Propagation of the First Flames in Type Ia Supernovae

We consider the competition of the different physical processes that can affect the evolution of a flame bubble in a Type Ia supernovae -- burning, turbulence and buoyancy. Even in the vigorously turbulent conditions of a convecting white dwarf, thermonuclear burning that begins at a point near the center (within 100 km) of the star is dominated by the spherical laminar expansion of the flame, until the burning region reaches kilometers in size. Consequently flames that ignite in the inner ~20 km promptly burn through the center, and flame bubbles anywhere must grow quite large--indeed, resolvable by large-scale simulations of the global system--for significant motion or deformation occur. As a result, any hot-spot that successfully ignites into a flame can burn a significant amount of white dwarf material. This potentially increases the stochastic nature of the explosion compared to a scenario where a simmering progenitor can have small early hot-spots float harmlessly away. Further, the size where the laminar flame speed dominates other relevant velocities sets a characteristic scale for fragmentation of larger flame structures, as nothing--by definition--can easily break the burning region into smaller volumes. This makes possible the development of semi-analytic descriptions of the earliest phase of the propagation of burning in a Type Ia supernovae, which we present here. Our analysis is supported by fully resolved numerical simulations of flame bubbles.Comment: 33 pages, 14 figures, accepted for publication in Ap

Wave turbulence in the two-layer ocean model

This paper looks at the two-layer ocean model from a wave turbulence perspective. A symmetric form of the two-layer kinetic equation for Rossby waves is derived using canonical variables, allowing the turbulent cascade of energy between the barotropic and baroclinic modes to be studied. It turns out that energy is transferred via local triad interactions from the large-scale baroclinic modes to the baroclinic and barotropic modes at the Rossby deformation scale. From there it is then transferred to the large-scale barotropic modes via a nonlocal inverse transfer. Using scale separation a sys- tem of coupled equations were obtained for the small-scale baroclinic component and the large-scale barotropic component. Since the total energy of the small-scale component is not conserved, but the total barotropic plus baroclinic energy is conserved, the baroclinic energy loss at small scales will be compensated by the growth of the barotropic energy at large scales. It is found that this transfer is mostly anisotropic and mostly to the zonal component

Book Review: Parental Authority: The Community and the Law

This book reports a cross-disciplinary research project which should be of particular interest to lawyers and sociologists, so far as theory, technique, and methodology are concerned, and to legislators and the public generally, as to the substance of the findings. The research group (I would have used the word team if it had not recently fallen into disrepute) consisted of a law professor and two sociologists. The data were collected in a field study in which the questionnaire-interview method was employed in an effort to ascertain the extent to which the law, in a limited area of human relations with which most laymen have a working familiarity, coincides with or deviates from the moral sense of the community

The Basis of the Immunity of an Employer of an Independent Contractor

Between the specious and often artificial legalistic concepts in which opinions of courts are couched and the plausible rationalizations devised by ingenious law professors, it is often difficult to determine the actual forces which have made the law, at any given time, what we find it to be. Man is a rational creature in one sense, but a thoroughly irrational one in another and by far the more important sense. He is adept in fashioning logical and even practical ratiocinations for his conduct to make it appear proper if not inevitable. But, on the whole, he has not developed the capacity for following a course of planned conduct according to blue prints prepared by the most competent social engineers. Thus, a rule of law is found in the reports to be based upon one or more supposed Blackstonean reasons . In the juristic literature, the principle is based upon a pyramid of premises and inferences or upon an array of actual or fictitious social and economic considerations which are supposed to furnish an adequate social policy for the principle. It is seldom that a rule is frankly stated to be the law because a complex conjury of popular notions make the principle appropriate. And still less often is such a reason offered as an adequate justification for a rule of law. Nevertheless, these vague and nebulous popular notions variously branded as public opinion , common sense , the general feeling of mankind and the like are probably responsible for more rules of law than any other single factor and, it is submitted, such a basis for a legal principle is probably the soundest and most adequate that can be found. The fact that such a basis frequently defies accurate analysis because of the impossibility of attributing the exact effect of the myriad of considerations of the experience and heritage of a given generation which constitute the motive power behind social forces, makes it none the less important. By overlooking such forces, we are apt the more easily to be misled in making predictions as to what courts will hold in a given situation. Accordingly, a consideration of the basis for the curious rules and exceptions thereto with respect to the liability of an employer of an independent contractor, must not ignore these variable and illusory factors

The Duty to Control the Conduct of Another

Whether a person is under a duty to make any effort to control the conduct of another to avoid harm to a third person presents a problem in the law of Torts which is generally treated as one of affirmative obligation. The distinction between misfeasance and mere non-feasance is an old one and, while the line is recognized as shadowy in places, it still affords a practical basis for analysis. Whether given conduct is to be described as the improper performance of proper acts or a failure to perform acts which should have been performed is the orthodox touchstone for deciding many tort cases. To be sure, this formula is capable of manipulation, and any given set of facts can be compressed to come within the concept of non-feasance or expanded to fit the mould of misfeasance. The trick is a simple one of selecting that point in the series of happenings from which the analysis is to start. An accident at a level crossing, for example, may logically be regarded as the result of the mere failure of the engineer to sound a warning or make timely application of his brakes; or it can be regarded as the improper operation of the locomotive. But although the formula is thus superficial and inexact, the basic principles for determining duty are the same in all cases. A sounder basis for analysis is the relationship of the parties. If the conduct of the actor has brought him into a human relationship with another, of such character that sound social policy requires either some affirmative action or some precaution on his part to avoid harm, the duty to act or take the precaution is imposed by law. Given a relation, says Judge Cardozo with characteristic insight, involving in its existence a duty of care . .. , a tort may result as well from acts of omission as of commission in the fulfillment of the duty thus recognized by law. What we need to know is not so much the conduct to be avoided when the relation and its attendant duty are established as existing. What we need to know is the conduct that engenders the relation. It is here that the formula, however incomplete, has its value and significance