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

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

Bulk commodities and the Liverpool and London markets of the mid-19th century

We study British prices and the degree of commodity market integration between Liverpool, the bulk commodity port of mid-19th century, and London. A new wholesale commodity price index is presented for Liverpool and this is compared with the Klovland-Sauerbeck index. Next, we examine the relationship between Liverpool and London markets in specific bulk commodities. Our data consist of price indices for identically described goods in both Liverpool and London: three commodity groups (metal products, wood products, and processed foods), and the specific commodities of wheat and flour. Tests for cointegration reveal convergence among the six price pairs. We also find that the markets were highly integrated in the short-run because three of the commodity group pairs (processed foods, wheat, and flour) shared common features or cycles. A common cycle implies that transitory price shocks in Liverpool had the same impact on prices in London and vice versa. The importance of the London and Liverpool common cycle to a shock is brief. Its shock explains less than 20 percent of the variation in the relevant price levels after twelve months, on average.

Investigation of Critical Burning of Fuel Droplets

An earlier analysis for the combustion response of a liquid monopropellant strand (hydrazine) was extended to consider individual droplets and sprays. While small drops gave low or negative response, large droplets provided response near unity at low frequencies, with the response declining at frequencies greater than the characteristic liquid phase frequency. Temperature gradients in the liquid phase resulted in response peaks greater than unity. A second response peak was found for large drops which corresponded to gas phase transient effects. Spray response was generally reduced from the response of the largest injected droplet, however, even a small percentage of large droplets can yield appreciable response. An apparatus was designed and fabricated to allow observation of bipropellant fuel spray combustion at elevated pressures. A locally homogeneous model was developed to describe this combustion process which allows for high pressure phenomena associated with the thermodynamic critical point

Unpulsed UBV Optical Emission from the Crab Pulsar

Based on observations of the Crab pulsar using the TRIFFID high speed imaging photometer in the UBV bands using the Special Astrophysical Observatory's 6m telescope in the Russian Caucasus, we report the detection of pronounced emission during the so-called `off' phase of emission. Following de-extinction, this unpulsed component of emission is shown to be consistent with a power law with an exponent of alpha = -0.60 +/- 0.37, the uncertainty being dominated by the error associated with the independent CCD photometry used to reference the TRIFFID data. This suggests a steeper power law form than that reported elsewhere in the literature for the total integrated spectrum, which is essentially flat with alpha ~ 0.1, although the difference in this case is only significant at the ~ 2 sigma level. Deeper reference integrated and TRIFFID phase-resolved photometry in these bands in conjunction with further observations in the UV and R region would constrain this fit further.Comment: 26 pages, 2 figures, uses aasms4.sty, accepted for publication in the Astrophysical Journa

Implications of the Optical Observations of Neutron Stars

We show that observations of pulsars with pulsed optical emission indicate that the peak flux scales according to the magnetic field strength at the light cylinder. The derived relationships indicate that the emission mechanism is common across all of the observed pulsars with periods ranging from 33ms to 385 ms and ages of 1000-300,000 years. It is noted that similar trends exist for $\gamma$ ray pulsars. Furthermore the model proposed by Pacini (1971) and developed by Pacini and Salvati (1983,1987) still has validity and gives an adequate explanation of the optical phenomena.Comment: 23 pages, 6 figures, accepted for publication in the Astrophysical Journa

Pesticide Application and Handling Technology: Proper Disposal of Empty Pesticide Containers

Recycling has become more and more popular as our awareness of environmental concerns grow. These environmental concerns have led to increased participation in recycling efforts among today\u27s farmers. Many farmers throughout Kentucky are now able to recycle their empty plastic pesticide containers (Five gallon or less) due to a statewide Rinse and Return program. Recycling of empty containers provides a safe means of disposal for applicators, reduces landfill space, and protects our valuable water resources

Pesticide Application and Handling Technology: Installing a Sprayer Tank Rinse Circuit

Proper tank rinsing techniques for agricultural sprayers are very important in order to protect against cross-contamination in subsequent loads and to ensure safe disposal of any excess chemicals and rinsate (rinse water). Spray tanks and other sprayer components should be cleaned after each use. In most situations, sprayer rinsate will have to be sprayed out in the field - either onto a reserved strip, or by over-spraying in the treated area (subject to the terms of the product label)