Correspondence of phase transition points and singularities of thermodynamic geometry of black holes

We explore a formulation of thermodynamic geometry of black holes and prove that the divergent points of the specific heat correspond exactly to the singularities of the thermodynamic curvature. We investigate this correspondence for different types of black holes. This formulation can also be applied to an arbitrary thermodynamic system.Comment: 10 pages, 4 figures, typos fixed, references adde

Non-Abelian Aharonov-Bohm effect with the time-dependent gauge fields

We investigate the non-Abelian Aharonov-Bohm (AB) effect for time-dependent gauge fields. We prove that the non-Abelian AB phase shift related to time-dependent gauge fields, in which the electric and magnetic fields are written in the adjoint representation of $SU(N)$ generators, vanishes up to the first order expansion of the phase factor. Therefore, the flux quantization in a superconductor ring does not appear in the time-dependent Abelian or non-Abelian AB effect.Comment: 4 page

Diffusivities bounds in the presence of Weyl corrections

In this paper, we investigate the behavior of the thermoelectric DC conductivities in the presence of Weyl corrections with momentum dissipation in the incoherent limit. Moreover, we compute the butterfly velocity and study the charge and energy diffusion with broken translational symmetry. Our results show that the Weyl coupling $\gamma$, violates the bounds on the charge and energy diffusivity. It is also shown that the Weyl corrections violate the bound on the DC electrical conductivity in the incoherent limit.Comment: v4: The appendix D and E were adde

Multiscale modelling of biorefineries

Current fuel ethanol research deals with process engineering trends for improving the efficiency of bioethanol production. This thesis is devoted to modelling and optimisation of the lignocellulosic to bioethanol conversion process with a special emphasis on pretreatment and enzymatic hydrolysis units. The first part of the thesis is devoted to the lignocellulosic biomass pretreatment process. A multiscale model for a pretreatment process is developed. This considers both the chemical and physical natures of the process. A new mechanism for hydrolysis of hemicellulose is proposed in which the reactivity is function of position in the hemicellulose chain and all the bonds with same position undergo breakage at the same time. A method to find the optimum chip size for pretreatment has been developed. We show that with the proposed optimization method, an average saving equivalent to a 5% improvement in the yield of biomass to ethanol conversion process can be achieved. In the second part of this thesis a new approach to consider the evolution of cellulose chain length during the enzymatic hydrolysis by endo- and exoglucanase is developed. This employs a population balance approach. Having established the models for the action of endo- and exoglucanase, a universal model for cellulose hydrolysis at the biomass surface and inside the particle is developed. An experimental procedure to locate unknown parameters in the holistic model is proposed. The third part of this thesis integrates the models developed into a rigorous mass and energy balances of typical biorefinery. It was found that, most of the energy input is for pretreatment and distillation. Two process modifications are considered capable of reducing the energy requirement for pretreatment and distillation by almost 50%. It is shown that with process optimization and some alternative design it is possible to save 21% of plant energy requirement. Finally, the novel features and advantages of the work are discussed, as are potential areas for future research

A new continuum based non-linear finite element formulation for modeling of dynamic response of deep water riser behavior

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The principal objective of this investigation is to develop a nonlinear continuum based finite element formulation to examine dynamic response of flexible riser structures with large displacement and large rotation. Updated Lagrangian incremental approach together with the 2nd Piola-Kirchhoff stress tensor and the Green-Lagrange strain tensor is employed to derive the nonlinear finite element formulation. The 2nd Piola-Kirchhoff stress and the Green-Lagrange strain tensors are energy conjugates. These two Lagrangian tensors are not affected by rigid body rotations. Thus, they are used to describe the equilibrium equation of the body independent of rigid rotations. While the current configuration in Updated Lagrangian incremental approach is unknown, the resulting equation becomes strongly nonlinear and has to be modified to a linearized form. The main contribution of this work is to obtain a modified linearization method during development of incremental Updated Lagrangian formulation for large displacement and large rotation analysis of riser structures. For this purpose, the Green-Lagrange strain and the 2nd Piola-Kirchhoff stress tensors are decomposed into two second-order six termed functions of through-thethickness parameters. This decomposition makes it possible to explicitly account for the nonlinearities in the direction along the riser thickness, as well. It is noted that using this linearization scheme avoids inaccuracies normally associated with other linearization schemes. The effects of buoyancy force, riser-seabed interaction as well as steady-state current loading are considered in the finite element solution for riser structure response. An efficient riser problem fluid-solid interaction Algorithm is also developed to maintain the quality of the mesh in the vicinity of the riser surface during riser and fluid mesh movements. To avoid distortions in the fluid mesh two different approaches are proposed to modify fluid mesh movement governing elasticity equation matrices values; 1) taking the element volume into account 2) taking both element volume and distance between riser centre and element centre into account. The formulation has been implemented in a nonlinear finite element code and the results are compared with those obtained from other schemes reported in the literature