenylsiloxane)

By making creep and recoverable creep measurements of a nearly monodisperse low molecular weight poly(methyl phenyl siloxane) sample, we have found on decreasing temperature towardsT _g that there is continuously a change in the viscoelastic spectrum concomitant with a decrease of the steadystate recoverable compliance. This behavior is exactly the same as previously observed in low molecular weight poly(styrene), proving that this spectacular anomaly in the viscoelasticity of low molecular weight polymers is general and deserves an explanation. Photon correlation spectroscopic measurements performed on the same sample have extended the observation of the viscoelastic response to shorter times and the result corroborates the trend of variation established by the creep data.Dedicated to Prof.Dr. E. W. Fischer on his 65th Birthday. Prof.Dr. Fischer is known for his valuable contribution to fosterine, international collaboration of research in polymer science. This work is an example of his contribution because it would not be possible without him bringing us together. One of us (KLN) would like to take this opportunity to thank Prof. Dr. Fischer for his unwaiving support of the 1st (Crete) and the 2nd (Alicante) International Discussion Meeting on Relaxations in Complex Systems     

Parameters for the inclined-path sensing of molecular hydrogen in the atmosphere by lidar with a YAG:Nd laser

The lidar equation for the vibrational backscattering of neodymium laser radiation and its harmonics by hydrogen molecules is solved numerically. Inclined paths in the atmosphere are investigated with the aim of selecting the transmitter wavelength for detecting the lowest concentrations of hydrogen. Zh. Tekh. Fiz. 68, 20–22 (January 1998)     

Electrostatic field of a thin, unclosed spherical shell and a torus

The electrostatic problem for a thin, unclosed spherical shell and a torus is reduced to paired summation equations in the Legendre polynomials by means of formulas relating the spherical and toroidal harmonic functions. The paired equations are transformed to a Fredholm integral equation of the second kind. Formulas are obtained for computing the charges of the conductors in the form of a series in a small parameter. The capacitance is computed for certain geometrical parameters of the conductors. Zh. Tekh. Fiz. 68, 1–6 (July 1998)     

Laser spectroscopy of the 1s HFS of H-like ions at a bunched beam in the storage ring ESR

The investigation of the 1s HFS provides a good possibility for testing QED effects in a combination of a strong electric and magnetic field. Here, we report about the laserspectroscopic measurements of the ground state hyperfine splitting in ²⁰⁷Pb⁸¹⁺. To handle this M1-transition in the infrared optical regime with its long lifetime, we developed a new detection technique using a bunched ion beam. For the observation of fluorescence light, a new mirror system is adapted to the emission characteristics from an ion beam at relativistic velocities. This revised version was published online in July 2006 with corrections to the Cover Date.     

First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice

We study the exact low energy spectra of the spin 1/2 Heisenberg antiferromagnet on small samples of the kagomé lattice of up to N=36 sites. In agreement with the conclusions of previous authors, we find that these low energy spectra contradict the hypothesis of Néel type long range order. Certainly, the ground state of this system is a spin liquid, but its properties are rather unusual. The magnetic () excitations are separated from the ground state by a gap. However, this gap is filled with nonmagnetic () excitations. In the thermodynamic limit the spectrum of these nonmagnetic excitations will presumably develop into a gapless continuum adjacent to the ground state. Surprisingly, the eigenstates of samples with an odd number of sites, i.e. samples with an unsaturated spin, exhibit symmetries which could support long range chiral order. We do not know if these states will be true thermodynamic states or only metastable ones. In any case, the low energy properties of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice clearly distinguish this system from either a short range RVB spin liquid or a standard chiral spin liquid. Presumably they are facets of a generically new state of frustrated two-dimensional quantum antiferromagnets. Received: 27 November 1997 / Accepted: 29 January 1998