Dispersive and diffusive-dispersive shock waves for nonconvex conservation laws

We consider two physically and mathematically distinct regularization mechanisms of scalar hyperbolic conservation laws. When the flux is convex, the combination of diffusion and dispersion are known to give rise to monotonic and oscillatory traveling waves that approximate shock waves. The zero-diffusion limits of these traveling waves are dynamically expanding dispersive shock waves (DSWs). A richer set of wave solutions can be found when the flux is non-convex. This review compares the structure of solutions of Riemann problems for a conservation law with non-convex, cubic flux regularized by two different mechanisms: 1) dispersion in the modified Korteweg--de Vries (mKdV) equation; and 2) a combination of diffusion and dispersion in the mKdV-Burgers equation. In the first case, the possible dynamics involve two qualitatively different types of DSWs, rarefaction waves (RWs) and kinks (monotonic fronts). In the second case, in addition to RWs, there are traveling wave solutions approximating both classical (Lax) and non-classical (undercompressive) shock waves. Despite the singular nature of the zero-diffusion limit and rather differing analytical approaches employed in the descriptions of dispersive and diffusive-dispersive regularization, the resulting comparison of the two cases reveals a number of striking parallels. In contrast to the case of convex flux, the mKdVB to mKdV mapping is not one-to-one. The mKdV kink solution is identified as an undercompressive DSW. Other prominent features, such as shock-rarefactions, also find their purely dispersive counterparts involving special contact DSWs, which exhibit features analogous to contact discontinuities. This review describes an important link between two major areas of applied mathematics, hyperbolic conservation laws and nonlinear dispersive waves.Comment: Revision from v2; 57 pages, 19 figure

Optical Observations of PSR J0205+6449

PSR J0205+6449 is a X-ray and radio pulsar in supernova remnant 3C 58. We report on observations of the central region of 3C 58 using the 4.2-m William Herschel Telescope with the intention of identifying the optical counterpart of PSR J0205+6449 and characterising its pulsar wind nebula. Around the pulsar position we identified extended emission with a magnitude of B = 23 \fm 97 \pm 0.10, V = 22 \fm 95 \pm 0.05 and R = 22 \fm 15 \pm 0.03 consistent with a pulsar wind nebula. From the R-band image we identified three knots with $m_R$ = 24 \fm 08 \pm 0.07 (o1), 24 \fm 15 \pm 0.07 (o2) and 24 \fm 24 \pm 0.08 (o3). We confirm the presence of an optical pulsar wind nebula around PSR J0205+6449 and give an upper limit of $m_R \approx$ 24 for the optical magnitude of the pulsar. Furthermore we make the tentative suggestion that our object o1, with an $m_R \approx$ 24.08 is the optical counterpart. If confirmed the pulsar would have an $L_R/L_x\approx 0.004$ and an optical efficiency of about 5% of the Crab pulsar. Such a low efficiency is more consistent with the characteristic age of the pulsar rather than that of SN 1181.Comment: The paper contains 3 figures and 3 tables, accepted for publication in MNRA

Combustion of liquid sprays at high pressures

The combustion of pressure atomized fuel sprays in high pressure stagnant air was studied. Measurements were made of flame and spray boundaries at pressures in the range 0.1-9 MPa for methanol and n-pentane. At the higher test pressure levels, critical phenomena are important. The experiments are compared with theoretical predictions based on a locally homogeneous two-phase flow model. The theory correctly predicted the trends of the data, but underestimates flame and spray boundaries by 30-50 percent, indicating that slip is still important for the present experiments (Sauter mean diameters of 30 microns at atmospheric pressure under cold flow conditions). Since the sprays are shorter at high pressures, slip effects are still important even though the density ratio of the phases approach one another as the droplets heat up. The model indicates the presence of a region where condensed water is present within the spray and provides a convenient means of treating supercritical phenomena

Purchasing Strategies to Improve Care Management for Complex Populations: A National Scan of State Purchasers

Explores cost-effective alternatives to fee-for-service plans and full-risk managed care for Medicaid's aged, blind, and disabled or Supplementary Security Income beneficiaries. Includes summaries of systems being implemented in twelve states

Roleplaying to Improve Resilience

This article presents an approach to improve urban resilience by examining crisis dynamics through a role-playing game. The set of exploratory exercises extend the Archaria 2035 scenario and geographic information system model, which was developed by the North Atlantic Treaty Organization (NATO) to advance concepts that support military operations. Participants (graduate students) worked in teams to identify and map critical relationships related to health, safety and welfare through a modified version of the Political, Military, Economic, Social, Infrastructure, Information (PMESII) framework. Next, each participant was given a one-page stakeholder profile that specified motives, kinds and degrees of influence, and connections to other stakeholders. This information was used to create maps that showed how each character understood the city. Crisis event details were revealed a day-and-a-half before the game. NATO staff contributed to the event by presenting courses of action to restore security and order. Participants gave opinions on how their characters might act during the event and react to the proposed military operations. Conversations created temporary collaborations among some stakeholders but also conflicts among others that could create additional problems. A post-game assignment asked participants to write memos on specific policies and plans that would reduce vulnerability to the crisis. As a matter of pedagogy, results the demonstrate the value of role-playing to consider multiple perspectives and second- and third-order effects of a crisis. Specifically, connecting gameplay conversations and results back to initial ideas about health, safety and welfare contributed to reconsiderations of assumptions about contingent relationships