Gas-surface scattering is speculated as a meaningful problem for understanding the physics of fractals. Fractal behaviour can be associated with a self-similar geometry on a solid surface. The interaction potential for a gas atom or molecule approaching the lattice depends primarily on local factors but a parametric dependence of the cross-section data on the fractal dimension can be conceived. Such a dependence on the self-similar character of a multi-centred target is more explicit when multiple scattering is included. Application of approximation schemes like the previously developed average wavefunction method to this problem is suggested.

The lattice gas automata (LGA) technique as an alternative to the partial differential equation (PDE) approach for studying dynamical processes, including those in reaction-diffusion systems, is reviewed. The LGA approach gained significance after the simulation of Navier-Stokes equation by Hardyet al (1976). In this approach, the dynamics of a system are simulated by constructing a microlattice on each node of which Boolean bits are associated with the presence or absence of particles indistinct velocity states. A complete description involves the composition of anelastic collision operator, areactive collision operator and apropagation operator. The Hardy, de Pazzis and Pomeau (HPP) model does not have the desired isotropy, but its subsequent modification in 1986, known as the Frisch, Hasselacher and Pomeau (FHP) model (Frischet al 1986), has been applied to a variety of nonequilibrium processes. Reaction-diffusion systems have been simulated in a manner analogous to the master equation approach in a continuum framework. The Boltzmann kinetic equation as well as the expected complex features at the macroscopic level are obtained in LGA simulations. An increasing trend is to use real numbers instead of Boolean bits for the velocity states. This gives the lattice Boltzmann (LB) model which is not only less noisy than LGA but also numerically superior to finite-difference approximations (FDAs) to PDEs. The most significant applications of LGA appear to be in the molecular-level understanding of reactive processes.

Fluorescence resonance energy transfer (FRET) is a popular tool to study equilibrium and dynamical properties of polymers and biopolymers in condensed phases and is now widely used in conjunction with single molecule spectroscopy. In the data analysis, one usually employs the Förster expression which predicts (l/R⁶) distance dependence of the energy transfer rate. However, critical analysis shows that this e_xpression can be of rather limited validity in many cases. We demonstrate this by explicitly considering a donor-acceptor system, polyfluorene (PF₆)-tetraphenylporphyrin (TPP), where the size of both donor and acceptor is comparable to the distance separating them. In such cases, one may expect much weaker distance (as l/R² or even weaker) dependence. We have also considered the case of energy transfer from a dye to a nanoparticle. Here we find l/R⁴ distance dependence at large separations, completely different from Förster. We also discuss recent application of FRET to study polymer conformational dynamics.

Optimal control theory is applied to obtain infrared laser pulses for selective vibrational excitation in a heteronuclear diatomic molecule. The problem of finding the optimized field is phrased as a maximization of a cost functional which depends on the laser field. A time dependent Gaussian factor is introduced in the field prior to evaluation of the cost functional for better field shape. Conjugate gradient method$^{21,24}$ is used for optimization of constructed cost functional. At each instant of time, the optimal electric field is calculated and used for the subsequent quantum dynamics, within the dipole approximation. The results are obtained using both Morse potential as well as potential energy obtained using ab initio calculations.

Controlling molecular energetics using laser pulses is exemplified for nuclear motion in two different diatomic systems. The problem of finding the optimized field for maximizing a desired quantum dynamical target is formulated using an iterative method. The method is applied for two diatomic systems, HF and OH. The power spectra of the fields and evolution of populations of different vibrational states during transitions are obtained.

The base pairing patterns in RNA structures are more versatile and completely different as compared to DNA. We present here results of ab-initio studies of structures and interaction energies of eight selected RNA base pairs reported in literature. Interaction energies, including BSSE correction, of hydrogen added crystal geometries of base pairs have been calculated at the HF/6-31G^∗∗ level. The structures and interaction energies of the base pairs in the crystal geometry are compared with those obtained after optimization of the base pairs. We find that the base pairs become more planar on full optimization. No change in the hydrogen bonding pattern is seen. It is expected that the inclusion of appropriate considerations of many of these aspects of RNA base pairing would significantly improve the accuracy of RNA secondary structure prediction.

Optimal control theory in combination with time-dependent quantum dynamics is employed to design laser pulses which can perform selective vibrational and rotational excitations in a heteronuclear diatomic system. We have applied the conjugate gradient method for the constrained optimization of a suitably designed functional incorporating the desired objectives and constraints. Laser pulses designed for several excitation processes of the $HF$ molecule were able to achieve predefined dynamical goals with almost 100% yield.