The effects of encodings in hard combinatorial optimization problems on the search for the minimum cost solutions have been studied. The issues related to the enrichment of low energy solutions and the smoothing of landscapes for the encoded problem has been examined. The dynamics of a shaken and poured sandpile have been investigated. The introduction of appropriate kinetic terms has been found to result in the asymptotic roughening of the interface.

The modified version of a conservative self-organized extremal model introduced by Pianegonda et. al. in the context of wealth distribution of the people in a society has been modified by the stochastic bipartite trading rule. Numerical analysis indicates that this model belongs to a new universality class.

To understand the fluctuations in non-equlibrium systems, having steady states, is one of the fundamental problems in Statistical Physics. Simple non-equilibrium model systems, e.g., mass transport models and driven lattice gases, are studied using numerical and analytical techniques with an aim to characterize a class of systems which can have a simple thermodynamic structure.

Chemotaxis motion of a single E.coli bacterium is being studied using numerical simulations and analytical techniques. A coarse grained model which differs from existing description of E.Coli movement has been developed. In another study a reaction diffusion model has been analyzed to describe features like molecular traffic control, i.e., channeling reactants and product molecules along different path ways which can greatly enhance the efficiency of the catalytic grain.

Theoretical analysis of the results of neutron scattering experiment performed on a quasi-two dimensional spin-1/2 ferromagnetic material {K2}Cu{F4} has been carried out based on the conventional semi-classical treatment involving a model of an ideal gas of vortices / anti-vortices corresponding to an anisotropic XY Heisenberg ferromagnet on a square lattice. The results show occurrence of negative values of the dynamical structure function in a large range of energy transfer encompassing the experimental range.

It has been found that the black holes which rotate around an axis do not allow non-zero configurations of massive Pauli-Fierz spin-2 or massive spin-½ fields in the region outside the black hole horizon. This result extends the known 'no-hair' theorems beyond spin-0 (scalar) and spin- 1 (vector) fields in de Sitter type space-times with a black hole.

The orthonormal loop states of SU(2) lattice gauge theory can be completely characterized by angular momentum quantum numbers. In the continuum weak coupling limit, the dynamics of lattice gauge theory is mainly governed by the non-linear magnetic field operator. Therefore, the magnetic field operator cannot be treated perturbatively like in the standard strong coupling expansion. In the above orthonormal loop basis this magnetic field operator has been shown to be 3nj Wigner coefficient. Diagonalization of this magnetic field operator or Wigner 3nj coefficients is relevant for the continuum limit of lattice gauge theory.

In Hilbert Schmidt operator formulation in Noncommutative Quantum Mechanics, the Connes spectral triplet is shown to arise naturally giving an algorithm for the computation of spectral distance in classical Hilbert space. Eventually the distance between pure and mixed states on the Quantum Hilbert space is also computed to establish a deep connection between entropy and geometry.

It has been shown that black hole thermodynamics were reasonably explained by a mean field theory type approach. The Ehrenfest scheme, as adapted for black holes, was found to be a successful scheme. The study of critical phenomena in this context further bolstered the validity of the mean field approximation. The analysis for charged AdS black holes in the context of AdS/CFT duality has been extended. The critical exponents estimated in this work strongly support the mean field analysis.

The generalized Riccati system has been studied and it is shown that for a specific value of the parameter the system admits a bilagrangian description. The dynamics has a node at the origin and it is a periodic for a parameter value much smaller than a critical value the dynamics, the origin being a centre. It is found that the solution changes from being periodic to aperiodic at a critical point which is independent of the initial conditions.

For light scattering from biomedical tissues, the possibility of distinguishing between normal and plasmodium falciparum infected red blood cells based on the small angle light scattering by RBC,s has been investigated. A possible method for discriminating infected RBC's from the healthy ones has been suggested.

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