Fractal index, central charge and fractons

We introduce the notion of fractal index associated with the universal class $h$ of particles or quasiparticles, termed fractons, which obey specific fractal statistics. A connection between fractons and conformal field theory(CFT)-quasiparticles is established taking into account the central charge $c[\nu]$ and the particle-hole duality $\nu\longleftrightarrow\frac{1}{\nu}$, for integer-value $\nu$ of the statistical parameter. In this way, we derive the Fermi velocity in terms of the central charge as $v\sim\frac{c[\nu]}{\nu+1}$. The Hausdorff dimension $h$ which labelled the universal classes of particles and the conformal anomaly are therefore related. Following another route, we also established a connection between Rogers dilogarithm function, Farey series of rational numbers and the Hausdorff dimension.Comment: latex, 12 pages, To appear in Mod. Phys. Lett. A (2000

Nonlinear elastic model for faceting of vesicles with soft grain boundaries

We use an elastic model to explore faceting of solid-wall vesicles with elastic heterogeneities. We show that faceting occurs in regions where the vesicle wall is softer, such as areas of reduced wall thicknesses or concentrated in crystalline defects. The elastic heterogeneities are modeled as a second component with reduced elastic parameters. Using simulated annealing Monte Carlo simulations we obtain the vesicle shape by optimizing the distributions of facets and boundaries. Our model allows us to reduce the effects of the residual stress generated by crystalline defects, and reveals a robust faceting mechanism into polyhedra other than the icosahedron.Comment: 4.5 pages, 4 figure

Electron Transfer Reaction Through an Adsorbed Layer

We consider electron transfer from a redox to an electrode through and adsorbed intermediate. The formalism is developed to cover all regimes of coverage factor, from lone adsorbate to monolayer regime. The randomness in the distribution of adsorbates is handled using coherent potential approximation. We give current-overpotential profile for all coverage regimes. We explictly analyse the low and high coverage regimes by supplementing with DOS profile for adsorbate in both weakly coupled and strongly coupled sector. The prominence of bonding and anti-bonding states in the strongly coupled adsorbates at low coverage gives rise to saddle point behaviour in current-overpotential profile. We were able to recover the marcus inverted region at low coverage and the traditional direct electron transfer behaviour at high coverage

Cusp Disruption in Minor Mergers

We present 0.55 x 10^6 particle simulations of the accretion of high-density dwarf galaxies by low-density giant galaxies, using models that contain both power-law central density cusps and point masses representing supermassive black holes. The cusp of the dwarf galaxy is disrupted during the merger, producing a remnant with a central density that is only slightly higher than that of the giant galaxy initially. Removing the black hole from the giant galaxy allows the dwarf galaxy to remain intact and leads to a remnant with a high central density, contrary to what is observed. Our results support the hypothesis that the persistence of low-density cores in giant galaxies is a consequence of supermassive black holes.Comment: 5 pages, 2 postscript figures, uses emulateapj.sty. Accepted for publication in The Astrophysical Journal Letter

Zeta Potential of Modified Multi-walled Carbon Nanotubes in Presence of poly (vinyl alcohol) Hydrogel

The main objective of this study is investigate the behavior of the Zeta Potential of the MWCNT modified with SDS(Sodium Dodecyl Sulfate) and CTAB(Cetyl Tetraethyl Ammonium Bromide) in presence of PVA. Full hydrolyzed PVA was used. As a result, adding PVA in the CNT solution led to decrease the Zeta Potential. The Zeta Potential of suspended colloid varied from 42.00mV to 6.48mV and -45.00mV to -6.4mV at 1.5% concentration of PVA; according with the changing pH, the Zeta Potential dropped to near zero at pH 3 and 11. The pH and PVA has strong influence in the reduction of ZP of MWCNT solution. MWCNT-PVA solution with 33.30mV, -35.69mV at 0.01% of PVA was exposed under AC field; a uniform coat was obtained, with the SDS-MWCNT-PVA solution.National Natural Science Foundation of China Project (Grant No.51073024), the Royal Society-NSFC international joint project (Grant No.51111130207) and Beijing Municipal Science and Technology Plan Projects (No. Z111103066611005)