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

On Identification of Bayesian DSGE Models

In recent years there has been increasing concern about the identification of parameters in dynamic stochastic general equilibrium (DSGE) models. Given the structure of DSGE models it may be difficult to determine whether a parameter is identified. For the researcher using Bayesian methods, a lack of identification may not be evident since the posterior of a parameter of interest may differ from its prior even if the parameter is unidentified. We show that this can be the case even if the priors assumed on the structural parameters are independent. We suggest two Bayesian identification indicators that do not suffer from this difficulty and are relatively easy to compute. The first applies to DSGE models where the parameters can be partitioned into those that are known to be identified and the rest where it is not known whether they are identified. In such cases the marginal posterior of an unidentified parameter will equal the posterior expectation of the prior for that parameter conditional on the identified parameters. The second indicator is more generally applicable and considers the rate at which the posterior precision gets updated as the sample size (T) is increased. For identified parameters the posterior precision rises with T, whilst for an unidentified parameter its posterior precision may be updated but its rate of update will be slower than T. This result assumes that the identified parameters are ãT-consistent, but similar differential rates of updates for identified and unidentified parameters can be established in the case of super consistent estimators. These results are illustrated by means of simple DSGE models.Bayesian identification, DSGE models, posterior updating, New Keynesian Phillips Curve

Oligonucleotide sequences forming short self-complimentary hairpins can expedite the down-regulation of Coprinopsis cinerea genes

Gene silencing in fungi is often induced by dsRNA hairpin forming constructs the preparation of which can require multiple cloning steps. To simplify gene silencing in the filamentous fungi we have evaluated a high throughput cloning method for target sequences using the homobasidiomycete Coprinopsis cinerea, the GFP reporter and a commercially available vector system. The pSUPER RNAi System™, which was developed for mammalian experiments, exploits the human H1 Polymerase III (Pol III) RNA gene promoter and expedites cloning/expression of specific user-defined oligonucleotide sequences to form short self-complimentary hairpins. Transformation of C. cinerea with pSUPER constructs harboring specific oligonucleotides (19 nt stem length) enabled recovery of transformants with reduced transcripts of the GFP transgene, that were less fluorescent in protein assays and microscopic phenotypes. This technological advance should expedite functional genomic studies in C. cinerea and has wider potential for utility in other homobasidiomycete and filamentous fungi

BPS states of D=4 N=1 supersymmetry

We find the combinations of momentum and domain-wall charges corresponding to BPS states preserving 1/4, 1/2 or 3/4 of D=4 N=1 supersymmetry, and we show how the supersymmetry algebra implies their stability. These states form the boundary of the convex cone associated with the Jordan algebra of $4\times 4$ real symmetric matrices, and we explore some implications of the associated geometry. For the Wess-Zumino model we derive the conditions for preservation of 1/4 supersymmetry when one of two parallel domain-walls is rotated and in addition show that this model does not admit any classical configurations with 3/4 supersymmetry. Our analysis also provides information about BPS states of N=1 D=4 anti-de Sitter supersymmetry.Comment: Latex, 27 pages. Various corrections and improvements including an expanded discussion on BPS states in ad

Census Snapshot: Illinois

Using data from the U.S. Census Bureau, this report provides demographic and economic information about same-sex couples and same-sex couples raising children in Illinois. We compare same-sex "unmarried partners," which the Census Bureau defines as an unmarried couple who "shares living quarters and has a close personal relationship," to different-sex married couples in Illinois

Public School Choice and Desegregation in Arkansas

Public school choice is an umbrella term for policies that allow students to enroll in a public school other than their residentially-assigned school. Public school choice, also called openenrollment, is typically divided into two categories: intra-district choice, transfers to schools in the same district, and inter-district choice, transfers to schools in other districts