Gasket Assembly for Sealing Mating Surfaces

A gasket assembly for securing a pair of surface together wherein an electrically conductive gasket base having a central opening is provided with a pair of layers secured to opposite sides of the gasket base, with the layers being a fusible alloy, a brazing alloy or a synthetic, thermoplastic material which will melt, without degrading, when the gasket base is heated. The surfaces may be secured to each other by a plurality of bolts to squeeze the gasket assembly there between or by some other clamping means. An electrical current is passed through the gasket base to heat it to a temperature sufficient to melt the layers to seal the surfaces to opposite sides of the gasket base

Direct Numerical Simulation of 3D Salt Fingers: From Secondary Instability to Chaotic Convection

The amplification and equilibration of three-dimensional salt fingers in unbounded uniform vertical gradients of temperature and salinity is modeled with a Direct Numerical Simulation in a triply periodic computational domain. A fluid dynamics video of the simulation shows that the secondary instability of the fastest growing square-planform finger mode is a combination of the well-known vertical shear instability of two-dimensional fingers [Holyer, 1984] and a new horizontal shear mode.Comment: APS DFD Gallery of Fluid Motion 200

Discrete Hamilton-Jacobi Theory

We develop a discrete analogue of Hamilton-Jacobi theory in the framework of discrete Hamiltonian mechanics. The resulting discrete Hamilton-Jacobi equation is discrete only in time. We describe a discrete analogue of Jacobi's solution and also prove a discrete version of the geometric Hamilton-Jacobi theorem. The theory applied to discrete linear Hamiltonian systems yields the discrete Riccati equation as a special case of the discrete Hamilton-Jacobi equation. We also apply the theory to discrete optimal control problems, and recover some well-known results, such as the Bellman equation (discrete-time HJB equation) of dynamic programming and its relation to the costate variable in the Pontryagin maximum principle. This relationship between the discrete Hamilton-Jacobi equation and Bellman equation is exploited to derive a generalized form of the Bellman equation that has controls at internal stages.Comment: 26 pages, 2 figure

Nonparametric Transient Classification using Adaptive Wavelets

Classifying transients based on multi band light curves is a challenging but crucial problem in the era of GAIA and LSST since the sheer volume of transients will make spectroscopic classification unfeasible. Here we present a nonparametric classifier that uses the transient's light curve measurements to predict its class given training data. It implements two novel components: the first is the use of the BAGIDIS wavelet methodology - a characterization of functional data using hierarchical wavelet coefficients. The second novelty is the introduction of a ranked probability classifier on the wavelet coefficients that handles both the heteroscedasticity of the data in addition to the potential non-representativity of the training set. The ranked classifier is simple and quick to implement while a major advantage of the BAGIDIS wavelets is that they are translation invariant, hence they do not need the light curves to be aligned to extract features. Further, BAGIDIS is nonparametric so it can be used for blind searches for new objects. We demonstrate the effectiveness of our ranked wavelet classifier against the well-tested Supernova Photometric Classification Challenge dataset in which the challenge is to correctly classify light curves as Type Ia or non-Ia supernovae. We train our ranked probability classifier on the spectroscopically-confirmed subsample (which is not representative) and show that it gives good results for all supernova with observed light curve timespans greater than 100 days (roughly 55% of the dataset). For such data, we obtain a Ia efficiency of 80.5% and a purity of 82.4% yielding a highly competitive score of 0.49 whilst implementing a truly "model-blind" approach to supernova classification. Consequently this approach may be particularly suitable for the classification of astronomical transients in the era of large synoptic sky surveys.Comment: 14 pages, 8 figures. Published in MNRA

How and When Pangaea Ruptured and the Continents Shifted

Because Pangaea comprised a hard, brittle granitic crust, the laws of brittle fracture apply in Its fragmentation. Application of these laws to map Pangaea revealed crucial evidence that ice caps caused it as well as continental shift. Three sound scientific dating methods emerging from the evidence substantiate biblical chronology

The Concept of National Law and the Rule of Recognition

It is a commonly held position that a rule cannot be a legal rule unless it is binding; or to put it differently, that one element that distinguishes legal rules from other kinds of rules is that legal rules are regarded as binding by duly constituted officials - typically, courts - who are called upon to apply them. Similarly, it is an often-held position that the law consists of the rules of a jurisdiction that are duly enacted or adopted by officials who have the power to make rules that are binding in the jurisdiction. The thesis of this article is that both positions are incorrect.I begin by developing a concept that I call national law. The concept of national law is that there is a body of law in the United States that is made by officials across jurisdictions, legal scholars, and scholarly institutions, which constitutes law despite the fact that it is not binding in, and is not necessarily made by, officials of a deciding jurisdiction. Examples of national law are the rules that a donative promise is enforceable if relied upon, that an acceptance is effective on dispatch, and that the remedy for breach of a bargain contract is expectation damages. National law is law because, as I show, under the practice of the legal profession, particularly the courts, the rules of national law (and not simply the reasons for those rules) are invoked as legal rules of decision.Next, I take the concept of a rule of recognition as a postulate, and develop the following four principles concerning the meaning, application, and scope of that concept, which are independent of, but exemplified by, the concept of national law: (1) The social group that must accept a secondary rule for the rule to constitute a rule of recognition is the legal profession, rather than simply judges and other officials. (2) Whether the legal profession accepts a secondary rule as a rule of recognition can be determined by examining the kinds of primary rules that are invoked by the profession as legal rules in resolving legal issues in general, and deciding cases in particular. (3) A rule can be a legal rule even though it is not binding. (4) In the United States, law is made not only by judges and other officials of the deciding jurisdiction, but also by the national judiciary, legal scholars, and professional institutions (in particular, the American Law Institute)