The problem of persistence in simple diffusion with stochastic initial conditions is discussed. The calculated persistence exponent, which is at variance with that obtained by Majumdar et al [Phys Rev Lett 77, 2867, (1996)] and Derrida et al [Phys Rev Lett 77, 2871,(1996)] numerically, is discussed along with a critical analysis of accepted results. The approach is further extended to the case of advection of a passive scalar by a stochastic velocity field to show that the persistence exponent changes continuously as the velocity field is switched on.

Solar energy conversion through design and development of dye-sensitizedTiO2 semiconductor solar cell has been a subject of intense research inrecent years. The most efficient cells of this type, based onRu(dcbpy)2(NCS)2 [dcbpy (4,4„S-dicarboxy-2,2„S-bipyridine)] (or Ru N3)sensitized nanocrystalline TiO2 thin films, can achieve a solar toelectric power conversion efficiency of about 10%. Recently we areinvolved in design and developing of suitable dye molecule with suitableanchoring group and useful molecular structure, and also synthesis of newtype of nanoparticles and quantum dot materials and then studyinginterfacial electron transfer dynamics of the dye-nanoparticle systems byfast and ultrafast spectroscopic techniques. It has been observed that dyemolecules with strong anchoring group helps ultrafast electron injection,however it also facilitate fast back electron transfer (BET), which isunwanted for higher conversion efficiency. It has been realized thatstrong coupling dyes not only inject electron in the conduction band butalso in to the surface states of nanoparticles. It is well known that oncethe electron injected into the surface states cannot be use energyconversion purpose. From our investigation we have shown that dyemolecules with twisted intramolecular charge transfer (TICT) state can bemore efficient electron injector to the conduction band of nanoparticlesas compared to that of dyes with no TICT states. We have also synthesizednew type of nanoparticles by modifying the surface of it with sodiumdodecyl benzene sulphonate (DBS), TOPO and benzophenone. Our measurementshave shown that in dye-nanoparticle systems BET reaction is much slower onmodified surface as compared to that on bare surface. It has been observedthat charge recombination reaction is very slow on dye-sensitized quantumdot semiconductor materials.