Supersymmetric quantum mechanics and the Korteweg-de Vries hierarchy

The connection between supersymmetric quantum mechanics and the Korteweg- de Vries (KdV) equation is discussed, with particular emphasis on the KdV conservation laws. It is shown that supersymmetric quantum mechanics aids in the derivation of the conservation laws, and gives some insight into the Miura transformation that converts the KdV equation into the modified KdV equation. The construction of the $\tau$-function by means of supersymmetric quantum mechanics is discussed.Comment: 16 pages, latex, EFI 93/2

Formation of standing shocks in stellar winds and related astrophysical flows

Stellar winds and other analogous astrophysical flows can be described, to lowest order, by the familiar one dimensional hydrodynamic equations which, being nonlinear, admit in some instances discontinuous as well as continuous transonic solutions for identical inner boundary conditions. The characteristics of the time dependent differential equations of motion are described to show how a perturbation changes profile in time and, under well defined conditions, develops into a stationary shock discontinuity. The formation of standing shocks in wind type astrophysical flows depends on the fulfillment of appropriate necessary conditions, which are determined by the conservation of mass, momentum and energy across the discontinuity, and certain sufficient conditions, which are determined by the flow's history

Recent Results in Bottomonium

Great strides have been made in the understanding of bound states of a bottom quark $b$ and its antiquark $\bar b$ since the discovery of the first $\Upsilon$ resonances in 1977. These {\it bottomonium} bound states have a rich spectrum whose masses and transition amplitudes shed valuable light on the strong interactions. The present article reviews some recent developments in bottomonium physics. These include the discovery of the spin-singlet states $\eta_b$ and $h_b$, the first D-wave states, one or more candidates for spin-triplet $\chi_b(3P)$ excitations, and above-threshold states with strong transitions to states below threshold. Information on transitions, production, and signatures of new physics is also presented.Comment: 47 pages, 2 figures, to be submitted to Annual Review of Nuclear and Particle Scienc

Trials and tribulations : what happens when historians enter the courtroom

In recent years, historians have been brought into legal cases in unprecedented numbers. As the courts have tried to adjudicate responsibility for environmental and occupational diseases, history has played an increasingly central role in decisions that affect the cases themselves and in social policy regarding risk. In suits over tobacco-related diseases, asbestosis, radiation, and other toxic substances, more historians of technology and science, social history, and public health are being sought to provide testimony aimed at assessing responsibility for damages that have arisen years--sometimes decades--after exposure. Here, Rosner traces the use of historians as experts in litigation

Nax_xCoO2_2 in the x -> 0 Regime: Coupling of Structure and Correlation effects

The study of the strength of correlations in Na$_x$CoO$_2$ is extended to the x=0 end of the phase diagram where Mott insulating behavior has been widely anticipated. Inclusion of correlation as modeled by the LDA+U approach leads to a Mott transition in the $a_g$ subband if U is no less than U$_c$=2.5 eV. Thus U smaller than U$_c$ is required to model the metallic, nonmagnetic CoO$_2$ compound reported by Tarascon and coworkers. The orbital-selective Mott transition of the $a_g$ state, which is essentially degenerate with the $e'_{g}$ states, occurs because of the slightly wider bandwidth of the $a_g$ bands. The metal-insulator transition is found to be strongly coupled to the Co-O bond length, due to associated changes in the $t_{2g}$ bandwidth, but the largest effects occur only at a reduced oxygen height that lies below the equilibrium position.Comment: 8 pages with 9 embedded figure

Multiple transonic solutions and a new class of shock transitions in solar and stellar winds

The steady isothermal solar wind equations are shown to admit, under certain circumstances, mutliple transonic solutions when, for example, momentum deposition gives rise to multiplee critical points in the flow. These multiple solutions consist of a continuous solution and solutions which involve shock transitions between critical solutions. The ambiguity arising from the multiplicity of the solutions can be resolved by following the time evolution of a wind profile with one critical point. Results of the numerical integration of the time-dependent equations with momentum addition show that each of these multiple solutions is physically accessible and depends on the rate of change of momentum deposition. These results suggest that standing shocks are likely to be present in the inner solar wind flow

The role of carbon for superconductivity in MgCx_{x}Ni3_{3} from specific heat

The influence of carbon deficiency on superconductivity of MgCNi$_{3}$ is investigated by specific heat measurements in the normal and superconducting state. In order to perform a detailed analysis of the normal state specific heat, a computer code is developed which allows for an instantaneous estimate of the main features of the lattice dynamics. By analyzing the evolution of the lattice vibrations within the series and simultaneously considering the visible mass enhancement, the loss in the electron-phonon coupling can be attributed to significant changes of the prominent Ni vibrations. The present data well supports the recently established picture of strong electron-phonon coupling and ferromagnetic spin fluctuations in this compound.Comment: 4 pages, latex, corrections to the text, one reference added, one figure correcte