Non-Deterministic and Polynomial Time Problem Simulator

The Non-Deterministic and Polynomial Time Problem is a problem in combinatorial op-timization. Finding the quickest route for an object to travel through a list of cities and return to the starting city is the goal of this problem. Cities are listed, along with the dis-tance between each pair. It belongs to the category of computer problems known as NP-complete problems, for which no effective algorithmic solution has yet been discov-ered; at this time, there is no polynomial solution. In order to discover a near-optimal solution as quickly as possible, we attempted to tackle this extremely challenging prob-lem in this study utilizing a variety of heuristics, including Simulated Annealing and Ge-netic Algorithm. Using these sophisticated heuristic techniques, we at-tempt to depart from the local optimum

Active Brownian particles can mimic the pattern of the substrate

Active Brownian particles (ABPs) are termed out to be a successful way of modeling the moving microorganism on the substrate. In recent studies, it is shown that such organisms can sense the characteristics of the substrate. Motivated by such work, we studied the dynamics and the steady state of ABP moving on a substrate with space-dependent activity. On the substrate, some regions are marked as high in activity, and other regions are such that particles behave as passive Brownian particles. The system is studied in two dimensions with step, sigmoid, Gaussian and cone shape distribution of activity profile on the substrate. The whole interface of the activity profile is symmetrically divided into two regions. This lead to the flow of particles from the active region to the passive region. The final steady state of particle density profile, polarisation and flux very much follows the structure of the inhomogeneous activity and the density in high activity region is lower, maximum at the interface and nearly constant with mean density in the passive region. Further, the steady state density profile for various shapes and designs on two-dimensional substrates. Hence the collection of ABPs on an inhomogeneous substrate can mimic the inhomogeneity of the substrate

Ordering kinetics and steady states of XY-model with ferromagnetic and nematic interaction

The two-dimensions XY model, undergoes the Berezinskii Kosterlitz Thouless (BKT) transition through unbinding of defect pairs of opposite signs. When the interaction between spins is purely ferromagnetic, these defects have +-1 charge, whereas for pure nematic interaction between spins, they have charge +-1/2. Two-dimensional XY-model in the presence of both ferromagnetic and nematic interactions has been studied both theoretically and experimentally. In this paper, we have studied dynamics of defects in the presence of both ferromagnetic and nematic interactions on a square lattice. Varying the strength of ferromagnetic and nematic interactions, we have observed behavior of both integer and half integer defects and based on that we propose a phase diagram which exhibit three distinct regions in the phase diagram below the critical TBKT : polar phase, nematic phase and coexistence phase and a disordered regions above it. Also, for pure polar and pure nematic case, our results show that the exponent, for algebraic decay of number of defects with time, decays linearly with temperature