Scale-free equilibria of self-gravitating gaseous disks with flat rotation curves

We introduce exact analytical solutions of the steady-state hydrodynamic equations of scale-free, self-gravitating gaseous disks with flat rotation curves. We express the velocity field in terms of a stream function and obtain a third-order ordinary differential equation (ODE) for the angular part of the stream function. We present the closed-form solutions of the obtained ODE and construct hydrodynamical counterparts of the power-law and elliptic disks, for which self-consistent stellar dynamical models are known. We show that the kinematics of the Large Magellanic Cloud can well be explained by our findings for scale-free elliptic disks.Comment: AAS preprint format, 21 pages, 8 figures, accepted for publication in The Astrophysical Journa

Universal Behavior of the Resistance Noise across the Metal-Insulator Transition in Silicon Inversion Layers

Studies of low-frequency resistance noise show that the glassy freezing of the two-dimensional (2D) electron system in the vicinity of the metal-insulator transition occurs in all Si inversion layers. The size of the metallic glass phase, which separates the 2D metal and the (glassy) insulator, depends strongly on disorder, becoming extremely small in high-mobility samples. The behavior of the second spectrum, an important fourth-order noise statistic, indicates the presence of long-range correlations between fluctuators in the glassy phase, consistent with the hierarchical picture of glassy dynamics.Comment: revtex4; 4+ pages, 5 figure

Constraints on the Formation and Evolution of Circumstellar Disks in Rotating Magnetized Cloud Cores

We use magnetic collapse models to place some constraints on the formation and angular momentum evolution of circumstellar disks which are embedded in magnetized cloud cores. Previous models have shown that the early evolution of a magnetized cloud core is governed by ambipolar diffusion and magnetic braking, and that the core takes the form of a nonequilibrium flattened envelope which ultimately collapses dynamically to form a protostar. In this paper, we focus on the inner centrifugally-supported disk, which is formed only after a central protostar exists, and grows by dynamical accretion from the flattened envelope. We estimate a centrifugal radius for the collapse of mass shells within a rotating, magnetized cloud core. The centrifugal radius of the inner disk is related to its mass through the two important parameters characterizing the background medium: the background rotation rate \Omb and the background magnetic field strength \Bref. We also revisit the issue of how rapidly mass is deposited onto the disk (the mass accretion rate) and use several recent models to comment upon the likely outcome in magnetized cores. Our model predicts that a significant centrifugal disk (much larger than a stellar radius) will be present in the very early (Class 0) stage of protostellar evolution. Additionally, we derive an upper limit for the disk radius as it evolves due to internal torques, under the assumption that the star-disk system conserves its mass and angular momentum even while most of the mass is transferred to a central star.Comment: 23 pages, 1 figure, aastex, to appear in the Astrophysical Journal (10 Dec 1998

Sample size requirements for separating out the effects of combination treatments: Randomised controlled trials of combination therapy vs. standard treatment compared to factorial designs for patients with tuberculous meningitis

<p>Abstract</p> <p>Background</p> <p>In certain diseases clinical experts may judge that the intervention with the best prospects is the addition of two treatments to the standard of care. This can either be tested with a simple randomized trial of combination versus standard treatment or with a 2 × 2 factorial design.</p> <p>Methods</p> <p>We compared the two approaches using the design of a new trial in tuberculous meningitis as an example. In that trial the combination of 2 drugs added to standard treatment is assumed to reduce the hazard of death by 30% and the sample size of the combination trial to achieve 80% power is 750 patients. We calculated the power of corresponding factorial designs with one- to sixteen-fold the sample size of the combination trial depending on the contribution of each individual drug to the combination treatment effect and the strength of an interaction between the two.</p> <p>Results</p> <p>In the absence of an interaction, an eight-fold increase in sample size for the factorial design as compared to the combination trial is required to get 80% power to jointly detect effects of both drugs if the contribution of the less potent treatment to the total effect is at least 35%. An eight-fold sample size increase also provides a power of 76% to detect a qualitative interaction at the one-sided 10% significance level if the individual effects of both drugs are equal. Factorial designs with a lower sample size have a high chance to be underpowered, to show significance of only one drug even if both are equally effective, and to miss important interactions.</p> <p>Conclusions</p> <p>Pragmatic combination trials of multiple interventions versus standard therapy are valuable in diseases with a limited patient pool if all interventions test the same treatment concept, it is considered likely that either both or none of the individual interventions are effective, and only moderate drug interactions are suspected. An adequately powered 2 × 2 factorial design to detect effects of individual drugs would require at least 8-fold the sample size of the combination trial.</p> <p>Trial registration</p> <p>Current Controlled Trials <a href="http://www.controlled-trials.com/ISRCTN61649292">ISRCTN61649292</a></p

Nonlocality vs. complementarity: a conservative approach to the information problem

A proposal for resolution of the information paradox is that "nice slice" states, which have been viewed as providing a sharp argument for information loss, do not in fact do so as they do not give a fully accurate description of the quantum state of a black hole. This however leaves an information *problem*, which is to provide a consistent description of how information escapes when a black hole evaporates. While a rather extreme form of nonlocality has been advocated in the form of complementarity, this paper argues that is not necessary, and more modest nonlocality could solve the information problem. One possible distinguishing characteristic of scenarios is the information retention time. The question of whether such nonlocality implies acausality, and particularly inconsistency, is briefly addressed. The need for such nonlocality, and its apparent tension with our empirical observations of local quantum field theory, may be a critical missing piece in understanding the principles of quantum gravity.Comment: 11 pages of text and figures, + references. v2 minor text. v3 small revisions to match final journal versio

Indication of the ferromagnetic instability in a dilute two-dimensional electron system

The magnetic field B_c, in which the electrons become fully spin-polarized, is found to be proportional to the deviation of the electron density from the zero-field metal-insulator transition in a two-dimensional electron system in silicon. The tendency of B_c to vanish at a finite electron density suggests a ferromagnetic instability in this strongly correlated electron system.Comment: 4 pages, postscript figures included. Revised versio