H\"{o}lder continuity of solutions to the kinematic dynamo equations

We study the propagation of regularity of solutions to a three dimensional system of linear parabolic PDE known as the kinematic dynamo equations. The divergence free drift velocity is assumed to be at the critical regularity level with respect to the natural scaling of the equations.Comment: 10 page

Pseudo-transient computational fluid dynamics analysis of an underbonnet compartment during thermal soak

Underbonnet simulations are proving to be crucially important within a vehicle development programme, reducing test work and time-to-market. While computational fluid dynamics (CFD) simulations of steady forced flows have been demonstrated to be reliable, studies of transient convective flows in engine compartments are not yet carried out owing to high computing demands and lack of validated work. The present work assesses the practical feasibility of applying the CFD tool at the initial stage of a vehicle development programme for investigating the thermally driven flow in an engine bay under thermal soak. A computation procedure that enables pseudo time-marching CFD simulations to be performed with significantly reduced central processing unit (CPU) time usage is proposed. The methodology was initially tested on simple geometries and then implemented for investigating a simplified half-scale underbonnet compartment. The numerical results are compared with experimental data taken with thermocouples and with particle image velocimetry (PIV). The novel computation methodology is successful in efficiently providing detailed and time-accurate time-dependent thermal and flow predictions. Its application will extend the use of the CFD tool for transient investigations, enabling improvements to the component packaging of engine bays and the refinement of thermal management strategies with reduced need for in-territory testing

Critical Phenomena in Head-on Collisions of Neutron Stars

We found type I critical collapses of compact objects modeled by a polytropic equation of state (EOS) with polytropic index $\Gamma=2$ without the ultra-relativistic assumption. The object is formed in head-on collisions of neutron stars. Further we showed that the critical collapse can occur due to a change of the EOS, without fine tuning of initial data. This opens the possibility that a neutron star like compact object, not just those formed in a collision, may undergo a critical collapse in processes which slowly change the EOS, such as cooling.Comment: 4 pages,6 figures, 15 reference

Concave Consumption Function under Borrowing Constraints

This paper analyzes the optimal consumption behavior of a consumer who faces uninsurable labor income risk and borrowing constraints. In particular, it provides conditions under which the decision rule for consumption is a concave function of existing assets. The current study presents two main findings. First, it is shown that the consumption function is concave if the period utility function is drawn from the HARA class and has either strictly positive or zero third derivative. Second, it is shown that the same result can be obtained for certain period utility functions that are not in the HARA class.Consumption function, borrowing constraints, precautionary saving