Simplified landscapes for optimization of shaken lattice interferometry

Motivated by recent results using shaken optical lattices to perform atom interferometry, we explore splitting of an atom cloud trapped in a phase-modulated ("shaken") optical lattice. Using a simple analytic model we are able to show that we can obtain the simplest case of $\pm2\hbar k_\mathrm{L}$ splitting via single-frequency shaking. This is confirmed both via simulation and experiment. Furthermore, we are able to split with a relative phase $\theta$ between the two split arms of $0$ or $\pi$ depending on our shaking frequency. Addressing higher-order splitting, we determine that $\pm6\hbar k_\mathrm{L}$ splitting is sufficient to be able to accelerate the atoms in counter-propagating lattices. Finally, we show that we can use a genetic algorithm to optimize $\pm4\hbar k_\mathrm{L}$ and $\pm6\hbar k_\mathrm{L}$ splitting to within $\approx0.1\%$ by restricting our optimization to the resonance frequencies corresponding to single- and two-photon transitions between Bloch bands

Justice Jackson and the Judicial Function

Much of the pattern of division in the present Supreme Court is traceable to basic differences of opinion regarding the proper role of a judge in the process of constitutional adjudication. Some students of the Court, yielding to the current fashion of reducing even intricate problems to capsule terms, have tried to explain the controversy by classifying the justices as either liberals or conservatives. A second school poses the disagreement largely in terms of judicial activism as opposed to judicial restraint. It is this view that has the greater relevance for the present discussion. C.H. Pritchett, one of the leading exponents of this view, says that the judicial activist appears to experience a deep sense of personal responsibility for the immediate consequences of his judicial decisions. He feels that the Court has a range of discretion, that there are alternatives available to him, and that he must make the choice which will give the right result. The activist does not pretend to exercise the power of judicial review in accordance with standards imposed by the legal system; he will apply formal legal concepts only if they assist him in reaching a desirable goal. On the present Court, Pritchett suggests, Justices Black and Douglas best reflect this goal-orientation of the activists. The proponents of judicial self-restraint see a justice at his best when he exercises the judicial power with restraint and prudence. This functionally- oriented view sees the Court not as crusader or advocate but as one of the instruments of political and social accommodation and adjustment in a complicated governmental system. Its stress is not on securing a result conforming to the jurist\u27s own scheme of values but upon adherence to appropriate judicial standards and proper manipulation of judicial techniques. Justice Frankfurter, Pritchett submits, is the modem leader of the restraint school, and his views are subjected to close scrutiny. While Pritchett\u27s approach is basically sound, it does have the effect of obscuring the constitutional views of Justice Robert H. Jackson, who often seems to be regarded as a mere intellectual appendage of Justice Frankfurter. In contrast to his elaborate analysis of Frankfurter\u27s conception of the judicial function, Pritchett, writing before Jackson\u27s death, summarized Jackson\u27s judicial philosophy only briefly and then concluded, The unpredictability of Jackson\u27s performance leads one to question whether he has developed any systematic theories about . . . the judicial function. This cursory conclusion suggests the need for a deeper penetration into the general writings and judicial opinions of Justice Jackson to discover if he had an integrated philosophy concerning the judicial function, and to appraise the extent to which he was an advocate of judicial self-restraint. This study is an attempt to fill that need. Its intent is not to summarize Justice Jackson\u27s political and judicial career; it is rather an inquiry into his conception of the judicial function as applied to certain basic types of review situations. If we can determine this, we may have the key that will enable us to interpret his Supreme Court experience

Orbiter/launch system

The system includes reusable turbojet propelled booster vehicles releasably connected to a reusable rocket powered orbit vehicle. The coupled orbiter-booster combination takes off horizontally and ascends to staging altitude and speed under booster power with both orbiter and booster wings providing lift. After staging, the booster vehicles fly back to Earth for horizontal landing and the orbiter vehicle continues ascending to orbit

Escaping stars from young low-N clusters

With the use of N-body calculations the amount and properties of escaping stars from low-N (N = 100 and 1000) young embedded star clusters prior to gas expulsion are studied over the first 5 Myr of their existence. Besides the number of stars also different initial radii and binary populations are examined as well as virialised and collapsing clusters. It is found that these clusters can loose substantial amounts (up to 20%) of stars within 5 Myr with considerable velocities up to more than 100 km/s. Even with their mean velocities between 2 and 8 km/s these stars will still be travelling between 2 and 30 pc during the 5 Myr. Therefore can large amounts of distributed stars in star-forming regions not necessarily be counted as evidence for the isolated formation of stars.Comment: 10 pages, 10 figures, accepted for publication by MNRA

