Efficiency analysis of reaction rate calculation methods using analytical models I: The 2D sharp barrier

We analyze the efficiency of different methods for the calculation of reaction rates in the case of two simple analytical benchmark systems. Two classes of methods are considered: the first are based on the free energy calculation along a reaction coordinate and the calculation of the transmission coefficient, the second on the sampling of dynamical pathways. We give scaling rules for how this efficiency depends on barrier height and width, and we hand out simple optimization rules for the method-specific parameters. We show that the path sampling methods, using the transition interface sampling technique, become exceedingly more efficient than the others when the reaction coordinate is not the optimal one.Comment: 22 pages, 5 figure

Cosmology and thermodynamics of FRW universe with bulk viscous stiff fluid

We consider a cosmological model dominated by stiff fluid with a constant bulk viscosity. We classify all the possible cases of the universe predicted by the model and analyzing the scale factor, density as well as the curvature scalar. We find that when the dimensionless constant bulk viscous parameter is in the range $0 < \bar\zeta <6$ the model began with a Big Bang, and make a transition form the decelerating expansion epoch to an accelerating epoch, then tends to the de Sitter phase as $t\to \infty$. The transition into the accelerating epoch would be in the recent past, when $4<\bar\zeta<6.$ For $\bar\zeta>6$ the model doesn't have a Big Bang and suffered an increase in the fluid density and scalar curvature as the universe expands, which are eventually saturates as the scale factor $a \to \infty$ in the future. We have analyzed the model with statefinder diagnostics and find that the model is different from $\Lambda$CDM model but approaches $\Lambda$CDM point as $a \to \infty.$ We have also analyzed the status of the generalized second law of thermodynamics with apparent horizon as the boundary of the universe and found that the law is generally satisfied when $0 \leq \bar\zeta <6$ and for $\bar\zeta >6$ the law is satisfied when the scale factor is larger than a minimum value

Projective construction of the Zk\mathbb{Z}_k Read-Rezayi fractional quantum Hall states and their excitations on the torus geometry

Multilayer fractional quantum Hall wave functions can be used to construct the non-Abelian states of the $\mathbb{Z}_k$ Read-Rezayi series upon symmetrization over the layer index. Unfortunately, this construction does not yield the complete set of $\mathbb{Z}_k$ ground states on the torus. We develop an alternative projective construction of $\mathbb{Z}_k$ Read-Rezayi states that complements the existing one. On the multi-layer torus geometry, our construction consists of introducing twisted boundary conditions connecting the layers before performing the symmetrization. We give a comprehensive account of this construction for bosonic states, and numerically show that the full ground state and quasihole manifolds are recovered for all computationally accessible system sizes. Furthermore, we analyze the neutral excitation modes above the Moore-Read on the torus through an extensive exact diagonalization study. We show numerically that our construction can be used to obtain excellent approximations to these modes. Finally, we extend the new symmetrization scheme to the plane and sphere geometries.Comment: 19 pages, 9 figure

ICT: Vehicle for Educational Development and Social Transformation

The world has become a global village as a result of the information tsunami and knowledge explosion being experienced as a result of Information Communication and Technology (ICT). The industrialized nations are miles ahead of the developing countries as a result of the information revolution. Education is a process by which society transmits its values, norms, mores, and ethos to generation yet unborn across time and space. The medium of transmission cuts across formal, non-formal and informal settings. This paper examines the impact/roles of ICT on education as an agent of social transformation and the hindrances of developing countries such as Nigeria in adopting ICT to aid their educational development and transformation of the society. The interconnection between information, ICT and social transformations is succinctly discussed in this paper. Furthermore, the paper examines the relationship between ICT and education and suggests measures that can be taken in adopting the use of ICT in Nigeria as well as the crucial role of government and the educational sector in this regard. The paper concludes that ICT make a significant contribution to the educational development and the social transformation of the Nigerian society