Reflectivity of cholesteric liquid crystals with spatially varying pitch

Solids with spatially varying photonic structure offer gaps to light of a wider range of frequencies than do simple photonic systems. We solve numerically the field distribution in a solid cholesteric with a linearly varying inverse pitch (helical wavevector) using equations we derive for the general case. The simple idea that the position where the Bragg condition is locally satisfied is where reflection takes place is only true in part. Here, reflection is due to a region where the waves are forced to become evanescent, and the rate of variation of structure determines over which distance the waves decay and therefore how complete reflection is. The approximate local Bragg-de Vries schemes are shown to break down in detail at the edges of the gap, and an analytical estimate is given for the transmission coefficient.Comment: 8 pages, accepted by EPJ E, corrections for publication implemente

Tube Model for the Elasticity of Entangled Nematic Rubbers

Dense rubbery networks are highly entangled polymer systems, with significant topological restrictions for the mobility of neighbouring chains and crosslinks preventing the reptation constraint release. In a mean field approach, entanglements are treated within the famous reptation approach, since they effectively confine each individual chain in a tube-like geometry. We apply the classical ideas of reptation dynamics to calculate the effective rubber-elastic free energy of anisotropic networks, nematic liquid crystal elastomers, and present the first theory of entanglements for such a material.Comment: amended version (typos corrected, appendix extended

Studies of hydrodynamic events in stellar evolution. 3: Ejection of planetary nebulae

The dynamic behavior of the H-rich envelope (0.101 solar mass) of an evolved star (1.1 solar mass) as the luminosity rises to 19000 solar luminosity during the second ascent of the red giant branch. For luminosities in the range 3100 L 19000 solar luminosity the H-rich envelope pulsates like a long-period variable (LPV) with periods of the order of a year. As L reaches 19000 solar luminosity, the entire H-rich envelope is ejected as a shell with speeds of a few 10 km/s. The ejection occurs on a timescale of a few LPV pulsation periods. This ejection is associated with the formation of a planetary nebula. The computations are based on an implicit hydrodynamic computer code. T- and RHO-dependent opacities and excitation and ionization energies are included. As the H-rich envelope is accelerated off the stellar core, the gap between envelope and core is approximated by a vacuum, filled with radiation. Across the vacuum, the luminosity is conserved and the anisotropy of the radiation is considered as well as the solid angle subtended by the remnant star at the inner surface of the H-rich envelope. Spherical symmetry and the diffusion approximation are assumed

Numerical modelling of the classical nova outburst

A mechanism is described that promises to explain how nova outbursts take place on white dwarf of 1 solar mass or less and for accretion rates of 4 x 10 to the -10 solar mass/yr or greater

Simulating Tsunami Inundation and Soil Response in a Large Centrifuge.

Tsunamis are rare, extreme events and cause significant damage to coastal infrastructure, which is often exacerbated by soil instability surrounding the structures. Simulating tsunamis in a laboratory setting is important to further understand soil instability induced by tsunami inundation processes. Laboratory simulations are difficult because the scale of such processes is very large, hence dynamic similitude cannot be achieved for small-scale models in traditional water-wave-tank facilities. The ability to control the body force in a centrifuge environment considerably reduces the mismatch in dynamic similitude. We review dynamic similitudes under a centrifuge condition for a fluid domain and a soil domain. A novel centrifuge apparatus specifically designed for exploring the physics of a tsunami-like flow on a soil bed is used to perform experiments. The present 1:40 model represents the equivalent geometric scale of a prototype soil field of 9.6 m deep, 21 m long, and 14.6 m wide. A laboratory facility capable of creating such conditions under the normal gravitational condition does not exist. With the use of a centrifuge, we are now able to simulate and measure tsunami-like loading with sufficiently high water pressure and flow velocities. The pressures and flow velocities in the model are identical to those of the prototype yielding realistic conditions of flow-soil interaction

Uniaxial and biaxial soft deformations of nematic elastomers

We give a geometric interpretation of the soft elastic deformation modes of nematic elastomers, with explicit examples, for both uniaxial and biaxial nematic order. We show the importance of body rotations in this non-classical elasticity and how the invariance under rotations of the reference and target states gives soft elasticity (the Golubovic and Lubensky theorem). The role of rotations makes the Polar Decomposition Theorem vital for decomposing general deformations into body rotations and symmetric strains. The role of the square roots of tensors is discussed in this context and that of finding explicit forms for soft deformations (the approach of Olmsted).Comment: 10 pages, 10 figures, RevTex, AmsTe

The boundary layer of VW Hyi in quiescence

In this letter, we suggest that the missing boundary layer luminosity of dwarf novae in quiescence is released mainly in the ultraviolet (UV) as the second component commonly identified in the far ultraviolet (FUV) as the "accretion belt". We present the well-studied SU UMa-type system VW Hyi in detail as a prototype for such a scenario. We consider detailed multiwavelength observations and in particular the recent FUSE observations of VW Hyi which confirm the presence of a second component (the "accretion belt") in the FUV spectrum of VW Hyi in quiescence. The temperature (50,000K) and rotational velocity (> 3,000km/s) of this second FUV component are entirely consistent with the optically thick region (tau = 1) located just at the outer edge of optically thin boundary layer in the simulations of Popham (1999). This second component contributes 20% of the FUV flux, therefore implying a boundary layer luminosity: $L_{BL} = 2 \times (0.2 \times L_{UV} + L_{X-ray}) = 0.6 \times L_{disc}$, while the theory (Klu\'zniak 1987) predicts, for the rotation rate of VW Hyi's WD, $L_{BL} \approx 0.77 L_{disc}$. The remaining accretion energy ($<0.1 L_{acc}$) is apparently advected into the star as expected for optically thin advection dominated boundary layers. This scenario is consistent with the recent simultaneous X-ray and UV observations of VW Hyi by (Pandel, C\'ordova & Howell 2003), from which we deduced here that the alpha viscosity parameter in the boundary layer region must be as small as $\alpha \approx 0.004$.Comment: 4 page

Earthquake Input Motions for Physical Model Tests

The results from several dynamic centrifuge experiments are presented in this paper; the experiments were performed as part of a study to assess the influence of local site conditions on earthquake ground motions. Medium dense dry sand and saturated soft clay models were subjected to the accelerogram recorded at Santa Cruz during the 1989 Loma Prieta Earthquake. Scaled versions of the input motion were used to shake the soil models; in addition, different time steps were used in order to study the effects of frequency content of the input motion. The results confirm that the characteristics of the input motion and the soil model combine to have important effects on soil response. This fact must be recognized when selecting input motions for physical model tests