Magnetic phase diagram of the frustrated S=1/2 chain magnet LiCu_2O_2

We present the results of the magnetization and dielectric constant measurements on untwinned single crystal samples of the frustrated S=1/2 chain cuprate LiCu_2O_2. Novel magnetic phase transitions were observed. A spin flop transition of the spiral spin plane was observed for the field orientations H||a,b. The second magnetic transition was observed at H~15 T for all three principal field directions. This high field magnetic phase is discussed as a collinear spin-modulated phase which is expected for an S=1/2 nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic chain system

Extensive infrared spectroscopic study of CuO: signatures of strong spin-phonon interaction and structural distortion

Optical properties of single-crystal monoclinic CuO in the range 70 - 6000 \cm were studied at temperatures from 7 to 300 K. Normal reflection spectra were obtained from the (001) and (010) crystal faces thus giving for the first time separate data for the $A_{u}$ and $B_{u}$ phonon modes excited in the purely transverse way (TO modes). Mode parameters, including polarizations of the $B_{u}$ modes not determined by the crystal symmetry, were extracted by the dispersion analysis of reflectivity curves as a function of temperature. Spectra of all the components of the optical conductivity tensor were obtained using the Kramers-Kronig method recently extended to the case of the low-symmetry crystals. The number of strong phonon modes is in agreement with the factor-group analysis for the crystal structure, currently accepted for the CuO. However, several "extra" modes of minor intensity are detected. Comparison of frequencies of "extra" modes with the available phonon dispersion curves points to possible "diagonal" doubling of the unit cell \{{\bf a}, {\bf b}, {\bf c}\} $\to$ \{{\bf a}+{\bf c}, {\bf b}, {\bf a}-{\bf c}\} and formation of the superlattice. The previously reported softening of the $A^{3}_{u}$ mode ($\sim$ 400 \cm) with cooling at $T_{N}$ is found to be $\sim$ 10 % for the TO mode. The mode is very broad at high temperatures and strongly narrows in the AFM phase. We attribute this effect to strong resonance coupling of this mode to optical or acoustic bi-magnons and reconstruction of the magnetic excitations spectrum at the N\'eel point. A significant anisotropy of $\epsilon^{\infty}$ is observed: it was found to be 5.9 along the {\bf b}-axis, 6.2 along the {[}101{]} chains and 7.8 the {[}10$\bar{1}${]} chains. The "transverse" effective charge is value is about 2 electrons.Comment: 23 pages, 14 figures, REVTeX, submitted to PR

NMR and LDA evidence for spiral magnetic order in the chain cuprate LiCu2O2

We report on {6,7}Li nuclear magnetic resonance measurements of the spin-chain compound LiCu2O2 in the paramagnetic and magnetically ordered states. Below T about 24 K the NMR lineshape presents a clear signature of incommensurate (IC) static modulation of the local magnetic field consistent with an IC spiral modulation of the magnetic moments. {7}Li NMR reveals strong phason-like dynamical fluctuations extending well below 24 K. We hypothesize that a series of phase transitions at 24.2, 22.5, and 9 K reflects a "Devil's staircase" type behavior generic for IC systems. LDA based calculations of exchange integrals reveal a large in-chain frustration leading to a magnetical spiral.Comment: 4 pages, 4 figure

Barriers to antigenic escape by pathogens: trade-off between reproductive rate and antigenic mutability

BackgroundA single measles vaccination provides lifelong protection. No antigenic variants that escape immunity have been observed. By contrast, influenza continually evolves new antigenic variants, and the vaccine has to be updated frequently with new strains. Both measles and influenza are RNA viruses with high mutation rates, so the mutation rate alone cannot explain the differences in antigenic variability.ResultsWe develop a new hypothesis to explain antigenic stasis versus change. We first note that the antigenically static viruses tend to have high reproductive rates and to concentrate infection in children, whereas antigenically variable viruses such as influenza tend to spread more widely across age classes. We argue that, for pathogens in a naive host population that spread more rapidly in younger individuals than in older individuals, natural selection weights more heavily a rise in reproductive rate. By contrast, pathogens that spread more readily among older individuals gain more by antigenic escape, so natural selection weights more heavily antigenic mutability.ConclusionThese divergent selective pressures on reproductive rate and antigenic mutability may explain some of the observed differences between pathogens in age-class bias, reproductive rate, and antigenic variation

Chaotic and pseudochaotic attractors of perturbed fractional oscillator

We consider a nonlinear oscillator with fractional derivative of the order alpha. Perturbed by a periodic force, the system exhibits chaotic motion called fractional chaotic attractor (FCA). The FCA is compared to the ``regular'' chaotic attractor. The properties of the FCA are discussed and the ``pseudochaotic'' case is demonstrated.Comment: 20 pages, 7 figure