Theory of Banana Liquid Crystal Phases and Phase Transitions

We study phases and phase transitions that can take place in the newly discovered banana (bow-shaped or bent-core) liquid crystal molecules. We show that to completely characterize phases exhibited by such bent-core molecules a third-rank tensor $T^{ijk}$ order parameter is necessary in addition to the vector and the nematic (second-rank) tensor order parameters. We present an exhaustive list of possible liquid phases, characterizing them by their space-symmetry group and order parameters, and catalog the universality classes of the corresponding phase transitions that we expect to take place in such bent-core molecular liquid crystals. In addition to the conventional liquid-crystal phases such as the nematic phase, we predict the existence of novel liquid phases, including the spontaneously chiral nematic $(N_T + 2)^*$ and chiral polar $(V_T + 2)^*$ phases, the orientationally-ordered but optically isotropic tetrahedratic $T$ phase, and a novel nematic $N_T$ phase with $D_{2d}$ symmetry that is neither uniaxial nor biaxial. Interestingly, the Isotropic-Tetrahedratic transition is {\em continuous} in mean-field theory, but is likely driven first-order by thermal fluctuations. We conclude with a discussion of smectic analogs of these phases and their experimental signatures.Comment: 28 pgs. RevTex, 32 eps figures, submitted to Phys. Rev.

Effective index of refraction, optical rotation, and circular dichroism in isotropic chiral liquid crystals

This paper concerns optical properties of the isotropic phase above the isotropic-cholesteric transition and of the blue phase BP III. We introduce an effective index, which describes spatial dispersion effects such as optical rotation, circular dichroism, and the modification of the average index due to the fluctuations. We derive the wavelength dependance of these spatial dispersion effects quite generally without relying on an expansion in powers of the chirality and without assuming that the pitch of the cholesteric $P$ is much shorter than the wavelength of the light $\lambda$, an approximation which has been made in previous studies of this problem. The theoretical predictions are supported by comparing them with experimental spectra of the optical activity in the BP III phase.Comment: 15 pages and 7 figures. Submitted to PR

Mathematical Properties of a New Levin-Type Sequence Transformation Introduced by \v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. I. Algebraic Theory

\v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la [J. Math. Phys. \textbf{44}, 962 - 968 (2003)] introduced in connection with the summation of the divergent perturbation expansion of the hydrogen atom in an external magnetic field a new sequence transformation which uses as input data not only the elements of a sequence $\{s_n \}_{n=0}^{\infty}$ of partial sums, but also explicit estimates $\{\omega_n \}_{n=0}^{\infty}$ for the truncation errors. The explicit incorporation of the information contained in the truncation error estimates makes this and related transformations potentially much more powerful than for instance Pad\'{e} approximants. Special cases of the new transformation are sequence transformations introduced by Levin [Int. J. Comput. Math. B \textbf{3}, 371 - 388 (1973)] and Weniger [Comput. Phys. Rep. \textbf{10}, 189 - 371 (1989), Sections 7 -9; Numer. Algor. \textbf{3}, 477 - 486 (1992)] and also a variant of Richardson extrapolation [Phil. Trans. Roy. Soc. London A \textbf{226}, 299 - 349 (1927)]. The algebraic theory of these transformations - explicit expressions, recurrence formulas, explicit expressions in the case of special remainder estimates, and asymptotic order estimates satisfied by rational approximants to power series - is formulated in terms of hitherto unknown mathematical properties of the new transformation introduced by \v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. This leads to a considerable formal simplification and unification.Comment: 41 + ii pages, LaTeX2e, 0 figures. Submitted to Journal of Mathematical Physic

Detection of crenosoma spp., angiostrongylus vasorum and aelurostrongylus abstrusus in gastropods in Eastern Austria

Canine and feline cardiorespiratory parasites are of utmost relevance in veterinary medicine. Key epizootiological information on major pet metastrongyloids, i.e., Angiostrongylus vasorum and Crenosoma vulpis infecting dogs, and Aelurostrongylus abstrusus and Troglostrongylus brevior infecting cats, is missing from Austria. This study investigated their occurrence in 1320 gastropods collected in the Austrian provinces of Styria, Burgenland, Lower Austria, and in metropolitan Vienna. Metastrongyloid larvae were microscopically detected in 25 samples, and sequence analysis confirmed the presence of metastrongyloids in nine samples, i.e., A. vasorum in one slug (Arion vulgaris) (0.07%), C. vulpis in five slugs (one Limax maximus and four A. vulgaris) (0.4%), A. abstrusus in two A. vulgaris (0.17%), and the hedgehog lungworm Crenosoma striatum was detected in one A. vulgaris. The present study confirms the enzooticity of major cardiorespiratory nematodes in Austria and that canine and feline populations are at risk of infection

QED Effective Action Revisited

The derivation of a convergent series representation for the quantum electrodynamic effective action obtained by two of us (S.R.V. and D.R.L.) in [Can. J. Phys. vol. 71, p. 389 (1993)] is reexamined. We present more details of our original derivation. Moreover, we discuss the relation of the electric-magnetic duality to the integral representation for the effective action, and we consider the application of nonlinear convergence acceleration techniques which permit the efficient and reliable numerical evaluation of the quantum correction to the Maxwell Lagrangian.Comment: 20 pages, LaTeX, 1 table; minor additions and adjustments; to appear in Can. J. Phy

Cofactorization on Graphics Processing Units

We show how the cofactorization step, a compute-intensive part of the relation collection phase of the number field sieve (NFS), can be farmed out to a graphics processing unit. Our implementation on a GTX 580 GPU, which is integrated with a state-of-the-art NFS implementation, can serve as a cryptanalytic co-processor for several Intel i7-3770K quad-core CPUs simultaneously. This allows those processors to focus on the memory-intensive sieving and results in more useful NFS-relations found in less time

Ordinal Excitation of Three-Magnon and Four-Magnon Processes of Magnetostatic Surface Waves in YIG Films

Ordinal excitations of three-magnon decay, modulation instability and four-magnon decay processes of magnetostatic surface waves propagating in a pure yttrium iron garnet film are investigated in accordance with the relationship between the magnetostatic wave frequency and the internal magnetic field. Onset of the modulation instability is realized as a result of modification of magnetostatic surface wave dispersion characteristics by a metallic ground plane

Induced surface anisotropy of amorphous iron-nickel alloys studied by ferromagnetic resonance and antiresonance

The thermally induced (by annealing) surface anisotropy (SA) is studied in ribbon-shaped iron-rich amorphous alloys (prepared by roller quenching method), mainly by the methods of ferromagnetic resonance and antiresonance at frequencies in the range 9 - 95 GHz, in external static magnetic fields oriented either in the plane of the ribbon or perpendicularly to the plane. The large difference between the ferromagnetic resonance and antiresonance penetration depths is pointed out. The magnetic homogeneity of the samples is checked. The induced surface anisotropy constant Ks amounts to several tenths of erg/cm2, its symmetry is uniaxial with the easy axis oriented along the normal to the sample surface. The temperature dependence of Ks reveals a critical point around 400 K, above which Ks=0. The origin of SA lies most probably in occurrence of non-stoichiometric ferrimagnetic oxides, which arise in the annealing process in a few surface atomic planes of the sample, and which interact with the bulk of the material. The magnetoelastic origin of the interaction is not probable