Railroads and micro-regional growth in Prussia

We study the effect of railroad access on urban population growth. Using GIS techniques, we match triennial population data for roughly 1000 cities in nineteenth-century Prussia to georeferenced maps of the German railroad network. We find positive short- and long-term effects of having a station on urban growth for different periods during 1840-1871. Causal effects of (potentially endogenous) railroad access on city growth are identified using instrumentalvariable and xed-effects estimation techniques. Our instrument identifies exogenous variation in railroad access by constructing straight-line corridors between terminal stations. Counterfactual models using pre-railroad growth yield no evidence in support of the hypothesis that railroads appeared as a consequence of a previous growth spurt

Regular and Mach reflection of shock waves

The properties that distinguish a shock wave from other waves are that its thickness is negligible compared with other characteristic lengths, and that the state of the medium is changed irreversibly by the passage of the wave. Shocks are therefore a highly nonlinear phenomenon, and parameter changes may be expected to lead to numerous bifurcations. The multitude of possibilities is compounded when more than one shock occurs, such as in the interaction of a shock with a solid surface or symmetry plane (i.e. in shock reflection). The subject of shock reflection is so complicated that it is necessary to introduce it at some length. In the interest of conciseness, this is done according to a logical rather than a historical sequence, with explicit reference to the important authors omitted in the text unless their work is relatively recent. Salient points in the early development of the subject should be mentioned here, however. These may be found in the experiments of Mach (1878), the theoretical work of von Neumann(1943), the experimental and theoretical work of the group around Bleakney at Princeton (e.g. Bleakney & Taub 1949, Smith 1945), the experiments of Kawamura & Saito (1956), Smith (1959), and Bryson & Gross (1961), and the theoretical work Lighthill (1949) and Jones et al. (195l). A review by Pack (1964) gives detailed references. Of the work since 1960, that of the group around Glass at Toronto (e.g. Law & Glass 1971, Ben-Dor & Glass 1979, 1980) and around Henderson at Sydney (e.g. Henderson & Lozzi 1975, 1979, Henderson & Gray 1981) stand out. A review by Griffith (1981) gives more detailed references. In this review the discussion is restricted to plane flow. This is because relatively little work has been done on three-dimensional situations, and because a compromise had to be made between depth and breadth of the field covered

Strong solutions to a nonlinear stochastic Maxwell equation with a retarded material law

We study the Cauchy problem for a semilinear stochastic Maxwell equation with Kerr-type nonlinearity and a retarded material law. We show existence and uniqueness of strong solutions using a refined Faedo-Galerkin method and spectral multiplier theorems for the Hodge-Laplacian. We also make use of a rescaling transformation that reduces the problem to an equation with additive noise to get an appropriate a priori estimate for the solution.Comment: 31 page

Oblique shock reflection from an axis of symmetry

An exploratory computational study of the reflection of an inward-facing conical shock wave from its axis of symmetry is presented. This is related to more complex practical situations in both steady and unsteady flows. The absence of a length scale in the problem studied makes features grow linearly with time. The ensuing flow is related to the Guderley singularity in a cylindrical imploding shock. The problem is explored by making a large number of computations of the Euler equations. Distinct reflection congurations are identied, and the regions of parameter space in which they occur are delineated

Some aspects of hypersonic flow over power law bodies

This study concerns the hypersonic flow over blunt bodies in two specific cases. The first is the case when the Mach number is infinite and the ratio of the specific heats approaches one. This is sometimes referred to as the ‘Newtonian limit’. The second is the case of infinite Mach number and very large streamwise distance from the blunt nose with a strong shock wave, or the ‘blast wave limit’. In both cases attention is restricted to power law bodies. Experiments are described of such flows at M∞ = 7.55 in air. The Newtonian flow over bodies of the shape y ∝ x^m at zero incidence is shown to be divisible into three regions: the attached layer at small x, the free layer and the blast wave region. As m increases from zero, the free-layer region reduces in extent until it disappears at m = 1/(2+j) (j = 1 and 0 for axisymmetric and plane flow respectively). A difficulty arises in a transition solution of the type given by Freeman (1962b) connecting the free layer with the blast wave result. At m > 2/(3+j) the attached layer merges smoothly into the Lees-Kubota solution which replaces the blast-wave result in this range. In the blast wave limit, solutions were obtained for flow over axisymmetric power law shapes in the range [fraction one-half]γ < m < ½. Second-order results taking account of the body shape are given. These solutions are compared with experimental results obtained in air at a free stream Mach number of 7.55 and stagnation temperature of 630 °K, as well as with numerical solutions at Mach number of 100. The numerical method is tested by comparing solutions corresponding to the experimental conditions with experiment

Non-equilibrium dissociating nitrogen flow over spheres and circular cylinders

Theoretical results based on the methods of Freeman and Garr & Marrone show that the stand-off distance and flow pattern of non-equilibrium dissociating flow of nitrogen over the front part of a blunt body can be correlated in terms of a single reaction rate parameter ω taking account of parameters describing the speed, density, dissociation and temperature of the free stream. The density pattern, which is sensitive to the reaction rate, consists of two distinct regions dominated by the effects of reaction and pressure respectively. The shape and size of these regions depend on Q. Experimental results obtained by optical interferometry in a free-piston shock tunnel confirm the theoretical results. A scale effect consistent with the induction time phenomenon suggested by Shui, Appleton & Keck modifies the theoretical results considerably in the case of small models

Quick trips to Mars

The design of a Mars Mission Vehicle that would have to be launched by two very heavy lift launch vehicles is described along with plans for a mission to Mars. The vehicle has three nuclear engine for rocket vehicle application (NERVA) boosters with a fourth in the center that acts as a dual mode system. The fourth generates electrical power while in route, but it also helps lift the vehicle out of earth orbit. A Mars Ascent Vehicle (MAV), a Mars transfer vehicle stage, and a Mars Excursion Vehicle (MEV) are located on the front end of this vehicle. Other aspects of this research including aerobraking, heat shielding, nuclear thermal rocket engines, a mars mission summary, closed Brayton cycle with and without regeneration, liquid hydrogen propellant storage, etc. are addressed