Flow establishment in a generic scramjet combustor

The establishment of a quasi-steady flow in a generic scramjet combustor was studied for the case of a time varying inflow to the combustor. Such transient flow is characteristic of the reflected shock tunnel and expansion tube test facilities. Several numerical simulations of hypervelocity flow through a straight duct combustor with either a side wall step fuel injector or a centrally located strut injector are presented. Comparisons were made between impulsively started but otherwise constant flow conditions (typical of the expansion tube or tailored operations of the reflected shock tunnel) and the relaxing flow produced by the 'undertailored' operations of the reflected shock tunnel. Generally the inviscid flow features, such as the shock pattern and pressure distribution, were unaffected by the time varying inlet conditions and approached steady state in approx. the times indicated by experimental correlations. However, viscous features, such as heat transfer and skin friction, were altered by the relaxing inlet flow conditions

Properties of hierarchically forming star clusters

We undertake a systematic analysis of the early (< 0.5 Myr) evolution of clustering and the stellar initial mass function in turbulent fragmentation simulations. These large scale simulations for the first time offer the opportunity for a statistical analysis of IMF variations and correlations between stellar properties and cluster richness. The typical evolutionary scenario involves star formation in small-n clusters which then progressively merge; the first stars to form are seeds of massive stars and achieve a headstart in mass acquisition. These massive seeds end up in the cores of clusters and a large fraction of new stars of lower mass is formed in the outer parts of the clusters. The resulting clusters are therefore mass segregated at an age of 0.5 Myr, although the signature of mass segregation is weakened during mergers. We find that the resulting IMF has a smaller exponent (alpha=1.8-2.2) than the Salpeter value (alpha=2.35). The IMFs in subclusters are truncated at masses only somewhat larger than the most massive stars (which depends on the richness of the cluster) and an universal upper mass limit of 150 Msun is ruled out. We also find that the simulations show signs of the IGIMF effect proposed by Weidner & Kroupa, where the frequency of massive stars is suppressed in the integrated IMF compared to the IMF in individual clusters. We identify clusters through the use of a minimum spanning tree algorithm which allows easy comparison between observational survey data and the predictions of turbulent fragmentation models. In particular we present quantitative predictions regarding properties such as cluster morphology, degree of mass segregation, upper slope of the IMF and the relation between cluster richness and maximum stellar mass. [abridged]Comment: 21 Pages, 25 Figure

Chemo-Archaeological Downsizing in a Hierarchical Universe: Impact of a Top Heavy IGIMF

We make use of a semi-analytical model of galaxy formation to investigate the origin of the observed correlation between [a/Fe] abundance ratios and stellar mass in elliptical galaxies. We implement a new galaxy-wide stellar initial mass function (Top Heavy Integrated Galaxy Initial Mass Function, TH-IGIMF) in the semi-analytic model SAG and evaluate its impact on the chemical evolution of galaxies. The SFR-dependence of the slope of the TH-IGIMF is found to be key to reproducing the correct [a/Fe]-stellar mass relation. Massive galaxies reach higher [a/Fe] abundance ratios because they are characterized by more top-heavy IMFs as a result of their higher SFR. As a consequence of our analysis, the value of the minimum embedded star cluster mass and of the slope of the embedded cluster mass function, which are free parameters involved in the TH-IGIMF theory, are found to be as low as 5 solar masses and 2, respectively. A mild downsizing trend is present for galaxies generated assuming either a universal IMF or a variable TH-IGIMF. We find that, regardless of galaxy mass, older galaxies (with formation redshifts > 2) are formed in shorter time-scales (< 2 Gyr), thus achieving larger [a/Fe] values. Hence, the time-scale of galaxy formation alone cannot explain the slope of the [a/Fe]-galaxy mass relation, but is responsible for the big dispersion of [a/Fe] abundance ratios at fixed stellar mass.We further test the hyphothesis of a TH-IGIMF in elliptical galaxies by looking into mass-to-light ratios, and luminosity functions. Models with a TH-IGIMF are also favoured by these constraints. In particular, mass-to-light ratios agree with observed values for massive galaxies while being overpredicted for less massive ones; this overprediction is present regardless of the IMF considered.Comment: 24 pages, 15 figures, 2 tables. (Comments most welcome). Summited to MNRA