Local and occupation time of a particle diffusing in a random medium

We consider a particle moving in a one-dimensional potential which has a symmetric deterministic part and a quenched random part. We study analytically the probability distributions of the local time (spent by the particle around its mean value) and the occupation time (spent above its mean value) within an observation time window of size t. In the absence of quenched randomness, these distributions have three typical asymptotic behaviors depending on whether the deterministic potential is unstable, stable, or flat. These asymptotic behaviors are shown to get drastically modified when the random part of the potential is switched on, leading to the loss of self-averaging and wide sample to sample fluctuations.     

Slow viscous flow through a membrane built up from porous cylindrical particles with an impermeable core

This paper concerns the slow viscous flow through an aggregate of concentric clusters of porous cylindrical particles with Happel boundary condition. An aggregate of clusters of porous cylindrical particles is considered as a hydro-dynamically equivalent to solid cylindrical core with concentric porous cylindrical shell. The Brinkman equation inside the porous cylindrical shell and the Stokes equation outside the porous cylindrical shell in their stream function formulations are used. The drag force acting on each porous cylindrical particle in a cell is evaluated. In certain limiting cases, drag force converges to pre-existing analytical results, such as, the drag on a porous circular cylinder and the drag on a solid cylinder in a Happel unit cell. Representative results are then discussed and presented in graphical forms. The hydrodynamic permeability of the membrane built up from porous particles is evaluated. The variation of hydrodynamic permeability with different parameters is graphically presented. Some new results are reported for flow pattern in the porous region. Being in resemblance with the model of colloid particles with a coating of porous layers due to adsorption phenomenon, results obtained through this model can be useful to study the membrane filtration process.     

Surface anchoring effect on guest–host ferroelectric liquid crystal response time – an electro-optical investigation

The effect is reported of surface anchoring on various electro-optical parameters of a pure ferroelectric liquid crystal (FLC) and five mixtures with different concentrations of dye. The Anthraquinone D5 dye was used as guest entity, whereas Felix 17-000 was used as host in this investigation. The presence of dye molecules in the FLC dramatically affects the electro-optical properties compared with those of the pure system. Electro-optical parameters such as spontaneous polarization and rotational viscosity not only change with the addition of dye but they are also strongly dependent on the concentration of dye in pure FLC. The effect of dye molecules on the anchoring energy of the pure FLC system was also investigated. Due to strong anchoring energy on FLC substrate, its effect on response time was also studied. An improvement in the contrast ratio after dye doping was observed. The value of spontaneous polarization increases due to addition of dye, suggesting that molecular alignment improves, which is very useful from the application point of view.     

Stereoselective Synthesis of β-Amino Ketones: A Three-Component Mannich-Type Reaction of Aromatic Aldehydes,Anilines, and Cyclohexanone Using Amberlyst-15

A three-component Mannich-type reaction of aromatic aldehydes, anilines, and cyclohexanone in the presence of Amberlyst-15 affords the corresponding β-amino ketones in good yields at room temperature. The conversion is highly diastereoselective, favoring the formation of anti-isomers.     

Novel Chiral,Sulfur-Containing Heteroarotinoids with Liquid Crystal Properties

Synthetic methods were developed to prepare ethyl (E)-4-[2-(3,4-dihydro-2-n-octyl-1-oxy-2H-1-benzothio-pyran-6-yl)-1-propenyl]benzoate ( 1 ) and ethyl (E)-4-[2-(3,4-dihydro-2-n-octyl-2H-1-benzothiopyran-6-yl)-1-propenyl]benzoate ( 10 ). These are the first examples of heteroarotinoids which possess properties of liquid crystals. The properties were evaluated using differential scanning calorimetry and by use of polarizing micrography. Both displayed textures which are typical of a smectic or cholesteric phase.