Lie symmetry analysis and exact solutions of the quasi-geostrophic two-layer problem

The quasi-geostrophic two-layer model is of superior interest in dynamic meteorology since it is one of the easiest ways to study baroclinic processes in geophysical fluid dynamics. The complete set of point symmetries of the two-layer equations is determined. An optimal set of one- and two-dimensional inequivalent subalgebras of the maximal Lie invariance algebra is constructed. On the basis of these subalgebras we exhaustively carry out group-invariant reduction and compute various classes of exact solutions. Where possible, reference to the physical meaning of the exact solutions is given. In particular, the well-known baroclinic Rossby wave solutions in the two-layer model are rediscovered.Comment: Extended version, 24 pages, 1 figur

Relaxation time spectrum of low-energy excitations in one- and two-dimensional materials with charge or spin density waves

The long-time thermal relaxation of (TMTTF)$_2$Br, Sr$_{14}$Cu$_{24}$O$_{41}$ and Sr$_2$Ca$_{12}$Cu$_{24}$O$_{41}$ single crystals at temperatures below 1 K and magnetic field up to 10 T is investigated. The data allow us to determine the relaxation time spectrum of the low energy excitations caused by the charge-density wave (CDW) or spin-density wave (SDW). The relaxation time is mainly determined by a thermal activated process for all investigated materials. The maximum relaxation time increases with increasing magnetic field. The distribution of barrier heights corresponds to one or two Gaussian functions. The doping of Sr$_{14-x}$Ca$_{x}$Cu$_{24}$O$_{41}$ with Ca leads to a drastic shift of the relaxation time spectrum to longer time. The maximum relaxation time changes from 50 s (x = 0) to 3000 s (x = 12) at 0.1 K and 10 T. The observed thermal relaxation at x=12 clearly indicates the formation of the SDW ground state at low temperatures

Multi-photon effects in energy losses spectra

Effect of radiation of many photons by a single electron traversing a target is discussed. When the summary energy of emitted photons (the energy losses spectrum) is measured only, the photon spectrum is distorted comparing with the photon spectrum in one interaction. Influence of this effect is discussed for the cases (1) bremsstrahlung (described by Bethe-Heitler formula), (2) the strong Landau-Pomeranchuk-Migdal effect and (3) transition radiation. Qualitative picture of the phenomenon is discussed in detail. Comparison with the recent SLAC experiment in relatively thick target (2.7% of the radiation length), where the effect of emission of many photons by a projectile is very essential, shows perfect agreement of the theory and data.Comment: LaTeX2.09, 19 pages, 5 PostScript figure

Theoretical model of structure-dependent conductance crossover in disordered carbon

We analyze the effects of sp^2/sp^3 bond-aspect ratio on the transport properties of amorphous carbon quasi-1D structures where structural disorder varies in a very non-linear manner with the effective bandgap. Using a tight-binding approach the calculated electron transmission showed a high probability over a wide region around the Fermi-level for sp^2-rich carbon and also distinct peaks close to the band edges for sp^3-rich carbon structures. This model shows a sharp rise of the structure resistance with the increase of sp^3C % followed by saturation in the wide bandgap regime for carbon superlattice-like structures and suggests the tuneable characteristic time of carbon-based devices.Comment: 6 pages, 6 figure

Tolerance of human embryonic stem cell derived islet progenitor cells to vitrification-relevant solutions

We have previously shown that human embryonic stem cell derived islet progenitors (hESC-IPs), encapsulated inside an immunoprotective device, mature in vivo and ameliorate diabetes in mice. The ability to cryopreserve hESC-IPs preloaded in these devices would enhance consistency and portability, but traditional ‘slow freezing’ methods did not work well for cells encapsulated in the device. Vitrification is an attractive alternative cryopreservation approach. To assess the tolerance of hESC-IPs to vitrification relevant conditions, we here are reporting cell survival following excursions in tonicity, exposure to fifteen 40% v/v combinations of 4 cryoprotectants, and varied methods for addition and elution. We find that 78% survival is achieved using a protocol in which cells are abruptly (in one step) exposed to a solution containing 10% v/v each dimethyl sulfoxide, propylene glycol, ethylene glycol, and glycerol on ice, and eluted step-wise with DPBS + 0.5 M sucrose at 37 °C. Importantly, the hESC-IPs also maintain expression of the critical islet progenitor markers PDX-1, NKX6.1, NGN3 and NEURO-D1. Thus, hESC-IPs exhibit robust tolerance to exposure to vitrification solutions in relevant conditions