The dynamics of incomes and occupational pensions after retirement

This paper uses two waves of the UK Retirement Survey to look at how incomes change during retirement. We concentrate on men aged 65-69 and women aged 60-69 in 1988-89 and look at how their incomes change over the following five years. Overall, we find a considerable degree of stability in real incomes. We use the panel data to look at the incomes of widows before and after they are widowed and find that, for this group of relatively young widows, their low incomes are in large part determined by the fact that it tends to be the relatively poorer husbands who die among this age-group. Finally, we consider the most important component of private income — occupational pensions — separately. We find a strong relationship between pension level and the probability of indexation — pensions that start low are less likely than higher pensions to keep up with inflation.

Properties of mass-loading shocks, 2. Magnetohydrodynamics

The one-dimensional magnetohydrodynamics of shocked flows subjected to significant mass loading are considered. Recent observations at comets Giacobini-Zinner and Halley suggest that simple nonreacting MHD is an inappropriate description for active cometary bow shocks. The thickness of the observed cometary shock implies that mass loading represents an important dynamical process within the shock itself, thereby requiring that the Rankine-Hugoniot condition for the mass flux possess a source term. In a formal sense, this renders mass-loading shocks qualitatively similar to combustion shocks, except that mass loading induces the shocked flow to shear. Nevertheless, a large class of stable shocks exist, identified by means of the Lax conditions appropriate to MHD. Thus mass-loading shocks represent a new and interesting class of shocks, which, although found frequently in the solar system, both at the head of comets and, under suitable conditions, upsteam of weakly magnetized and nonmagnetized planets, has not been discussed in any detail. Owing to the shearing of the flow, mass-loading shocks can behave like switch-on shocks regardless of the magnitude of the plasma beta. Thus the behavior of the magnetic field in mass-loading shocks is significantly different from that occurring in nonreacting classical MHD shocks. It is demonstrated that there exist two types of mass-loading fronts for which no classical MHD analogue exists, these being the fast and slow compound mass-loading shocks. These shocks are characterized by an initial deceleration of the fluid flow to either the fast or the slow magnetosonic speed followed by an isentropic expansion to the final decelerated downstream state. Thus these transitions take the flow from a supersonic to a supersonic, although decelerated, downstream state, unlike shocks which occur in classical MHD or gasdynamics. It is possible that such structures have been observed during the Giotto-Halley encounter, and a brief discussion of the appropriate Halley parameters is therefore given, together with a short discussion of the determination of the shock normal from observations. A further interesting new form of mass-loading shock is the “slow-intermediate” shock, a stable shock which possesses many of the properties of intermediate MHD shocks yet which propagates like a slow mode MHD shock. An important property of mass-loading shocks is the large parameter regime (compared with classical MHD) which does not admit simple or stable transitions from a given upstream to a downstream state. This suggests that it is often necessary to construct compound structures consisting of shocks, slip waves, rarefactions, and fast and slow compound waves in order to connect given upstream and downstream states. Thus the Riemann problem is significantly different from that of classical MHD

Mass-loading and parallel magnetized shocks

Recent observations at comets Giacobini-Zinner and Halley suggest that simple non-reacting gas dynamics or MHD is an inappropriate description for the bow shock. The thickness of the observed (sub)shock implies that mass-loading is an important dynamical process within the shock itself, thereby requiring that the Rankine-Hugoniot conditions possess source terms. This leads to shocks with properties similar to those of combustion shocks. We consider parallel magnetized shocks subjected to mass-loading, describe some properties which distinguish them from classical MHD parallel shocks, and establish the existence of a new kind of MHD compound shock. These results will be of importance both to observations and numerical simulations of the comet-solar wind interaction