Can an odd number of fermions be created due to chiral anomaly?

We describe a possibility of creation of an odd number of fractionally charged fermions in 1+1 dimensional Abelian Higgs model. We point out that for 1+1 dimensions this process does not violate any symmetries of the theory, nor makes it mathematically inconsistent. We construct the proper definition of the fermionic determinant in this model and underline its non-trivial features that are of importance for realistic 3+1 dimensional models with fermion number violation.Comment: 12 pages revtex, 2 figure

Numerical modelling of a fast pyrolysis process in a bubbling fluidized bed reactor

In this study, the Eulerian-Granular approach is applied to simulate a fast pyrolysis bubbling fluidized bed reactor. Fast pyrolysis converts biomass to bio-products through thermochemical conversion in absence of oxygen. The aim of this study is to employ a numerical framework for simulation of the fast pyrolysis process and extend this to more complex reactor geometries. The framework first needs to be validated and this was accomplished by modelling a lab-scale pyrolysis fluidized bed reactor in 2-D and comparing with published data. A multi-phase CFD model has been employed to obtain clearer insights into the physical phenomena associated with flow dynamics and heat transfer, and by extension the impact on reaction rates. Biomass thermally decomposes to solid, condensable and non-condensable and therefore a multi-fluid model is used. A simplified reaction model is sued where the many components are grouped into a solid reacting phase, condensable/non-condensable phase, and non-reacting solid phase (the heat carrier). The biomass decomposition is simplified to four reaction mechanisms based on the thermal decomposition of cellulose. A time-splitting method is used for coupling of multi-fluid model and reaction rates. A good agreement is witnessed in the products yield between the CFD simulation and the experiment

Energy Distribution in f(R) Gravity

The well-known energy problem is discussed in f(R) theory of gravity. We use the generalized Landau-Lifshitz energy-momentum complex in the framework of metric f(R) gravity to evaluate the energy density of plane symmetric solutions for some general f(R) models. In particular, this quantity is found for some popular choices of f(R) models. The constant scalar curvature condition and the stability condition for these models are also discussed. Further, we investigate the energy distribution of cosmic string spacetime.Comment: 15 pages, accepted for publication in Gen. Relativ. & Gra

A rr-mode in a magnetic rotating spherical layer: application to neutron stars

The impact of the combination of rotation and magnetic fields on oscillations of stellar fluids is still not well known theoretically. It mixes Alfv\'en and inertial waves. Neutron stars are a place where both effects may be at work. We wish to decipher the solution of this problem in the context of $r$-modes instability in neutron stars, as it appears when these modes are coupled to gravitational radiation. We consider a rotating spherical shell filled with a viscous fluid but of infinite electrical conductivity and analyze propagation of modal perturbations when a dipolar magnetic field is bathing the fluid layer. We perform an extensive numerical analysis and find that the $m=2$ $r$-mode oscillation is influenced by the magnetic field when the Lehnert number (ratio of Alfv\'en speed to rotation speed) exceeds a value proportional to the one-fourth power of the Ekman number (non-dimensional measure of viscosity). This scaling is interpreted as the coincidence of the width of internal shear layers of inertial modes and the wavelength of the Alfv\'en waves. Applied to the case of rotating magnetic neutron stars, we find that dipolar magnetic fields above $10^{14}$ G are necessary to perturb the $r$-modes instability.Comment: 9 pages, 6 figures, to appear in Monthly Notices of RA